{"id": "hv3-cnf_n8-i0-none::none", "rec_id": "hv3-cnf_n8-i0", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38142}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition s1 is true. Proposition bad is true if proposition w2 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w6 is true. Proposition s2 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t0 is true if proposition t1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i0-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i0", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38142}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition s1 is true. Proposition bad is true if proposition w2 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w6 is true. Proposition s2 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t0 is true if proposition t1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i0-cred::cred", "rec_id": "hv3-cnf_n8-i0", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38142}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition s1 is true. Proposition bad is true if proposition w2 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w6 is true. Proposition s2 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t0 is true if proposition t1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i0-skept::skept", "rec_id": "hv3-cnf_n8-i0", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38142}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition s1 is true. Proposition bad is true if proposition w2 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w6 is true. Proposition s2 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t0 is true if proposition t1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i0-wfs::wfs", "rec_id": "hv3-cnf_n8-i0", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38142}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition s1 is true. Proposition bad is true if proposition w2 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w6 is true. Proposition s2 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t0 is true if proposition t1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i1-none::none", "rec_id": "hv3-cnf_n8-i1", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38143}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w2 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v7 is true if proposition w7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s3 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition t5 is true if proposition v1 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i1-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i1", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38143}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w2 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v7 is true if proposition w7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s3 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition t5 is true if proposition v1 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i1-cred::cred", "rec_id": "hv3-cnf_n8-i1", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38143}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w2 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v7 is true if proposition w7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s3 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition t5 is true if proposition v1 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i1-skept::skept", "rec_id": "hv3-cnf_n8-i1", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38143}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w2 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v7 is true if proposition w7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s3 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition t5 is true if proposition v1 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i1-wfs::wfs", "rec_id": "hv3-cnf_n8-i1", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 38143}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w2 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v7 is true if proposition w7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s3 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition t5 is true if proposition v1 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i2-none::none", "rec_id": "hv3-cnf_n8-i2", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 4, "n_filler": 0, "variant_seed": 38144}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v5 is true if proposition w5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i2-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i2", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 4, "n_filler": 0, "variant_seed": 38144}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v5 is true if proposition w5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i2-cred::cred", "rec_id": "hv3-cnf_n8-i2", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 4, "n_filler": 0, "variant_seed": 38144}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v5 is true if proposition w5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i2-skept::skept", "rec_id": "hv3-cnf_n8-i2", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 4, "n_filler": 0, "variant_seed": 38144}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v5 is true if proposition w5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i2-wfs::wfs", "rec_id": "hv3-cnf_n8-i2", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 4, "n_filler": 0, "variant_seed": 38144}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v5 is true if proposition w5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i3-none::none", "rec_id": "hv3-cnf_n8-i3", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 38145}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v0 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition t0 is true if proposition t1 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s2 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i3-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i3", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 38145}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v0 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition t0 is true if proposition t1 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s2 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i3-cred::cred", "rec_id": "hv3-cnf_n8-i3", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 38145}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v0 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition t0 is true if proposition t1 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s2 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i3-skept::skept", "rec_id": "hv3-cnf_n8-i3", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 38145}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v0 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition t0 is true if proposition t1 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s2 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i3-wfs::wfs", "rec_id": "hv3-cnf_n8-i3", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 38145}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v0 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition t0 is true if proposition t1 is true. Proposition w3 is true if proposition v3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s2 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i4-none::none", "rec_id": "hv3-cnf_n8-i4", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 14, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 38146}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition q is true if proposition w4 is true and proposition etrue is true. Proposition w3 is true if proposition v3 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i4-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i4", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 14, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 38146}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition q is true if proposition w4 is true and proposition etrue is true. Proposition w3 is true if proposition v3 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i4-cred::cred", "rec_id": "hv3-cnf_n8-i4", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 14, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 38146}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition q is true if proposition w4 is true and proposition etrue is true. Proposition w3 is true if proposition v3 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i4-skept::skept", "rec_id": "hv3-cnf_n8-i4", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 14, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 38146}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition q is true if proposition w4 is true and proposition etrue is true. Proposition w3 is true if proposition v3 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i4-wfs::wfs", "rec_id": "hv3-cnf_n8-i4", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 14, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 38146}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition q is true if proposition w4 is true and proposition etrue is true. Proposition w3 is true if proposition v3 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i5-none::none", "rec_id": "hv3-cnf_n8-i5", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 38147}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition w1 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition t1 is true if proposition t2 is true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w2 is true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition s0 is true. Proposition t4 is true if proposition t5 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s1 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i5-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i5", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 38147}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition w1 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition t1 is true if proposition t2 is true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w2 is true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition s0 is true. Proposition t4 is true if proposition t5 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s1 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i5-cred::cred", "rec_id": "hv3-cnf_n8-i5", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 38147}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition w1 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition t1 is true if proposition t2 is true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w2 is true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition s0 is true. Proposition t4 is true if proposition t5 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s1 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i5-skept::skept", "rec_id": "hv3-cnf_n8-i5", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 38147}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition w1 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition t1 is true if proposition t2 is true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w2 is true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition s0 is true. Proposition t4 is true if proposition t5 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s1 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i5-wfs::wfs", "rec_id": "hv3-cnf_n8-i5", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 38147}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w6 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition w1 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition t1 is true if proposition t2 is true. Proposition v0 is true if proposition w0 is not true. Proposition t5 is true if proposition w2 is true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition s0 is true. Proposition t4 is true if proposition t5 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition s1 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i6-none::none", "rec_id": "hv3-cnf_n8-i6", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 6, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 7, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38148}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v4 is true and proposition bad is not true. Proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i6-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i6", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 6, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 7, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38148}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v4 is true and proposition bad is not true. Proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i6-cred::cred", "rec_id": "hv3-cnf_n8-i6", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 6, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 7, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38148}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v4 is true and proposition bad is not true. Proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i6-skept::skept", "rec_id": "hv3-cnf_n8-i6", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 6, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 7, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38148}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v4 is true and proposition bad is not true. Proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i6-wfs::wfs", "rec_id": "hv3-cnf_n8-i6", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 6, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 2, "clingo_choices": 7, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38148}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v4 is true and proposition bad is not true. Proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i7-none::none", "rec_id": "hv3-cnf_n8-i7", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 2, "width": 4, "n_filler": 0, "variant_seed": 38150}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v2 is true and proposition v6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t1 is true if proposition w7 is true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i7-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i7", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 2, "width": 4, "n_filler": 0, "variant_seed": 38150}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v2 is true and proposition v6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t1 is true if proposition w7 is true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i7-cred::cred", "rec_id": "hv3-cnf_n8-i7", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 2, "width": 4, "n_filler": 0, "variant_seed": 38150}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v2 is true and proposition v6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t1 is true if proposition w7 is true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i7-skept::skept", "rec_id": "hv3-cnf_n8-i7", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 2, "width": 4, "n_filler": 0, "variant_seed": 38150}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v2 is true and proposition v6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t1 is true if proposition w7 is true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i7-wfs::wfs", "rec_id": "hv3-cnf_n8-i7", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 2, "width": 4, "n_filler": 0, "variant_seed": 38150}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v2 is true and proposition v6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w4 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition w4 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition w1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t1 is true if proposition w7 is true. Proposition bad is true if proposition w1 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i8-none::none", "rec_id": "hv3-cnf_n8-i8", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 0, "n_filler": 0, "variant_seed": 38152}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition w5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition bad is true if proposition w5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i8-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i8", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 0, "n_filler": 0, "variant_seed": 38152}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition w5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition bad is true if proposition w5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i8-cred::cred", "rec_id": "hv3-cnf_n8-i8", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 0, "n_filler": 0, "variant_seed": 38152}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition w5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition bad is true if proposition w5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i8-skept::skept", "rec_id": "hv3-cnf_n8-i8", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 0, "n_filler": 0, "variant_seed": 38152}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition w5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition bad is true if proposition w5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i8-wfs::wfs", "rec_id": "hv3-cnf_n8-i8", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 0, "n_filler": 0, "variant_seed": 38152}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v4 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v2 is true and proposition w5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition w4 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition bad is true if proposition w5 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i9-none::none", "rec_id": "hv3-cnf_n8-i9", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 38154}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition v6 is true and proposition wide is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition s1 is true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i9-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i9", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 38154}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition v6 is true and proposition wide is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition s1 is true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i9-cred::cred", "rec_id": "hv3-cnf_n8-i9", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 38154}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition v6 is true and proposition wide is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition s1 is true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i9-skept::skept", "rec_id": "hv3-cnf_n8-i9", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 38154}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition v6 is true and proposition wide is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition s1 is true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i9-wfs::wfs", "rec_id": "hv3-cnf_n8-i9", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 38154}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition v6 is true and proposition wide is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition s1 is true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v1 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i10-none::none", "rec_id": "hv3-cnf_n8-i10", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38165}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition t3 is true if proposition v1 is true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i10-closed_world::closed_world", "rec_id": "hv3-cnf_n8-i10", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38165}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition t3 is true if proposition v1 is true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i10-cred::cred", "rec_id": "hv3-cnf_n8-i10", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38165}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition t3 is true if proposition v1 is true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i10-skept::skept", "rec_id": "hv3-cnf_n8-i10", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38165}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition t3 is true if proposition v1 is true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n8-i10-wfs::wfs", "rec_id": "hv3-cnf_n8-i10", "axis": "cnf", "difficulty": "cnf_n8", "hardness_kind": "search", "n_stable_models": 1, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "cnf", "n_vars": 8, "n_clauses": 34, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": true, "depth": 4, "width": 2, "n_filler": 0, "variant_seed": 38165}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition v1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w6 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v6 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v2 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition t3 is true if proposition v1 is true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i0-none::none", "rec_id": "hv3-cnf_n14-i0", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 60920}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v13 is true if proposition w13 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w8 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v8 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v9 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w10 is true if proposition v10 is not true. Proposition t5 is true if proposition v4 is true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i0-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i0", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 60920}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v13 is true if proposition w13 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w8 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v8 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v9 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w10 is true if proposition v10 is not true. Proposition t5 is true if proposition v4 is true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i0-cred::cred", "rec_id": "hv3-cnf_n14-i0", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 60920}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v13 is true if proposition w13 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w8 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v8 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v9 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w10 is true if proposition v10 is not true. Proposition t5 is true if proposition v4 is true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i0-skept::skept", "rec_id": "hv3-cnf_n14-i0", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 60920}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v13 is true if proposition w13 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w8 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v8 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v9 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w10 is true if proposition v10 is not true. Proposition t5 is true if proposition v4 is true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i0-wfs::wfs", "rec_id": "hv3-cnf_n14-i0", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 4, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 60920}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v13 is true if proposition w13 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w8 is true and proposition v5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v8 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v3 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v9 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w10 is true if proposition v10 is not true. Proposition t5 is true if proposition v4 is true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i1-none::none", "rec_id": "hv3-cnf_n14-i1", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60921}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition w2 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w11 is true if proposition v11 is not true. Proposition t5 is true if proposition v11 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w7 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w11 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition w9 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v6 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w9 is true and proposition w6 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i1-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i1", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60921}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition w2 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w11 is true if proposition v11 is not true. Proposition t5 is true if proposition v11 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w7 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w11 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition w9 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v6 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w9 is true and proposition w6 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i1-cred::cred", "rec_id": "hv3-cnf_n14-i1", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60921}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition w2 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w11 is true if proposition v11 is not true. Proposition t5 is true if proposition v11 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w7 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w11 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition w9 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v6 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w9 is true and proposition w6 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i1-skept::skept", "rec_id": "hv3-cnf_n14-i1", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60921}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition w2 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w11 is true if proposition v11 is not true. Proposition t5 is true if proposition v11 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w7 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w11 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition w9 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v6 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w9 is true and proposition w6 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i1-wfs::wfs", "rec_id": "hv3-cnf_n14-i1", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 3, "clingo_choices": 6, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": true, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60921}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition v6 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w7 is true and proposition w1 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition w2 is true and proposition bad is not true. Proposition s3 is true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v5 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w11 is true if proposition v11 is not true. Proposition t5 is true if proposition v11 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w7 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition v6 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w11 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition w9 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v6 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w9 is true and proposition w6 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i2-none::none", "rec_id": "hv3-cnf_n14-i2", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 16, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 60922}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v5 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v10 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w0 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v0 is true and proposition w8 is true and proposition w7 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w4 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i2-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i2", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 16, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 60922}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v5 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v10 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w0 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v0 is true and proposition w8 is true and proposition w7 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w4 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i2-cred::cred", "rec_id": "hv3-cnf_n14-i2", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 16, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 60922}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v5 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v10 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w0 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v0 is true and proposition w8 is true and proposition w7 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w4 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i2-skept::skept", "rec_id": "hv3-cnf_n14-i2", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 16, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 60922}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v5 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v10 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w0 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v0 is true and proposition w8 is true and proposition w7 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w4 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i2-wfs::wfs", "rec_id": "hv3-cnf_n14-i2", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 16, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 6, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 60922}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v4 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v5 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w2 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w3 is true and proposition v10 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w0 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition v13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition v6 is true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v0 is true and proposition w8 is true and proposition w7 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w7 is true and proposition v0 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w4 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w4 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i3-none::none", "rec_id": "hv3-cnf_n14-i3", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 4, "width": 0, "n_filler": 0, "variant_seed": 60923}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v6 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v13 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v6 is true and proposition w2 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition v9 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition t3 is true if proposition w12 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w11 is true if proposition v11 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition v13 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v13 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v2 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i3-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i3", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 4, "width": 0, "n_filler": 0, "variant_seed": 60923}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v6 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v13 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v6 is true and proposition w2 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition v9 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition t3 is true if proposition w12 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w11 is true if proposition v11 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition v13 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v13 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v2 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i3-cred::cred", "rec_id": "hv3-cnf_n14-i3", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 4, "width": 0, "n_filler": 0, "variant_seed": 60923}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v6 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v13 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v6 is true and proposition w2 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition v9 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition t3 is true if proposition w12 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w11 is true if proposition v11 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition v13 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v13 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v2 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i3-skept::skept", "rec_id": "hv3-cnf_n14-i3", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 4, "width": 0, "n_filler": 0, "variant_seed": 60923}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v6 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v13 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v6 is true and proposition w2 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition v9 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition t3 is true if proposition w12 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w11 is true if proposition v11 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition v13 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v13 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v2 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i3-wfs::wfs", "rec_id": "hv3-cnf_n14-i3", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 4, "width": 0, "n_filler": 0, "variant_seed": 60923}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v6 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w7 is true and proposition v6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v7 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v13 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v6 is true and proposition w2 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w11 is true and proposition v4 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition v9 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v2 is true and proposition v12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w6 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w7 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition t3 is true if proposition w12 is true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w11 is true if proposition v11 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition v13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v3 is true and proposition v1 is true and proposition v13 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v13 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w10 is true and proposition w11 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v2 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i4-none::none", "rec_id": "hv3-cnf_n14-i4", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 9, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 60924}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v6 is true if proposition w6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition v13 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v13 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition q is true if proposition w11 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition v13 is true and proposition bad is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w12 is true and proposition v4 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition v13 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i4-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i4", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 9, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 60924}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v6 is true if proposition w6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition v13 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v13 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition q is true if proposition w11 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition v13 is true and proposition bad is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w12 is true and proposition v4 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition v13 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i4-cred::cred", "rec_id": "hv3-cnf_n14-i4", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 9, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 60924}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v6 is true if proposition w6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition v13 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v13 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition q is true if proposition w11 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition v13 is true and proposition bad is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w12 is true and proposition v4 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition v13 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i4-skept::skept", "rec_id": "hv3-cnf_n14-i4", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 9, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 60924}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v6 is true if proposition w6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition v13 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v13 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition q is true if proposition w11 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition v13 is true and proposition bad is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w12 is true and proposition v4 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition v13 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i4-wfs::wfs", "rec_id": "hv3-cnf_n14-i4", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 3, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 9, "prolog_inferences": null, "n_stable_models": 3}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 60924}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v6 is true if proposition w6 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition v13 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v7 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v13 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w0 is true and proposition bad is not true. Proposition q is true if proposition w11 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition v13 is true and proposition bad is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w12 is true and proposition v4 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w4 is true and proposition w11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition v13 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w1 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition s0 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition v12 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i5-none::none", "rec_id": "hv3-cnf_n14-i5", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 60925}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition w0 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition v13 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition s0 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w13 is true if proposition v13 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition w9 is true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w12 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i5-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i5", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 60925}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition w0 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition v13 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition s0 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w13 is true if proposition v13 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition w9 is true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w12 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i5-cred::cred", "rec_id": "hv3-cnf_n14-i5", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 60925}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition w0 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition v13 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition s0 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w13 is true if proposition v13 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition w9 is true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w12 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i5-skept::skept", "rec_id": "hv3-cnf_n14-i5", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 60925}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition w0 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition v13 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition s0 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w13 is true if proposition v13 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition w9 is true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w12 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i5-wfs::wfs", "rec_id": "hv3-cnf_n14-i5", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 5, "clingo_choices": 4, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 60925}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w10 is true and proposition v2 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition w0 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v7 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w2 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition v13 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition s0 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w13 is true if proposition v13 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition t1 is true if proposition w9 is true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v3 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v10 is true and proposition w1 is true and proposition v8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w12 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition w10 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w12 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i6-none::none", "rec_id": "hv3-cnf_n14-i6", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 10, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60926}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v10 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition w11 is true and proposition bad is not true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition v10 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v9 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w6 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w13 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t5 is true if proposition w11 is true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i6-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i6", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 10, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60926}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v10 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition w11 is true and proposition bad is not true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition v10 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v9 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w6 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w13 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t5 is true if proposition w11 is true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i6-cred::cred", "rec_id": "hv3-cnf_n14-i6", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 10, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60926}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v10 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition w11 is true and proposition bad is not true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition v10 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v9 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w6 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w13 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t5 is true if proposition w11 is true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i6-skept::skept", "rec_id": "hv3-cnf_n14-i6", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 10, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60926}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v10 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition w11 is true and proposition bad is not true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition v10 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v9 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w6 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w13 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t5 is true if proposition w11 is true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i6-wfs::wfs", "rec_id": "hv3-cnf_n14-i6", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 10, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 11, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 60926}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w0 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v10 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition w6 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition w11 is true and proposition bad is not true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w7 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w8 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition v10 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v6 is true and proposition v9 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition w13 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w6 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition v5 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w13 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v13 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w8 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition t5 is true if proposition w11 is true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v9 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v13 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i7-none::none", "rec_id": "hv3-cnf_n14-i7", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 60927}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v12 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w3 is true and proposition v12 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v7 is true and proposition v8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition q is true if proposition w7 is true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition v0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w5 is true and proposition w13 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i7-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i7", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 60927}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v12 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w3 is true and proposition v12 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v7 is true and proposition v8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition q is true if proposition w7 is true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition v0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w5 is true and proposition w13 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i7-cred::cred", "rec_id": "hv3-cnf_n14-i7", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 60927}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w12 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v12 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w3 is true and proposition v12 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v7 is true and proposition v8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition q is true if proposition w7 is true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition v0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w5 is true and proposition w13 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i7-skept::skept", "rec_id": "hv3-cnf_n14-i7", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 60927}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w12 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v12 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w3 is true and proposition v12 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v7 is true and proposition v8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition q is true if proposition w7 is true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition v0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w5 is true and proposition w13 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i7-wfs::wfs", "rec_id": "hv3-cnf_n14-i7", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 60927}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v12 is true and proposition w2 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w3 is true and proposition v12 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v7 is true and proposition v8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition q is true if proposition w7 is true. Proposition bad is true if proposition w7 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w3 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w11 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v1 is true and proposition w11 is true and proposition v0 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w5 is true and proposition w13 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w8 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w12 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v3 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w1 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i8-none::none", "rec_id": "hv3-cnf_n14-i8", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 13, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 27, "prolog_inferences": null, "n_stable_models": 13}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 60928}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v12 is true and proposition v9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w1 is true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition w12 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition w10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition s1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition etrue is true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition s2 is true. Proposition v5 is true if proposition w5 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition w1 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i8-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i8", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 13, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 27, "prolog_inferences": null, "n_stable_models": 13}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 60928}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v12 is true and proposition v9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w1 is true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition w12 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition w10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition s1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition etrue is true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition s2 is true. Proposition v5 is true if proposition w5 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition w1 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i8-cred::cred", "rec_id": "hv3-cnf_n14-i8", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 13, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 27, "prolog_inferences": null, "n_stable_models": 13}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 60928}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v12 is true and proposition v9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w1 is true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition w12 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition w10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition s1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition etrue is true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition s2 is true. Proposition v5 is true if proposition w5 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition w1 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i8-skept::skept", "rec_id": "hv3-cnf_n14-i8", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 13, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 27, "prolog_inferences": null, "n_stable_models": 13}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 60928}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v12 is true and proposition v9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w1 is true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition w12 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition w10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition s1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition etrue is true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition s2 is true. Proposition v5 is true if proposition w5 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition w1 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i8-wfs::wfs", "rec_id": "hv3-cnf_n14-i8", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 13, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 27, "prolog_inferences": null, "n_stable_models": 13}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 1, "query_sign": false, "depth": 6, "width": 3, "n_filler": 0, "variant_seed": 60928}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v6 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v8 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v7 is true and proposition w5 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w5 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v4 is true and proposition w10 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v8 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition s0 is true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w1 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v12 is true and proposition v9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v7 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w1 is true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition w12 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition w10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w7 is true if proposition v7 is not true. Proposition s1 is true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w4 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition w9 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition etrue is true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v4 is true and proposition bad is not true. Proposition s2 is true. Proposition v5 is true if proposition w5 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v12 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition w12 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v10 is true and proposition w8 is true and proposition w1 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition v7 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w0 is true and proposition v5 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i9-none::none", "rec_id": "hv3-cnf_n14-i9", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 9, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 8, "query_sign": false, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 60929}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w3 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v12 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w8 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w8 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w0 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v11 is true and proposition w8 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v8 is true and proposition v1 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition t1 is true if proposition w8 is true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i9-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i9", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 9, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 8, "query_sign": false, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 60929}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w3 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v12 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w8 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w8 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w0 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v11 is true and proposition w8 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v8 is true and proposition v1 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition t1 is true if proposition w8 is true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i9-cred::cred", "rec_id": "hv3-cnf_n14-i9", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 9, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 8, "query_sign": false, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 60929}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w3 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v12 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w8 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w8 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w0 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v11 is true and proposition w8 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v8 is true and proposition v1 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition t1 is true if proposition w8 is true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i9-skept::skept", "rec_id": "hv3-cnf_n14-i9", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 9, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 8, "query_sign": false, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 60929}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w3 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v12 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w8 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w8 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w0 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v11 is true and proposition w8 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v8 is true and proposition v1 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition t1 is true if proposition w8 is true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i9-wfs::wfs", "rec_id": "hv3-cnf_n14-i9", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 9, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 8, "query_sign": false, "depth": 2, "width": 3, "n_filler": 0, "variant_seed": 60929}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v8 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w3 is true and proposition w10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v12 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition w4 is true if proposition v4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w8 is true and proposition w1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w6 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w8 is true and proposition v6 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition v2 is true and proposition w12 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w0 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v0 is true and proposition v8 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w8 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v11 is true and proposition w8 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v0 is true if proposition w0 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v8 is true and proposition v1 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition w10 is true and proposition bad is not true. Proposition t1 is true if proposition w8 is true. Proposition bad is true if proposition w7 is true and proposition w13 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w8 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v9 is true and proposition v11 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v6 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v0 is true and proposition w13 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i10-none::none", "rec_id": "hv3-cnf_n14-i10", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 8, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 60931}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v10 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w9 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w13 is true if proposition v13 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w12 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v8 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w1 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition v12 is true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i10-closed_world::closed_world", "rec_id": "hv3-cnf_n14-i10", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 8, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 60931}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v10 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w9 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w13 is true if proposition v13 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w12 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v8 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w1 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition v12 is true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i10-cred::cred", "rec_id": "hv3-cnf_n14-i10", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 8, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 60931}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v10 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w9 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w13 is true if proposition v13 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w12 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v8 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w1 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition v12 is true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i10-skept::skept", "rec_id": "hv3-cnf_n14-i10", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 8, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 60931}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v10 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w9 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w13 is true if proposition v13 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w12 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v8 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w1 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition v12 is true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n14-i10-wfs::wfs", "rec_id": "hv3-cnf_n14-i10", "axis": "cnf", "difficulty": "cnf_n14", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 6, "clingo_choices": 8, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 14, "n_clauses": 60, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 60931}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w6 is true if proposition v6 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w8 is true and proposition v7 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v10 is true and proposition w4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v7 is true and proposition w4 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition w9 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v7 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w8 is true and proposition v4 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v8 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w3 is true and proposition v13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition w13 is true if proposition v13 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w4 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w5 is true and proposition bad is not true. Proposition etrue is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w12 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition s2 is true. Proposition w0 is true if proposition v0 is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v8 is true and proposition v5 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v0 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w0 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w6 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w1 is true and proposition v10 is true and proposition v9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v13 is true and proposition v2 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition v13 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w1 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v1 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition s1 is true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition v12 is true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition v8 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v12 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w3 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w2 is true and proposition v8 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v3 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i0-none::none", "rec_id": "hv3-cnf_n22-i0", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 32, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 15, "clingo_choices": 46, "prolog_inferences": null, "n_stable_models": 32}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 19, "query_sign": false, "depth": 0, "width": 4, "n_filler": 0, "variant_seed": 74990}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v17 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w10 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v20 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition v18 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition w7 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w4 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w20 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w17 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w0 is true and proposition v20 is true and proposition bad is not true. Proposition s3 is true. Proposition w6 is true if proposition v6 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v10 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition w19 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v0 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v7 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w1 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition etrue is true. Proposition bad is true if proposition w11 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v20 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v17 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w9 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v1 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v1 is true and proposition w15 is true and proposition v14 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition w17 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v0 is true and proposition w20 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v1 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v16 is true and proposition w4 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w20 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w17 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i0-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i0", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 32, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 15, "clingo_choices": 46, "prolog_inferences": null, "n_stable_models": 32}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 19, "query_sign": false, "depth": 0, "width": 4, "n_filler": 0, "variant_seed": 74990}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v17 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w10 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v20 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition v18 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition w7 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w4 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w20 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w17 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w0 is true and proposition v20 is true and proposition bad is not true. Proposition s3 is true. Proposition w6 is true if proposition v6 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v10 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition w19 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v0 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v7 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w1 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition etrue is true. Proposition bad is true if proposition w11 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v20 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v17 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w9 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v1 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v1 is true and proposition w15 is true and proposition v14 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition w17 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v0 is true and proposition w20 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v1 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v16 is true and proposition w4 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w20 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w17 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i0-cred::cred", "rec_id": "hv3-cnf_n22-i0", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 32, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 15, "clingo_choices": 46, "prolog_inferences": null, "n_stable_models": 32}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 19, "query_sign": false, "depth": 0, "width": 4, "n_filler": 0, "variant_seed": 74990}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v17 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w10 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v20 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition v18 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition w7 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w4 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w20 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w17 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w0 is true and proposition v20 is true and proposition bad is not true. Proposition s3 is true. Proposition w6 is true if proposition v6 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v10 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition w19 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v0 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v7 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w1 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition etrue is true. Proposition bad is true if proposition w11 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v20 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v17 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w9 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v1 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v1 is true and proposition w15 is true and proposition v14 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition w17 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v0 is true and proposition w20 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v1 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v16 is true and proposition w4 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w20 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w17 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i0-skept::skept", "rec_id": "hv3-cnf_n22-i0", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 32, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 15, "clingo_choices": 46, "prolog_inferences": null, "n_stable_models": 32}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 19, "query_sign": false, "depth": 0, "width": 4, "n_filler": 0, "variant_seed": 74990}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v17 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w10 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v20 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition v18 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition w7 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w4 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w20 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w17 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w0 is true and proposition v20 is true and proposition bad is not true. Proposition s3 is true. Proposition w6 is true if proposition v6 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v10 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition w19 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v0 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v7 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w1 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition etrue is true. Proposition bad is true if proposition w11 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v20 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v17 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w9 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v1 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v1 is true and proposition w15 is true and proposition v14 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition w17 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v0 is true and proposition w20 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v1 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v16 is true and proposition w4 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w20 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w17 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i0-wfs::wfs", "rec_id": "hv3-cnf_n22-i0", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 32, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 15, "clingo_choices": 46, "prolog_inferences": null, "n_stable_models": 32}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 19, "query_sign": false, "depth": 0, "width": 4, "n_filler": 0, "variant_seed": 74990}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v17 is true and proposition v0 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w4 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w10 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w1 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v20 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition v18 is true and proposition w9 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w0 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w1 is true and proposition v13 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition w7 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w4 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w20 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v0 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w17 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w0 is true and proposition v20 is true and proposition bad is not true. Proposition s3 is true. Proposition w6 is true if proposition v6 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v10 is true and proposition w0 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition w19 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v0 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v0 is true and proposition w3 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition w0 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v7 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition bad is true if proposition w1 is true and proposition v8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v11 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v3 is true and proposition v13 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w1 is true and proposition v7 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition v6 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w6 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition etrue is true. Proposition bad is true if proposition w11 is true and proposition w2 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v20 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition v17 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w9 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v1 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v1 is true and proposition w15 is true and proposition v14 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w4 is true and proposition v7 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w12 is true and proposition w17 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v12 is true and proposition v21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v0 is true and proposition w20 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v1 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v16 is true and proposition w4 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v6 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w20 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w15 is true and proposition w17 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i1-none::none", "rec_id": "hv3-cnf_n22-i1", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 15, "query_sign": true, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 74993}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v16 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w6 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w21 is true and proposition w13 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v14 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w18 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v19 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition v12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w14 is true if proposition v14 is not true. Proposition q is true if proposition v15 is true and proposition wide is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v17 is true and proposition w15 is true and proposition v4 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v19 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w16 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v19 is true and proposition w0 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition v19 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v5 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition v18 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v20 is true and proposition v15 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v14 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v21 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w16 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v11 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w10 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i1-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i1", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 15, "query_sign": true, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 74993}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v16 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w6 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w21 is true and proposition w13 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v14 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w18 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v19 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition v12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w14 is true if proposition v14 is not true. Proposition q is true if proposition v15 is true and proposition wide is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v17 is true and proposition w15 is true and proposition v4 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v19 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w16 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v19 is true and proposition w0 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition v19 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v5 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition v18 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v20 is true and proposition v15 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v14 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v21 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w16 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v11 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w10 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i1-cred::cred", "rec_id": "hv3-cnf_n22-i1", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 15, "query_sign": true, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 74993}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v16 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w6 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w21 is true and proposition w13 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v14 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w18 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v19 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition v12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w14 is true if proposition v14 is not true. Proposition q is true if proposition v15 is true and proposition wide is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v17 is true and proposition w15 is true and proposition v4 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v19 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w16 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v19 is true and proposition w0 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition v19 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v5 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition v18 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v20 is true and proposition v15 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v14 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v21 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w16 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v11 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w10 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i1-skept::skept", "rec_id": "hv3-cnf_n22-i1", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 15, "query_sign": true, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 74993}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v16 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w6 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w21 is true and proposition w13 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v14 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w18 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v19 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition v12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w14 is true if proposition v14 is not true. Proposition q is true if proposition v15 is true and proposition wide is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v17 is true and proposition w15 is true and proposition v4 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v19 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w16 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v19 is true and proposition w0 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition v19 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v5 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition v18 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v20 is true and proposition v15 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v14 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v21 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w16 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v11 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w10 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i1-wfs::wfs", "rec_id": "hv3-cnf_n22-i1", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 10, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 22, "prolog_inferences": null, "n_stable_models": 10}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 15, "query_sign": true, "depth": 0, "width": 3, "n_filler": 0, "variant_seed": 74993}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v0 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition v6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v16 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v5 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w6 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w21 is true and proposition w13 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v10 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v3 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition s0 is true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v14 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w4 is true and proposition v0 is true and proposition bad is not true. Proposition s2 is true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w18 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v19 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition v12 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v2 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w14 is true if proposition v14 is not true. Proposition q is true if proposition v15 is true and proposition wide is true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w1 is true and proposition w9 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v17 is true and proposition w15 is true and proposition v4 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w11 is true and proposition v2 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v5 is true and proposition v2 is true and proposition v19 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v6 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w16 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v8 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition w13 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v19 is true and proposition w0 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w3 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition v19 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v11 is true and proposition w6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v5 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition v18 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v20 is true and proposition v15 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v14 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v21 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w11 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v11 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w16 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v11 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w10 is true and proposition w7 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i2-none::none", "rec_id": "hv3-cnf_n22-i2", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 74994}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v20 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w8 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v8 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w15 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v17 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w15 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v17 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w10 is true and proposition v15 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w10 is true and proposition v12 is true and proposition v16 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v13 is true and proposition w18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v18 is true and proposition v12 is true and proposition bad is not true. Proposition q is true if proposition w13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w15 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i2-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i2", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 74994}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v20 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w8 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v8 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w15 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v17 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w15 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v17 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w10 is true and proposition v15 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w10 is true and proposition v12 is true and proposition v16 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v13 is true and proposition w18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v18 is true and proposition v12 is true and proposition bad is not true. Proposition q is true if proposition w13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w15 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i2-cred::cred", "rec_id": "hv3-cnf_n22-i2", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 74994}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v20 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w8 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v8 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w15 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v17 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w15 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v17 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w10 is true and proposition v15 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w10 is true and proposition v12 is true and proposition v16 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v13 is true and proposition w18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v18 is true and proposition v12 is true and proposition bad is not true. Proposition q is true if proposition w13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w15 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i2-skept::skept", "rec_id": "hv3-cnf_n22-i2", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 74994}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v20 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w8 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v8 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w15 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v17 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w15 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v17 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w10 is true and proposition v15 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w10 is true and proposition v12 is true and proposition v16 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v13 is true and proposition w18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v18 is true and proposition v12 is true and proposition bad is not true. Proposition q is true if proposition w13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w15 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i2-wfs::wfs", "rec_id": "hv3-cnf_n22-i2", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 7, "clingo_choices": 10, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": false, "depth": 0, "width": 0, "n_filler": 0, "variant_seed": 74994}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w3 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v20 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v1 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w8 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v8 is true and proposition v5 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w13 is true and proposition w9 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v13 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w11 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w15 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition w3 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v17 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w4 is true and proposition w3 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w9 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w19 is true and proposition w1 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v1 is true and proposition v5 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w15 is true and proposition v2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v1 is true and proposition w4 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v2 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v17 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v9 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition w2 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w10 is true and proposition v15 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v16 is true and proposition w5 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w10 is true and proposition w21 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w10 is true and proposition v12 is true and proposition v16 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v1 is true and proposition w12 is true and proposition w2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition v6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v3 is true and proposition v17 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v13 is true and proposition w18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v18 is true and proposition v12 is true and proposition bad is not true. Proposition q is true if proposition w13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w15 is true and proposition w2 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w0 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i3-none::none", "rec_id": "hv3-cnf_n22-i3", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 26, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 74995}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w17 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v12 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w13 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w18 is true and proposition bad is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v12 is true and proposition v20 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w7 is true and proposition v18 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v14 is true and proposition w20 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v19 is true and proposition v6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w2 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v20 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w15 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v7 is true and proposition v21 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w18 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v18 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v15 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v21 is true and proposition v8 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t1 is true if proposition v13 is true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w18 is true and proposition v10 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w18 is true and proposition v13 is true and proposition w19 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v9 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w19 is true if proposition v19 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w15 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v14 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i3-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i3", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 26, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 74995}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w17 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v12 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w13 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w18 is true and proposition bad is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v12 is true and proposition v20 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w7 is true and proposition v18 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v14 is true and proposition w20 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v19 is true and proposition v6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w2 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v20 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w15 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v7 is true and proposition v21 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w18 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v18 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v15 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v21 is true and proposition v8 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t1 is true if proposition v13 is true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w18 is true and proposition v10 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w18 is true and proposition v13 is true and proposition w19 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v9 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w19 is true if proposition v19 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w15 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v14 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i3-cred::cred", "rec_id": "hv3-cnf_n22-i3", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 26, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 74995}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w17 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v12 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w13 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w18 is true and proposition bad is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v12 is true and proposition v20 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w7 is true and proposition v18 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v14 is true and proposition w20 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v19 is true and proposition v6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w2 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v20 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w15 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v7 is true and proposition v21 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w18 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v18 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v15 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v21 is true and proposition v8 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t1 is true if proposition v13 is true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w18 is true and proposition v10 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w18 is true and proposition v13 is true and proposition w19 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v9 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w19 is true if proposition v19 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w15 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v14 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i3-skept::skept", "rec_id": "hv3-cnf_n22-i3", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 26, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 74995}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w17 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v12 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w13 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w18 is true and proposition bad is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v12 is true and proposition v20 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w7 is true and proposition v18 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v14 is true and proposition w20 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v19 is true and proposition v6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w2 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v20 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w15 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v7 is true and proposition v21 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w18 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v18 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v15 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v21 is true and proposition v8 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t1 is true if proposition v13 is true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w18 is true and proposition v10 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w18 is true and proposition v13 is true and proposition w19 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v9 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w19 is true if proposition v19 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w15 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v14 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i3-wfs::wfs", "rec_id": "hv3-cnf_n22-i3", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 11, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 26, "prolog_inferences": null, "n_stable_models": 11}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 2, "width": 0, "n_filler": 0, "variant_seed": 74995}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w17 is true and proposition v10 is true and proposition w7 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w9 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w10 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v12 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v11 is true and proposition w2 is true and proposition w13 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v13 is true and proposition w1 is true and proposition w18 is true and proposition bad is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v12 is true and proposition v20 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w7 is true and proposition v18 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v14 is true and proposition w20 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v19 is true and proposition v6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w2 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v20 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w15 is true and proposition w17 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v16 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v7 is true and proposition v21 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w18 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w0 is true and proposition v18 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w11 is true and proposition w14 is true and proposition v13 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w7 is true and proposition w12 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition v5 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v15 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v12 is true and proposition w10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w10 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w12 is true and proposition w10 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w3 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v13 is true and proposition w4 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w7 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v21 is true and proposition v8 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition t1 is true if proposition v13 is true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition w7 is true and proposition v9 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w18 is true and proposition v10 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w16 is true and proposition w21 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w18 is true and proposition v13 is true and proposition w19 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v9 is true and proposition v13 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w4 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v17 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w19 is true if proposition v19 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w15 is true and proposition v19 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition w9 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w12 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w15 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v14 is true and proposition w8 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i4-none::none", "rec_id": "hv3-cnf_n22-i4", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74997}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition t3 is true if proposition w2 is true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition v2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition v17 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w19 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v15 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v6 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w15 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w16 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w15 is true and proposition w1 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v20 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v18 is true and proposition v20 is true and proposition w15 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w21 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v20 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w11 is true and proposition w17 is true and proposition w6 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v6 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v16 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v11 is true and proposition v14 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition s2 is true. Proposition bad is true if proposition w9 is true and proposition w8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v20 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition s0 is true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v10 is true if proposition w10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v20 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition s1 is true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w10 is true and proposition v5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v11 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w1 is true and proposition w15 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v14 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v21 is true and proposition w7 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v19 is true if proposition w19 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v15 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v17 is true and proposition w6 is true and proposition w19 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i4-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i4", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74997}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition t3 is true if proposition w2 is true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition v2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition v17 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w19 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v15 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v6 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w15 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w16 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w15 is true and proposition w1 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v20 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v18 is true and proposition v20 is true and proposition w15 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w21 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v20 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w11 is true and proposition w17 is true and proposition w6 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v6 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v16 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v11 is true and proposition v14 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition s2 is true. Proposition bad is true if proposition w9 is true and proposition w8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v20 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition s0 is true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v10 is true if proposition w10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v20 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition s1 is true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w10 is true and proposition v5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v11 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w1 is true and proposition w15 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v14 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v21 is true and proposition w7 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v19 is true if proposition w19 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v15 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v17 is true and proposition w6 is true and proposition w19 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i4-cred::cred", "rec_id": "hv3-cnf_n22-i4", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74997}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition t3 is true if proposition w2 is true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition v2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition v17 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w19 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v15 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v6 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w15 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w16 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w15 is true and proposition w1 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v20 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v18 is true and proposition v20 is true and proposition w15 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w21 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v20 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w11 is true and proposition w17 is true and proposition w6 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v6 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v16 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v11 is true and proposition v14 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition s2 is true. Proposition bad is true if proposition w9 is true and proposition w8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v20 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition s0 is true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v10 is true if proposition w10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v20 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition s1 is true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w10 is true and proposition v5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v11 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w1 is true and proposition w15 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v14 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v21 is true and proposition w7 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v19 is true if proposition w19 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v15 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v17 is true and proposition w6 is true and proposition w19 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i4-skept::skept", "rec_id": "hv3-cnf_n22-i4", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74997}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition t3 is true if proposition w2 is true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition v2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition v17 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w19 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v15 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v6 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w15 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w16 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w15 is true and proposition w1 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v20 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v18 is true and proposition v20 is true and proposition w15 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w21 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v20 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w11 is true and proposition w17 is true and proposition w6 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v6 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v16 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v11 is true and proposition v14 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition s2 is true. Proposition bad is true if proposition w9 is true and proposition w8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v20 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition s0 is true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v10 is true if proposition w10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v20 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition s1 is true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w10 is true and proposition v5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v11 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w1 is true and proposition w15 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v14 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v21 is true and proposition w7 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v19 is true if proposition w19 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v15 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v17 is true and proposition w6 is true and proposition w19 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i4-wfs::wfs", "rec_id": "hv3-cnf_n22-i4", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 5, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 5}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 2, "query_sign": false, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74997}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition t3 is true if proposition w2 is true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition v2 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition v17 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w19 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w4 is true and proposition v10 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v15 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v6 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w15 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w16 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w15 is true and proposition w1 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v20 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v1 is true and proposition w12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w0 is true and proposition w2 is true and proposition w11 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v14 is true if proposition w14 is not true. Proposition w12 is true if proposition v12 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v18 is true and proposition v20 is true and proposition w15 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v18 is true and proposition v11 is true and proposition w20 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w21 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v21 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v1 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v20 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v11 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w11 is true and proposition w17 is true and proposition w6 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition v6 is true and proposition w13 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v15 is true and proposition v5 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v16 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v0 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v11 is true and proposition v14 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition s2 is true. Proposition bad is true if proposition w9 is true and proposition w8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v20 is true and proposition v9 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w9 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w18 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v10 is true and proposition bad is not true. Proposition s0 is true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition v10 is true if proposition w10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v20 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition s1 is true. Proposition w19 is true if proposition v19 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w10 is true and proposition v5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w14 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v18 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w2 is true and proposition w1 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v11 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w4 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v20 is true and proposition v21 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w1 is true and proposition w15 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v2 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v14 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v21 is true and proposition w7 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v19 is true if proposition w19 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w8 is true and proposition v7 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition v10 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w16 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v9 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w13 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v11 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v15 is true and proposition v4 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v4 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w5 is true and proposition v0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v17 is true and proposition w6 is true and proposition w19 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i5-none::none", "rec_id": "hv3-cnf_n22-i5", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74999}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition t3 is true if proposition v7 is true. Proposition bad is true if proposition v9 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w15 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v18 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w13 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w1 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition v0 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v8 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition v15 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v4 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v6 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition etrue is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition v17 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition v4 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w18 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition v13 is true if proposition w13 is not true. Proposition s0 is true. Proposition bad is true if proposition w5 is true and proposition w12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w18 is true and proposition v4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w11 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w1 is true and proposition v21 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w10 is true if proposition v10 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v15 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w14 is true and proposition v10 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w21 is true and proposition w6 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v20 is true and proposition v21 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w19 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w10 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v18 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w20 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i5-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i5", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74999}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition t3 is true if proposition v7 is true. Proposition bad is true if proposition v9 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w15 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v18 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w13 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w1 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition v0 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v8 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition v15 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v4 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v6 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition etrue is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition v17 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition v4 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w18 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition v13 is true if proposition w13 is not true. Proposition s0 is true. Proposition bad is true if proposition w5 is true and proposition w12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w18 is true and proposition v4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w11 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w1 is true and proposition v21 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w10 is true if proposition v10 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v15 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w14 is true and proposition v10 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w21 is true and proposition w6 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v20 is true and proposition v21 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w19 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w10 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v18 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w20 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i5-cred::cred", "rec_id": "hv3-cnf_n22-i5", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74999}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition t3 is true if proposition v7 is true. Proposition bad is true if proposition v9 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w15 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v18 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w13 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w1 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition v0 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v8 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition v15 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v4 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v6 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition etrue is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition v17 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition v4 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w18 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition v13 is true if proposition w13 is not true. Proposition s0 is true. Proposition bad is true if proposition w5 is true and proposition w12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w18 is true and proposition v4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w11 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w1 is true and proposition v21 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w10 is true if proposition v10 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v15 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w14 is true and proposition v10 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w21 is true and proposition w6 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v20 is true and proposition v21 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w19 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w10 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v18 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w20 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i5-skept::skept", "rec_id": "hv3-cnf_n22-i5", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74999}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition t3 is true if proposition v7 is true. Proposition bad is true if proposition v9 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w15 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v18 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w13 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w1 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition v0 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v8 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition v15 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v4 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v6 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition etrue is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition v17 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition v4 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w18 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition v13 is true if proposition w13 is not true. Proposition s0 is true. Proposition bad is true if proposition w5 is true and proposition w12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w18 is true and proposition v4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w11 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w1 is true and proposition v21 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w10 is true if proposition v10 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v15 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w14 is true and proposition v10 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w21 is true and proposition w6 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v20 is true and proposition v21 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w19 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w10 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v18 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w20 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i5-wfs::wfs", "rec_id": "hv3-cnf_n22-i5", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 8, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 11, "clingo_choices": 18, "prolog_inferences": null, "n_stable_models": 8}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": true, "depth": 4, "width": 3, "n_filler": 0, "variant_seed": 74999}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w3 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true. Proposition t3 is true if proposition v7 is true. Proposition bad is true if proposition v9 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w7 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w0 is true and proposition v6 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v10 is true and proposition v5 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w10 is true and proposition w15 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v18 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w4 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w13 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w1 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v20 is true and proposition v0 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v8 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v13 is true and proposition w3 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition v15 is true and proposition v21 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v20 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v4 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v5 is true and proposition v14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v6 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v3 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition w8 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v10 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v15 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w14 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v8 is true and proposition w2 is true and proposition bad is not true. Proposition etrue is true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w10 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v11 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w9 is true and proposition w12 is true and proposition v17 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w18 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition v4 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v12 is true and proposition w2 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w18 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition v13 is true if proposition w13 is not true. Proposition s0 is true. Proposition bad is true if proposition w5 is true and proposition w12 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v1 is true and proposition v0 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w18 is true and proposition v4 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v1 is true and proposition w0 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w11 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w10 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition s2 is true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w1 is true and proposition v21 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w10 is true if proposition v10 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v15 is true and proposition w16 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w14 is true and proposition v10 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w21 is true and proposition w6 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition w2 is true if proposition v2 is not true. Proposition w4 is true if proposition v4 is not true. Proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v10 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v6 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v20 is true and proposition v21 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w6 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w19 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w10 is true and proposition v13 is true and proposition w16 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w2 is true and proposition v16 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v18 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w12 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w20 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i6-none::none", "rec_id": "hv3-cnf_n22-i6", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 12, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": true, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 75000}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w8 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w7 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v18 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v16 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v11 is true and proposition w19 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v6 is true and proposition w15 is true and proposition w0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w16 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v17 is true and proposition v10 is true and proposition w14 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w1 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v7 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v16 is true and proposition w4 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition v18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w0 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w21 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w15 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v10 is true and proposition v14 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w17 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v1 is true and proposition w17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v19 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w0 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v16 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v18 is true and proposition w21 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v20 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w18 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w20 is true and proposition v11 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w9 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition t1 is true if proposition v9 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i6-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i6", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 12, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": true, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 75000}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w8 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w7 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v18 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v16 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v11 is true and proposition w19 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v6 is true and proposition w15 is true and proposition w0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w16 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v17 is true and proposition v10 is true and proposition w14 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w1 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v7 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v16 is true and proposition w4 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition v18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w0 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w21 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w15 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v10 is true and proposition v14 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w17 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v1 is true and proposition w17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v19 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w0 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v16 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v18 is true and proposition w21 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v20 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w18 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w20 is true and proposition v11 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w9 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition t1 is true if proposition v9 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i6-cred::cred", "rec_id": "hv3-cnf_n22-i6", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 12, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": true, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 75000}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w8 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w7 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v18 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v16 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v11 is true and proposition w19 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v6 is true and proposition w15 is true and proposition w0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w16 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v17 is true and proposition v10 is true and proposition w14 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w1 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v7 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v16 is true and proposition w4 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition v18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w0 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w21 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w15 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v10 is true and proposition v14 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w17 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v1 is true and proposition w17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v19 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w0 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v16 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v18 is true and proposition w21 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v20 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w18 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w20 is true and proposition v11 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w9 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition t1 is true if proposition v9 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i6-skept::skept", "rec_id": "hv3-cnf_n22-i6", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 12, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": true, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 75000}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w8 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w7 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v18 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v16 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v11 is true and proposition w19 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v6 is true and proposition w15 is true and proposition w0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w16 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v17 is true and proposition v10 is true and proposition w14 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w1 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v7 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v16 is true and proposition w4 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition v18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w0 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w21 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w15 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v10 is true and proposition v14 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w17 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v1 is true and proposition w17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v19 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w0 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v16 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v18 is true and proposition w21 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v20 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w18 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w20 is true and proposition v11 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w9 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition t1 is true if proposition v9 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i6-wfs::wfs", "rec_id": "hv3-cnf_n22-i6", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 12, "clingo_choices": 12, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 9, "query_sign": true, "depth": 2, "width": 2, "n_filler": 0, "variant_seed": 75000}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w7 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition v12 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w8 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w11 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w7 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v3 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v18 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v16 is true and proposition v2 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v11 is true and proposition w19 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v11 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v6 is true and proposition w15 is true and proposition w0 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w16 is true and proposition v4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w2 is true and proposition w18 is true and proposition v16 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v17 is true and proposition v10 is true and proposition w14 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w1 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w11 is true and proposition v9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w9 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w7 is true if proposition v7 is not true. Proposition s0 is true. Proposition bad is true if proposition w17 is true and proposition v5 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v7 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w11 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition v6 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v16 is true and proposition w4 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w8 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v10 is true and proposition w5 is true and proposition v1 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v14 is true and proposition v21 is true and proposition v11 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition v14 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w5 is true and proposition v18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v11 is true and proposition v2 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w0 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w21 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v4 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v9 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w15 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v16 is true and proposition v15 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition v10 is true and proposition v14 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w17 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v1 is true and proposition w17 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v5 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v19 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w0 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w6 is true and proposition w18 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w2 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition v5 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w1 is true and proposition w2 is true and proposition v16 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v5 is true and proposition v3 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w3 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v18 is true and proposition w21 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v19 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition v20 is true and proposition v10 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w20 is true and proposition v17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v13 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w12 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v8 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v15 is true and proposition w14 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v4 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w18 is true and proposition w11 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v18 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v5 is true and proposition w13 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition w20 is true and proposition v11 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v8 is true and proposition v4 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition w15 is true if proposition v15 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w9 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v15 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition t1 is true if proposition v9 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i7-none::none", "rec_id": "hv3-cnf_n22-i7", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 8, "clingo_choices": 13, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75003}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v14 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition s0 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v17 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w19 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w16 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v16 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w14 is true and proposition v21 is true and proposition w11 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v4 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w14 is true and proposition w16 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v14 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition v6 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w0 is true and proposition v14 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v5 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v17 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w18 is true and proposition v15 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v16 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w6 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v21 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w18 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w11 is true and proposition v10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v21 is true and proposition w16 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition v11 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w11 is true and proposition w1 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w15 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v19 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition t5 is true if proposition v13 is true. Proposition bad is true if proposition w14 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition v17 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition v15 is true and proposition bad is not true. Proposition etrue is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v4 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v11 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i7-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i7", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 8, "clingo_choices": 13, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75003}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v14 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition s0 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v17 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w19 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w16 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v16 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w14 is true and proposition v21 is true and proposition w11 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v4 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w14 is true and proposition w16 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v14 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition v6 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w0 is true and proposition v14 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v5 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v17 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w18 is true and proposition v15 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v16 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w6 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v21 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w18 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w11 is true and proposition v10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v21 is true and proposition w16 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition v11 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w11 is true and proposition w1 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w15 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v19 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition t5 is true if proposition v13 is true. Proposition bad is true if proposition w14 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition v17 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition v15 is true and proposition bad is not true. Proposition etrue is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v4 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v11 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i7-cred::cred", "rec_id": "hv3-cnf_n22-i7", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 8, "clingo_choices": 13, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75003}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v7 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v14 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition s0 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v17 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w19 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w16 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v16 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w14 is true and proposition v21 is true and proposition w11 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v4 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w14 is true and proposition w16 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v14 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition v6 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w0 is true and proposition v14 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v5 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v17 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w18 is true and proposition v15 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v16 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w6 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v21 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w18 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w11 is true and proposition v10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v21 is true and proposition w16 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition v11 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w11 is true and proposition w1 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w15 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v19 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition t5 is true if proposition v13 is true. Proposition bad is true if proposition w14 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition v17 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition v15 is true and proposition bad is not true. Proposition etrue is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v4 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v11 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i7-skept::skept", "rec_id": "hv3-cnf_n22-i7", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 8, "clingo_choices": 13, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75003}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v7 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v14 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition s0 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v17 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w19 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w16 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v16 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w14 is true and proposition v21 is true and proposition w11 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v4 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w14 is true and proposition w16 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v14 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition v6 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w0 is true and proposition v14 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v5 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v17 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w18 is true and proposition v15 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v16 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w6 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v21 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w18 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w11 is true and proposition v10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v21 is true and proposition w16 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition v11 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w11 is true and proposition w1 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w15 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v19 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition t5 is true if proposition v13 is true. Proposition bad is true if proposition w14 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition v17 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition v15 is true and proposition bad is not true. Proposition etrue is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v4 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v11 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i7-wfs::wfs", "rec_id": "hv3-cnf_n22-i7", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 4, "divergence_bin": "sig_TTuloop", "signature": "TTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 8, "clingo_choices": 13, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 13, "query_sign": true, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75003}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v7 is true and proposition w9 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w1 is true and proposition w19 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v11 is true and proposition v1 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w12 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v14 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w3 is true and proposition v11 is true and proposition bad is not true. Proposition s0 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v3 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition w14 is true and proposition v7 is true and proposition v18 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v1 is true and proposition v0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w9 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v17 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition w9 is true and proposition v16 is true and proposition w18 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition v6 is true if proposition w6 is not true. Proposition t4 is true if proposition t5 is true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v4 is true and proposition w19 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w16 is true and proposition w3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w10 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w15 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w20 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v16 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition v14 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w14 is true and proposition v21 is true and proposition w11 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v10 is true and proposition v4 is true and proposition w0 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v4 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v19 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition w14 is true and proposition w16 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v14 is true and proposition w12 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition v6 is true and proposition bad is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w0 is true and proposition v14 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v13 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w6 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v5 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v1 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v17 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w10 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition w20 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v1 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w2 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v20 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w19 is true and proposition v12 is true and proposition bad is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v20 is true and proposition w19 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w20 is true and proposition w14 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v18 is true and proposition v12 is true and proposition w7 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition w18 is true and proposition v15 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v3 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v8 is true and proposition w17 is true and proposition w10 is true and proposition bad is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v16 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w21 is true and proposition v11 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition v13 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w6 is true and proposition w19 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v21 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w18 is true and proposition v12 is true and proposition v8 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition w11 is true and proposition v10 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition w5 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v21 is true and proposition w16 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition v13 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v11 is true and proposition v4 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition w4 is true and proposition v8 is true and proposition v11 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v16 is true and proposition w11 is true and proposition w1 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w15 is true and proposition v21 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition v10 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition v19 is true and proposition v3 is true and proposition v14 is true and proposition bad is not true. Proposition t5 is true if proposition v13 is true. Proposition bad is true if proposition w14 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition v15 is true and proposition v3 is true and proposition v17 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition w9 is true and proposition w20 is true and proposition v15 is true and proposition bad is not true. Proposition etrue is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v4 is true and proposition v10 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v2 is true and proposition w13 is true and proposition bad is not true. Proposition v10 is true if proposition w10 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v2 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v11 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i8-none::none", "rec_id": "hv3-cnf_n22-i8", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 75005}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w17 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w17 is true and proposition v7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w14 is true and proposition bad is not true. Proposition s2 is true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v4 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w17 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition s3 is true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v9 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w21 is true and proposition w18 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition w12 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v21 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w14 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v14 is true and proposition w18 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition w7 is true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w16 is true and proposition w5 is true and proposition w15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v21 is true and proposition w9 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition v20 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w21 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w16 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w15 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition v18 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w12 is true if proposition v12 is not true. Proposition s0 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v13 is true if proposition w13 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i8-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i8", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 75005}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w17 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w17 is true and proposition v7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w14 is true and proposition bad is not true. Proposition s2 is true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v4 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w17 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition s3 is true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v9 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w21 is true and proposition w18 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition w12 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v21 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w14 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v14 is true and proposition w18 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition w7 is true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w16 is true and proposition w5 is true and proposition w15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v21 is true and proposition w9 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition v20 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w21 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w16 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w15 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition v18 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w12 is true if proposition v12 is not true. Proposition s0 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v13 is true if proposition w13 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i8-cred::cred", "rec_id": "hv3-cnf_n22-i8", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 75005}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w17 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w17 is true and proposition v7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w14 is true and proposition bad is not true. Proposition s2 is true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v4 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w17 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition s3 is true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v9 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w21 is true and proposition w18 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition w12 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v21 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w14 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v14 is true and proposition w18 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition w7 is true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w16 is true and proposition w5 is true and proposition w15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v21 is true and proposition w9 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition v20 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w21 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w16 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w15 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition v18 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w12 is true if proposition v12 is not true. Proposition s0 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v13 is true if proposition w13 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i8-skept::skept", "rec_id": "hv3-cnf_n22-i8", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 75005}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w17 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w17 is true and proposition v7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w14 is true and proposition bad is not true. Proposition s2 is true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v4 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w17 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition s3 is true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v9 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w21 is true and proposition w18 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition w12 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v21 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w14 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v14 is true and proposition w18 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition w7 is true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w16 is true and proposition w5 is true and proposition w15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v21 is true and proposition w9 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition v20 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w21 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w16 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w15 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition v18 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w12 is true if proposition v12 is not true. Proposition s0 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v13 is true if proposition w13 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i8-wfs::wfs", "rec_id": "hv3-cnf_n22-i8", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 13, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 7, "query_sign": false, "depth": 6, "width": 4, "n_filler": 0, "variant_seed": 75005}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v16 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w6 is true and proposition w8 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w17 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v5 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v19 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w2 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v13 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w1 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w8 is true and proposition v0 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w13 is true and proposition w5 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition w0 is true and proposition w17 is true and proposition v7 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w9 is true and proposition w10 is true and proposition w14 is true and proposition bad is not true. Proposition s2 is true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v4 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition v7 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition v8 is true and proposition w3 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w17 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w11 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v3 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition w13 is true and proposition w3 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w12 is true and proposition w8 is true and proposition bad is not true. Proposition s3 is true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition w15 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w18 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w20 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v2 is true and proposition bad is not true. Proposition t1 is true if proposition t2 is true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition v12 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v9 is true and proposition v19 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v10 is true and proposition w21 is true and proposition w18 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v1 is true and proposition v12 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w0 is true and proposition v11 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v8 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition w12 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v21 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w0 is true and proposition w2 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w9 is true and proposition w3 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v19 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v10 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v7 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w8 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v20 is true and proposition w13 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition bad is true if proposition v11 is true and proposition w7 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w4 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w14 is true and proposition v7 is true and proposition bad is not true. Proposition v21 is true if proposition w21 is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v5 is true and proposition w2 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition v18 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w0 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v14 is true and proposition w18 is true and proposition bad is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition w7 is true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w8 is true and proposition v15 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v15 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w16 is true and proposition w5 is true and proposition w15 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w2 is true and proposition v13 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v10 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w5 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w14 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w4 is true and proposition v21 is true and proposition w9 is true and proposition bad is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition v7 is true and proposition v20 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition w21 is true and proposition w9 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w4 is true and proposition w5 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w13 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w16 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w3 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w15 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition bad is true if proposition v5 is true and proposition v15 is true and proposition v18 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w12 is true if proposition v12 is not true. Proposition s0 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v21 is true and proposition w5 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition v13 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition v16 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition v0 is true and proposition v15 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v2 is true and proposition v4 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition w16 is true if proposition v16 is not true. Proposition v10 is true if proposition w10 is not true. Proposition t0 is true if proposition t1 is true. Proposition bad is true if proposition v12 is true and proposition w20 is true and proposition v16 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition v13 is true if proposition w13 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i9-none::none", "rec_id": "hv3-cnf_n22-i9", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 17, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 21, "query_sign": false, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 75006}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition w16 is true and proposition v10 is true and proposition w17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v20 is true and proposition v14 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v19 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition w5 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v18 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v19 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition w13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition v16 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition v12 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v21 is true if proposition w21 is not true. Proposition w17 is true if proposition v17 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v18 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition w2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v12 is true and proposition w19 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v21 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v18 is true and proposition v16 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w16 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition q is true if proposition w21 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v9 is true if proposition w9 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition v18 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition etrue is true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v5 is true and proposition w18 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w21 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v18 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i9-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i9", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 17, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 21, "query_sign": false, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 75006}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition w16 is true and proposition v10 is true and proposition w17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v20 is true and proposition v14 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v19 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition w5 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v18 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v19 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition w13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition v16 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition v12 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v21 is true if proposition w21 is not true. Proposition w17 is true if proposition v17 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v18 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition w2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v12 is true and proposition w19 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v21 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v18 is true and proposition v16 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w16 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition q is true if proposition w21 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v9 is true if proposition w9 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition v18 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition etrue is true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v5 is true and proposition w18 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w21 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v18 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i9-cred::cred", "rec_id": "hv3-cnf_n22-i9", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 17, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 21, "query_sign": false, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 75006}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition w16 is true and proposition v10 is true and proposition w17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v20 is true and proposition v14 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v19 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition w5 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v18 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v19 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition w13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition v16 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition v12 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v21 is true if proposition w21 is not true. Proposition w17 is true if proposition v17 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v18 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition w2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v12 is true and proposition w19 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v21 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v18 is true and proposition v16 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w16 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition q is true if proposition w21 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v9 is true if proposition w9 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition v18 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition etrue is true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v5 is true and proposition w18 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w21 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v18 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i9-skept::skept", "rec_id": "hv3-cnf_n22-i9", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "skept", "gold": "A", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 17, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 21, "query_sign": false, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 75006}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition w16 is true and proposition v10 is true and proposition w17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v20 is true and proposition v14 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v19 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition w5 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v18 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v19 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition w13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition v16 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition v12 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v21 is true if proposition w21 is not true. Proposition w17 is true if proposition v17 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v18 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition w2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v12 is true and proposition w19 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v21 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v18 is true and proposition v16 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w16 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition q is true if proposition w21 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v9 is true if proposition w9 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition v18 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition etrue is true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v5 is true and proposition w18 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w21 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v18 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i9-wfs::wfs", "rec_id": "hv3-cnf_n22-i9", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 0, "divergence_bin": "sig_FTuloop", "signature": "FTuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "T", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 17, "clingo_choices": 16, "prolog_inferences": null, "n_stable_models": 0}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 21, "query_sign": false, "depth": 0, "width": 2, "n_filler": 0, "variant_seed": 75006}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition w16 is true and proposition v10 is true and proposition w17 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w15 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w11 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w5 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w2 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w15 is true and proposition w7 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition bad is true if proposition v20 is true and proposition v14 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w3 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v19 is true and proposition w5 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition w5 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v18 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v7 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition v12 is true and proposition v17 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v19 is true and proposition w18 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition v6 is true and proposition w9 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w6 is true and proposition w13 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition bad is true if proposition v2 is true and proposition v16 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition v12 is true and proposition bad is not true. Proposition w19 is true if proposition v19 is not true. Proposition v21 is true if proposition w21 is not true. Proposition w17 is true if proposition v17 is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v2 is true and proposition v14 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v21 is true and proposition v7 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v18 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition s0 is true. Proposition bad is true if proposition w20 is true and proposition v8 is true and proposition v14 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w4 is true and proposition w18 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v20 is true and proposition w2 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v12 is true and proposition w19 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition v21 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v18 is true and proposition v16 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition bad is true if proposition w17 is true and proposition w9 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w6 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w12 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v2 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v6 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w16 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w3 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w11 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w2 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v13 is true and proposition w16 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition q is true if proposition w21 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w12 is true and proposition w7 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w0 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w5 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition v7 is true and proposition v4 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v12 is true and proposition v10 is true and proposition w4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v12 is true if proposition w12 is not true. Proposition v6 is true if proposition w6 is not true. Proposition v9 is true if proposition w9 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition v16 is true and proposition w6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v17 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w18 is true and proposition v2 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w14 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w5 is true and proposition w2 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition w2 is true and proposition v7 is true and proposition v5 is true and proposition bad is not true. Proposition v14 is true if proposition w14 is not true. Proposition bad is true if proposition v2 is true and proposition v5 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v3 is true and proposition v5 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v4 is true and proposition v18 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition etrue is true. Proposition bad is true if proposition v14 is true and proposition v0 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v11 is true and proposition w10 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w11 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition bad is true if proposition w9 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v5 is true and proposition w18 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w17 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w9 is true and proposition w1 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v18 is true and proposition w1 is true and proposition v17 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v1 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v8 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w21 is true and proposition w1 is true and proposition bad is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w7 is true and proposition w14 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition w21 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w1 is true and proposition v18 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w6 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w20 is true and proposition v10 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition w7 is true and proposition v9 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w13 is true and proposition v4 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v7 is true if proposition w7 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i10-none::none", "rec_id": "hv3-cnf_n22-i10", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 19, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75011}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition bad is true if proposition v15 is true and proposition v10 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w11 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v2 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w8 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v14 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v7 is true and proposition w21 is true and proposition v1 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v3 is true if proposition w3 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w20 is true and proposition w15 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w14 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v14 is true and proposition w18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w16 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v16 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v18 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w21 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v14 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition v15 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v12 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w14 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w11 is true if proposition v11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w18 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v16 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w7 is true and proposition w19 is true and proposition w11 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition etrue is true. Proposition w8 is true if proposition v8 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w21 is true and proposition w12 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v15 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v10 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w12 is true. Proposition bad is true if proposition v12 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition t0 is true if proposition t1 is true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i10-closed_world::closed_world", "rec_id": "hv3-cnf_n22-i10", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 19, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75011}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition bad is true if proposition v15 is true and proposition v10 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w11 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v2 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w8 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v14 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v7 is true and proposition w21 is true and proposition v1 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v3 is true if proposition w3 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w20 is true and proposition w15 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w14 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v14 is true and proposition w18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w16 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v16 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v18 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w21 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v14 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition v15 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v12 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w14 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w11 is true if proposition v11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w18 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v16 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w7 is true and proposition w19 is true and proposition w11 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition etrue is true. Proposition w8 is true if proposition v8 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w21 is true and proposition w12 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v15 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v10 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w12 is true. Proposition bad is true if proposition v12 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition t0 is true if proposition t1 is true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i10-cred::cred", "rec_id": "hv3-cnf_n22-i10", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 19, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75011}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition bad is true if proposition v15 is true and proposition v10 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w11 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v2 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w8 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v14 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v7 is true and proposition w21 is true and proposition v1 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v3 is true if proposition w3 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w20 is true and proposition w15 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w14 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v14 is true and proposition w18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w16 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v16 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v18 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w21 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v14 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition v15 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v12 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w14 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w11 is true if proposition v11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w18 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v16 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w7 is true and proposition w19 is true and proposition w11 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition etrue is true. Proposition w8 is true if proposition v8 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w21 is true and proposition w12 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v15 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v10 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w12 is true. Proposition bad is true if proposition v12 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition t0 is true if proposition t1 is true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i10-skept::skept", "rec_id": "hv3-cnf_n22-i10", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 19, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75011}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition bad is true if proposition v15 is true and proposition v10 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w11 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v2 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w8 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v14 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v7 is true and proposition w21 is true and proposition v1 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v3 is true if proposition w3 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w20 is true and proposition w15 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w14 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v14 is true and proposition w18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w16 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v16 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v18 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w21 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v14 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition v15 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v12 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w14 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w11 is true if proposition v11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w18 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v16 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w7 is true and proposition w19 is true and proposition w11 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition etrue is true. Proposition w8 is true if proposition v8 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w21 is true and proposition w12 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v15 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v10 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w12 is true. Proposition bad is true if proposition v12 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition t0 is true if proposition t1 is true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-cnf_n22-i10-wfs::wfs", "rec_id": "hv3-cnf_n22-i10", "axis": "cnf", "difficulty": "cnf_n22", "hardness_kind": "search", "n_stable_models": 2, "divergence_bin": "sig_FFuloop", "signature": "FFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 16, "clingo_choices": 19, "prolog_inferences": null, "n_stable_models": 2}, "meta": {"family": "cnf", "n_vars": 22, "n_clauses": 94, "ratio": 4.26, "query": "q", "query_var": 12, "query_sign": false, "depth": 6, "width": 2, "n_filler": 0, "variant_seed": 75011}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition bad is true if proposition v15 is true and proposition v10 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition w0 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition v14 is true if proposition w14 is not true. Proposition v20 is true if proposition w20 is not true. Proposition bad is true if proposition w11 is true and proposition w21 is true and proposition v16 is true and proposition bad is not true. Proposition v18 is true if proposition w18 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w2 is true and proposition v12 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v17 is true and proposition v2 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w3 is true and proposition v13 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v8 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition v8 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition v3 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v9 is true and proposition w6 is true and proposition w20 is true and proposition bad is not true. Proposition w20 is true if proposition v20 is not true. Proposition bad is true if proposition w8 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v14 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w9 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v7 is true and proposition w21 is true and proposition v1 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition v3 is true if proposition w3 is not true. Proposition v21 is true if proposition w21 is not true. Proposition bad is true if proposition w20 is true and proposition w15 is true and proposition v8 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition w12 is true if proposition v12 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w14 is true and proposition v4 is true and proposition v2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w1 is true and proposition v3 is true and proposition w2 is true and proposition bad is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition v14 is true and proposition w18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w17 is true and proposition w20 is true and proposition w3 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w8 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w3 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition w1 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition w4 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v12 is true and proposition w1 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w20 is true and proposition w16 is true and proposition bad is not true. Proposition w17 is true if proposition v17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v0 is true and proposition w16 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition v18 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v16 is true and proposition v2 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w9 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition v18 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v21 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w21 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v19 is true and proposition v14 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v3 is true and proposition v7 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w19 is true and proposition w9 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition w12 is true and proposition v13 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v3 is true and proposition v15 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v6 is true and proposition v4 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition w4 is true and proposition bad is not true. Proposition t2 is true if proposition t3 is true. Proposition s0 is true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition v12 is true and proposition v7 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w8 is true and proposition w14 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v13 is true and proposition v12 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition v18 is true and proposition v5 is true and proposition w6 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w11 is true if proposition v11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v10 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w18 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition v1 is true and proposition v16 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition w7 is true and proposition w19 is true and proposition w11 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition v6 is true and proposition v3 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v3 is true and proposition w0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition v9 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition w3 is true and proposition bad is not true. Proposition etrue is true. Proposition w8 is true if proposition v8 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition w2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition w9 is true and proposition v12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition w7 is true and proposition v0 is true and proposition bad is not true. Proposition bad is true if proposition v15 is true and proposition v20 is true and proposition v11 is true and proposition bad is not true. Proposition bad is true if proposition v17 is true and proposition w7 is true and proposition w18 is true and proposition bad is not true. Proposition v12 is true if proposition w12 is not true. Proposition bad is true if proposition w21 is true and proposition w12 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w0 is true and proposition v13 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v15 is true and proposition w11 is true and proposition w9 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition t1 is true if proposition t2 is true. Proposition bad is true if proposition v10 is true and proposition v16 is true and proposition v3 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v6 is true and proposition v19 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w12 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v8 is true and proposition w19 is true and proposition bad is not true. Proposition bad is true if proposition v10 is true and proposition w12 is true and proposition v14 is true and proposition bad is not true. Proposition bad is true if proposition v7 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v6 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v14 is true and proposition v17 is true and proposition v8 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition w7 is true and proposition v18 is true and proposition bad is not true. Proposition bad is true if proposition v8 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v14 is true and proposition v3 is true and proposition v8 is true and proposition bad is not true. Proposition w10 is true if proposition v10 is not true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition w0 is true and proposition w13 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition w16 is true and proposition v0 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition w11 is true and proposition v19 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w20 is true and proposition w6 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v21 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w4 is true and proposition v19 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v14 is true and proposition w20 is true and proposition v11 is true and proposition bad is not true. Proposition t5 is true if proposition w12 is true. Proposition bad is true if proposition v12 is true and proposition v20 is true and proposition w21 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition t0 is true if proposition t1 is true. Proposition w9 is true if proposition v9 is not true. Proposition w14 is true if proposition v14 is not true. Proposition bad is true if proposition v4 is true and proposition w19 is true and proposition v16 is true and proposition bad is not true. Proposition bad is true if proposition v20 is true and proposition w18 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w7 is true and proposition w9 is true and proposition bad is not true. Proposition t4 is true if proposition t5 is true. Proposition w1 is true if proposition v1 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w6 is true if proposition v6 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i0-none::none", "rec_id": "hv3-parity_n4-i0", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 0, "width": 4, "variant_seed": 76454}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition s2 is true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition q is true if proposition e4 is true and proposition wide is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition s0 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition v2 is true if proposition w2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s3 is true. Proposition w3 is true if proposition v3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i0-closed_world::closed_world", "rec_id": "hv3-parity_n4-i0", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 0, "width": 4, "variant_seed": 76454}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition s2 is true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition q is true if proposition e4 is true and proposition wide is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition s0 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition v2 is true if proposition w2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s3 is true. Proposition w3 is true if proposition v3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i0-cred::cred", "rec_id": "hv3-parity_n4-i0", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 0, "width": 4, "variant_seed": 76454}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition s2 is true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition q is true if proposition e4 is true and proposition wide is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition s0 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition v2 is true if proposition w2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s3 is true. Proposition w3 is true if proposition v3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i0-skept::skept", "rec_id": "hv3-parity_n4-i0", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 0, "width": 4, "variant_seed": 76454}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition s2 is true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition q is true if proposition e4 is true and proposition wide is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition s0 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition v2 is true if proposition w2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s3 is true. Proposition w3 is true if proposition v3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i0-wfs::wfs", "rec_id": "hv3-parity_n4-i0", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 0, "width": 4, "variant_seed": 76454}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition s2 is true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition q is true if proposition e4 is true and proposition wide is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition s1 is true. Proposition s0 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition v2 is true if proposition w2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s3 is true. Proposition w3 is true if proposition v3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i1-none::none", "rec_id": "hv3-parity_n4-i1", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 2, "width": 0, "variant_seed": 76455}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition etrue is true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v0 is true if proposition w0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w0 is true if proposition v0 is not true. Proposition t1 is true if proposition e4 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w3 is true if proposition v3 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e0 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i1-closed_world::closed_world", "rec_id": "hv3-parity_n4-i1", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 2, "width": 0, "variant_seed": 76455}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition etrue is true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v0 is true if proposition w0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w0 is true if proposition v0 is not true. Proposition t1 is true if proposition e4 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w3 is true if proposition v3 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e0 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i1-cred::cred", "rec_id": "hv3-parity_n4-i1", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 2, "width": 0, "variant_seed": 76455}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition etrue is true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v0 is true if proposition w0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w0 is true if proposition v0 is not true. Proposition t1 is true if proposition e4 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w3 is true if proposition v3 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e0 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i1-skept::skept", "rec_id": "hv3-parity_n4-i1", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 2, "width": 0, "variant_seed": 76455}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition etrue is true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v0 is true if proposition w0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w0 is true if proposition v0 is not true. Proposition t1 is true if proposition e4 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w3 is true if proposition v3 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e0 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n4-i1-wfs::wfs", "rec_id": "hv3-parity_n4-i1", "axis": "parity", "difficulty": "parity_n4", "hardness_kind": "bookkeeping", "n_stable_models": 16, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 15, "prolog_inferences": null, "n_stable_models": 16}, "meta": {"family": "parity", "n_cycles": 4, "query": "q", "depth": 2, "width": 0, "variant_seed": 76455}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition etrue is true. Proposition w1 is true if proposition v1 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v0 is true if proposition w0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w0 is true if proposition v0 is not true. Proposition t1 is true if proposition e4 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w3 is true if proposition v3 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e0 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i0-none::none", "rec_id": "hv3-parity_n6-i0", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 4, "width": 4, "variant_seed": 19434}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition e6 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e0 is true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true. Proposition s2 is true. Proposition v1 is true if proposition w1 is not true. Proposition t1 is true if proposition t2 is true. Proposition w4 is true if proposition v4 is not true. Proposition s3 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition v5 is true if proposition w5 is not true. Proposition s1 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i0-closed_world::closed_world", "rec_id": "hv3-parity_n6-i0", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 4, "width": 4, "variant_seed": 19434}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition e6 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e0 is true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true. Proposition s2 is true. Proposition v1 is true if proposition w1 is not true. Proposition t1 is true if proposition t2 is true. Proposition w4 is true if proposition v4 is not true. Proposition s3 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition v5 is true if proposition w5 is not true. Proposition s1 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i0-cred::cred", "rec_id": "hv3-parity_n6-i0", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 4, "width": 4, "variant_seed": 19434}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition e6 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e0 is true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true. Proposition s2 is true. Proposition v1 is true if proposition w1 is not true. Proposition t1 is true if proposition t2 is true. Proposition w4 is true if proposition v4 is not true. Proposition s3 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition v5 is true if proposition w5 is not true. Proposition s1 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i0-skept::skept", "rec_id": "hv3-parity_n6-i0", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 4, "width": 4, "variant_seed": 19434}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition e6 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e0 is true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true. Proposition s2 is true. Proposition v1 is true if proposition w1 is not true. Proposition t1 is true if proposition t2 is true. Proposition w4 is true if proposition v4 is not true. Proposition s3 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition v5 is true if proposition w5 is not true. Proposition s1 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i0-wfs::wfs", "rec_id": "hv3-parity_n6-i0", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 4, "width": 4, "variant_seed": 19434}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition e6 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e0 is true. Proposition w2 is true if proposition v2 is not true. Proposition v3 is true if proposition w3 is not true. Proposition etrue is true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true. Proposition s2 is true. Proposition v1 is true if proposition w1 is not true. Proposition t1 is true if proposition t2 is true. Proposition w4 is true if proposition v4 is not true. Proposition s3 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition v5 is true if proposition w5 is not true. Proposition s1 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i1-none::none", "rec_id": "hv3-parity_n6-i1", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 6, "width": 4, "variant_seed": 19435}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition t1 is true if proposition t2 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s0 is true. Proposition t3 is true if proposition t4 is true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v3 is true if proposition w3 is not true. Proposition s3 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v1 is true if proposition w1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition e6 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition etrue is true. Proposition e0 is true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s2 is true. Proposition w4 is true if proposition v4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i1-closed_world::closed_world", "rec_id": "hv3-parity_n6-i1", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 6, "width": 4, "variant_seed": 19435}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition t1 is true if proposition t2 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s0 is true. Proposition t3 is true if proposition t4 is true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v3 is true if proposition w3 is not true. Proposition s3 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v1 is true if proposition w1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition e6 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition etrue is true. Proposition e0 is true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s2 is true. Proposition w4 is true if proposition v4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i1-cred::cred", "rec_id": "hv3-parity_n6-i1", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 6, "width": 4, "variant_seed": 19435}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition t1 is true if proposition t2 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s0 is true. Proposition t3 is true if proposition t4 is true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v3 is true if proposition w3 is not true. Proposition s3 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v1 is true if proposition w1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition e6 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition etrue is true. Proposition e0 is true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s2 is true. Proposition w4 is true if proposition v4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i1-skept::skept", "rec_id": "hv3-parity_n6-i1", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 6, "width": 4, "variant_seed": 19435}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition t1 is true if proposition t2 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s0 is true. Proposition t3 is true if proposition t4 is true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v3 is true if proposition w3 is not true. Proposition s3 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v1 is true if proposition w1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition e6 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition etrue is true. Proposition e0 is true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s2 is true. Proposition w4 is true if proposition v4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n6-i1-wfs::wfs", "rec_id": "hv3-parity_n6-i1", "axis": "parity", "difficulty": "parity_n6", "hardness_kind": "bookkeeping", "n_stable_models": 64, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 63, "prolog_inferences": null, "n_stable_models": 64}, "meta": {"family": "parity", "n_cycles": 6, "query": "q", "depth": 6, "width": 4, "variant_seed": 19435}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition t1 is true if proposition t2 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s0 is true. Proposition t3 is true if proposition t4 is true. Proposition w1 is true if proposition v1 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition v3 is true if proposition w3 is not true. Proposition s3 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v1 is true if proposition w1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition e6 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition etrue is true. Proposition e0 is true. Proposition s1 is true. Proposition v0 is true if proposition w0 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition s2 is true. Proposition w4 is true if proposition v4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w3 is true if proposition v3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i0-none::none", "rec_id": "hv3-parity_n8-i0", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 0, "width": 0, "variant_seed": 52941}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v2 is true if proposition w2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w1 is true if proposition v1 is not true. Proposition q is true if proposition e8 is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w4 is true if proposition v4 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e0 is true. Proposition v0 is true if proposition w0 is not true. Proposition w5 is true if proposition v5 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i0-closed_world::closed_world", "rec_id": "hv3-parity_n8-i0", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 0, "width": 0, "variant_seed": 52941}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v2 is true if proposition w2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w1 is true if proposition v1 is not true. Proposition q is true if proposition e8 is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w4 is true if proposition v4 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e0 is true. Proposition v0 is true if proposition w0 is not true. Proposition w5 is true if proposition v5 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i0-cred::cred", "rec_id": "hv3-parity_n8-i0", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 0, "width": 0, "variant_seed": 52941}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v2 is true if proposition w2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w1 is true if proposition v1 is not true. Proposition q is true if proposition e8 is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w4 is true if proposition v4 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e0 is true. Proposition v0 is true if proposition w0 is not true. Proposition w5 is true if proposition v5 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i0-skept::skept", "rec_id": "hv3-parity_n8-i0", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 0, "width": 0, "variant_seed": 52941}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v2 is true if proposition w2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w1 is true if proposition v1 is not true. Proposition q is true if proposition e8 is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w4 is true if proposition v4 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e0 is true. Proposition v0 is true if proposition w0 is not true. Proposition w5 is true if proposition v5 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i0-wfs::wfs", "rec_id": "hv3-parity_n8-i0", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 0, "width": 0, "variant_seed": 52941}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w0 is true if proposition v0 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v2 is true if proposition w2 is not true. Proposition w3 is true if proposition v3 is not true. Proposition v3 is true if proposition w3 is not true. Proposition w1 is true if proposition v1 is not true. Proposition q is true if proposition e8 is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w4 is true if proposition v4 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v5 is true if proposition w5 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition w2 is true if proposition v2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e0 is true. Proposition v0 is true if proposition w0 is not true. Proposition w5 is true if proposition v5 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i1-none::none", "rec_id": "hv3-parity_n8-i1", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 4, "width": 3, "variant_seed": 52942}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w4 is true if proposition v4 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w2 is true if proposition v2 is not true. Proposition s0 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition t2 is true if proposition t3 is true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v0 is true if proposition w0 is not true. Proposition s1 is true. Proposition w0 is true if proposition v0 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition t3 is true if proposition e8 is true. Proposition e0 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v5 is true if proposition w5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i1-closed_world::closed_world", "rec_id": "hv3-parity_n8-i1", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 4, "width": 3, "variant_seed": 52942}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w4 is true if proposition v4 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w2 is true if proposition v2 is not true. Proposition s0 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition t2 is true if proposition t3 is true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v0 is true if proposition w0 is not true. Proposition s1 is true. Proposition w0 is true if proposition v0 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition t3 is true if proposition e8 is true. Proposition e0 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v5 is true if proposition w5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i1-cred::cred", "rec_id": "hv3-parity_n8-i1", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 4, "width": 3, "variant_seed": 52942}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w4 is true if proposition v4 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w2 is true if proposition v2 is not true. Proposition s0 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition t2 is true if proposition t3 is true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v0 is true if proposition w0 is not true. Proposition s1 is true. Proposition w0 is true if proposition v0 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition t3 is true if proposition e8 is true. Proposition e0 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v5 is true if proposition w5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i1-skept::skept", "rec_id": "hv3-parity_n8-i1", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 4, "width": 3, "variant_seed": 52942}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w4 is true if proposition v4 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w2 is true if proposition v2 is not true. Proposition s0 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition t2 is true if proposition t3 is true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v0 is true if proposition w0 is not true. Proposition s1 is true. Proposition w0 is true if proposition v0 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition t3 is true if proposition e8 is true. Proposition e0 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v5 is true if proposition w5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-parity_n8-i1-wfs::wfs", "rec_id": "hv3-parity_n8-i1", "axis": "parity", "difficulty": "parity_n8", "hardness_kind": "bookkeeping", "n_stable_models": 256, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 255, "prolog_inferences": null, "n_stable_models": 256}, "meta": {"family": "parity", "n_cycles": 8, "query": "q", "depth": 4, "width": 3, "variant_seed": 52942}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition v2 is true if proposition w2 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w4 is true if proposition v4 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w2 is true if proposition v2 is not true. Proposition s0 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition w3 is true if proposition v3 is not true. Proposition t1 is true if proposition t2 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition t2 is true if proposition t3 is true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v0 is true if proposition w0 is not true. Proposition s1 is true. Proposition w0 is true if proposition v0 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition w6 is true if proposition v6 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition w1 is true if proposition v1 is not true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition v4 is true if proposition w4 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition t3 is true if proposition e8 is true. Proposition e0 is true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v5 is true if proposition w5 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i0-none::none", "rec_id": "hv3-coupled_n3-i0", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 6, "width": 3, "query": "q", "variant_seed": 26389}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h0 is true if proposition a0 is not true. Proposition t5 is true if proposition qcore is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition h0 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i0-closed_world::closed_world", "rec_id": "hv3-coupled_n3-i0", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 6, "width": 3, "query": "q", "variant_seed": 26389}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h0 is true if proposition a0 is not true. Proposition t5 is true if proposition qcore is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition h0 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i0-cred::cred", "rec_id": "hv3-coupled_n3-i0", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 6, "width": 3, "query": "q", "variant_seed": 26389}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h0 is true if proposition a0 is not true. Proposition t5 is true if proposition qcore is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition h0 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i0-skept::skept", "rec_id": "hv3-coupled_n3-i0", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 6, "width": 3, "query": "q", "variant_seed": 26389}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h0 is true if proposition a0 is not true. Proposition t5 is true if proposition qcore is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition h0 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i0-wfs::wfs", "rec_id": "hv3-coupled_n3-i0", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 6, "width": 3, "query": "q", "variant_seed": 26389}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h0 is true if proposition a0 is not true. Proposition t5 is true if proposition qcore is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition h0 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true. Proposition s2 is true. Proposition t2 is true if proposition t3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i1-none::none", "rec_id": "hv3-coupled_n3-i1", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 0, "width": 4, "query": "q", "variant_seed": 26390}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s0 is true. Proposition a2 is true if proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition etrue is true. Proposition qcore is true if proposition h0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition s3 is true. Proposition h0 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i1-closed_world::closed_world", "rec_id": "hv3-coupled_n3-i1", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 0, "width": 4, "query": "q", "variant_seed": 26390}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s0 is true. Proposition a2 is true if proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition etrue is true. Proposition qcore is true if proposition h0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition s3 is true. Proposition h0 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i1-cred::cred", "rec_id": "hv3-coupled_n3-i1", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 0, "width": 4, "query": "q", "variant_seed": 26390}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s0 is true. Proposition a2 is true if proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition etrue is true. Proposition qcore is true if proposition h0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition s3 is true. Proposition h0 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i1-skept::skept", "rec_id": "hv3-coupled_n3-i1", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 0, "width": 4, "query": "q", "variant_seed": 26390}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s0 is true. Proposition a2 is true if proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition etrue is true. Proposition qcore is true if proposition h0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition s3 is true. Proposition h0 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n3-i1-wfs::wfs", "rec_id": "hv3-coupled_n3-i1", "axis": "coupled", "difficulty": "coupled_n3", "hardness_kind": "entanglement", "n_stable_models": 4, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 3, "prolog_inferences": null, "n_stable_models": 4}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 3, "cycle_len": 2, "depth": 0, "width": 4, "query": "q", "variant_seed": 26390}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s0 is true. Proposition a2 is true if proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition etrue is true. Proposition qcore is true if proposition h0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition s3 is true. Proposition h0 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i0-none::none", "rec_id": "hv3-coupled_n5-i0", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 0, "query": "q", "variant_seed": 40832}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h3 is true if proposition a3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition qcore is true if proposition h0 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h1 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i0-closed_world::closed_world", "rec_id": "hv3-coupled_n5-i0", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 0, "query": "q", "variant_seed": 40832}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h3 is true if proposition a3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition qcore is true if proposition h0 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h1 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i0-cred::cred", "rec_id": "hv3-coupled_n5-i0", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 0, "query": "q", "variant_seed": 40832}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h3 is true if proposition a3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition qcore is true if proposition h0 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h1 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i0-skept::skept", "rec_id": "hv3-coupled_n5-i0", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 0, "query": "q", "variant_seed": 40832}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h3 is true if proposition a3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition qcore is true if proposition h0 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h1 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i0-wfs::wfs", "rec_id": "hv3-coupled_n5-i0", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 0, "query": "q", "variant_seed": 40832}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h3 is true if proposition a3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition qcore is true if proposition h0 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h1 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i1-none::none", "rec_id": "hv3-coupled_n5-i1", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 3, "query": "q", "variant_seed": 40834}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition etrue is true. Proposition h1 is true if proposition a1 is not true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h4 is true if proposition a4 is not true. Proposition s0 is true. Proposition h3 is true if proposition a3 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a4 is true if proposition h4 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i1-closed_world::closed_world", "rec_id": "hv3-coupled_n5-i1", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 3, "query": "q", "variant_seed": 40834}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition etrue is true. Proposition h1 is true if proposition a1 is not true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h4 is true if proposition a4 is not true. Proposition s0 is true. Proposition h3 is true if proposition a3 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a4 is true if proposition h4 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i1-cred::cred", "rec_id": "hv3-coupled_n5-i1", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 3, "query": "q", "variant_seed": 40834}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition etrue is true. Proposition h1 is true if proposition a1 is not true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h4 is true if proposition a4 is not true. Proposition s0 is true. Proposition h3 is true if proposition a3 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a4 is true if proposition h4 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i1-skept::skept", "rec_id": "hv3-coupled_n5-i1", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 3, "query": "q", "variant_seed": 40834}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition etrue is true. Proposition h1 is true if proposition a1 is not true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h4 is true if proposition a4 is not true. Proposition s0 is true. Proposition h3 is true if proposition a3 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a4 is true if proposition h4 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-coupled_n5-i1-wfs::wfs", "rec_id": "hv3-coupled_n5-i1", "axis": "coupled", "difficulty": "coupled_n5", "hardness_kind": "entanglement", "n_stable_models": 6, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 5, "prolog_inferences": null, "n_stable_models": 6}, "meta": {"family": "coupled", "subtype": "interdependent", "n_cycles": 5, "cycle_len": 2, "depth": 0, "width": 3, "query": "q", "variant_seed": 40834}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition etrue is true. Proposition h1 is true if proposition a1 is not true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h4 is true if proposition a4 is not true. Proposition s0 is true. Proposition h3 is true if proposition a3 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a4 is true if proposition h4 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i0-none::none", "rec_id": "hv3-decided_d1-i0", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97384}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s0 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i0-closed_world::closed_world", "rec_id": "hv3-decided_d1-i0", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97384}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s0 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i0-cred::cred", "rec_id": "hv3-decided_d1-i0", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97384}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s0 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i0-skept::skept", "rec_id": "hv3-decided_d1-i0", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97384}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s0 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i0-wfs::wfs", "rec_id": "hv3-decided_d1-i0", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97384}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s0 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i1-none::none", "rec_id": "hv3-decided_d1-i1", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 4, "variant_seed": 97385}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a1 is true. Proposition s0 is true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i1-closed_world::closed_world", "rec_id": "hv3-decided_d1-i1", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 4, "variant_seed": 97385}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a1 is true. Proposition s0 is true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i1-cred::cred", "rec_id": "hv3-decided_d1-i1", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 4, "variant_seed": 97385}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a1 is true. Proposition s0 is true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i1-skept::skept", "rec_id": "hv3-decided_d1-i1", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 4, "variant_seed": 97385}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a1 is true. Proposition s0 is true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i1-wfs::wfs", "rec_id": "hv3-decided_d1-i1", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 4, "variant_seed": 97385}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a1 is true. Proposition s0 is true. Proposition s3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i2-none::none", "rec_id": "hv3-decided_d1-i2", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 2, "variant_seed": 97386}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition t1 is true if proposition a1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i2-closed_world::closed_world", "rec_id": "hv3-decided_d1-i2", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 2, "variant_seed": 97386}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition t1 is true if proposition a1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i2-cred::cred", "rec_id": "hv3-decided_d1-i2", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 2, "variant_seed": 97386}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition t1 is true if proposition a1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i2-skept::skept", "rec_id": "hv3-decided_d1-i2", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 2, "variant_seed": 97386}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition t1 is true if proposition a1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i2-wfs::wfs", "rec_id": "hv3-decided_d1-i2", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 9, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 2, "width": 2, "variant_seed": 97386}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition t1 is true if proposition a1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i3-none::none", "rec_id": "hv3-decided_d1-i3", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 11, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 4, "width": 0, "variant_seed": 97388}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true. Proposition t3 is true if proposition a1 is true. Proposition t1 is true if proposition t2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i3-closed_world::closed_world", "rec_id": "hv3-decided_d1-i3", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 11, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 4, "width": 0, "variant_seed": 97388}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true. Proposition t3 is true if proposition a1 is true. Proposition t1 is true if proposition t2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i3-cred::cred", "rec_id": "hv3-decided_d1-i3", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 11, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 4, "width": 0, "variant_seed": 97388}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true. Proposition t3 is true if proposition a1 is true. Proposition t1 is true if proposition t2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i3-skept::skept", "rec_id": "hv3-decided_d1-i3", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 11, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 4, "width": 0, "variant_seed": 97388}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true. Proposition t3 is true if proposition a1 is true. Proposition t1 is true if proposition t2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i3-wfs::wfs", "rec_id": "hv3-decided_d1-i3", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 11, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 4, "width": 0, "variant_seed": 97388}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true. Proposition t3 is true if proposition a1 is true. Proposition t1 is true if proposition t2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i4-none::none", "rec_id": "hv3-decided_d1-i4", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97389}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true. Proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i4-closed_world::closed_world", "rec_id": "hv3-decided_d1-i4", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97389}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true. Proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i4-cred::cred", "rec_id": "hv3-decided_d1-i4", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97389}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true. Proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i4-skept::skept", "rec_id": "hv3-decided_d1-i4", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97389}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true. Proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d1-i4-wfs::wfs", "rec_id": "hv3-decided_d1-i4", "axis": "decided", "difficulty": "decided_d1", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 7, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 1, "query": "q", "depth": 0, "width": 3, "variant_seed": 97389}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition q is true if proposition a1 is true and proposition wide is true. Proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i0-none::none", "rec_id": "hv3-decided_d2-i0", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 4, "variant_seed": 78258}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition t5 is true if proposition a2 is true. Proposition t3 is true if proposition t4 is true. Proposition t4 is true if proposition t5 is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i0-closed_world::closed_world", "rec_id": "hv3-decided_d2-i0", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 4, "variant_seed": 78258}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition t5 is true if proposition a2 is true. Proposition t3 is true if proposition t4 is true. Proposition t4 is true if proposition t5 is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i0-cred::cred", "rec_id": "hv3-decided_d2-i0", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 4, "variant_seed": 78258}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition t5 is true if proposition a2 is true. Proposition t3 is true if proposition t4 is true. Proposition t4 is true if proposition t5 is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i0-skept::skept", "rec_id": "hv3-decided_d2-i0", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 4, "variant_seed": 78258}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition t5 is true if proposition a2 is true. Proposition t3 is true if proposition t4 is true. Proposition t4 is true if proposition t5 is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i0-wfs::wfs", "rec_id": "hv3-decided_d2-i0", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 4, "variant_seed": 78258}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition t5 is true if proposition a2 is true. Proposition t3 is true if proposition t4 is true. Proposition t4 is true if proposition t5 is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s2 is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i1-none::none", "rec_id": "hv3-decided_d2-i1", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 4, "width": 4, "variant_seed": 78259}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition etrue is true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i1-closed_world::closed_world", "rec_id": "hv3-decided_d2-i1", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 4, "width": 4, "variant_seed": 78259}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition etrue is true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i1-cred::cred", "rec_id": "hv3-decided_d2-i1", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 4, "width": 4, "variant_seed": 78259}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition etrue is true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i1-skept::skept", "rec_id": "hv3-decided_d2-i1", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 4, "width": 4, "variant_seed": 78259}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition etrue is true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i1-wfs::wfs", "rec_id": "hv3-decided_d2-i1", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 4, "width": 4, "variant_seed": 78259}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s0 is true. Proposition etrue is true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i2-none::none", "rec_id": "hv3-decided_d2-i2", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 0, "width": 3, "variant_seed": 78260}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition etrue is true. Proposition s0 is true. Proposition s2 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition a2 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i2-closed_world::closed_world", "rec_id": "hv3-decided_d2-i2", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 0, "width": 3, "variant_seed": 78260}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition etrue is true. Proposition s0 is true. Proposition s2 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition a2 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i2-cred::cred", "rec_id": "hv3-decided_d2-i2", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 0, "width": 3, "variant_seed": 78260}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition etrue is true. Proposition s0 is true. Proposition s2 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition a2 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i2-skept::skept", "rec_id": "hv3-decided_d2-i2", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 0, "width": 3, "variant_seed": 78260}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition etrue is true. Proposition s0 is true. Proposition s2 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition a2 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i2-wfs::wfs", "rec_id": "hv3-decided_d2-i2", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 0, "width": 3, "variant_seed": 78260}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition etrue is true. Proposition s0 is true. Proposition s2 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition a2 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i3-none::none", "rec_id": "hv3-decided_d2-i3", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78261}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition etrue is true. Proposition s1 is true. Proposition a0 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition t2 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition s2 is true. Proposition t3 is true if proposition t4 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition a2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i3-closed_world::closed_world", "rec_id": "hv3-decided_d2-i3", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78261}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition etrue is true. Proposition s1 is true. Proposition a0 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition t2 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition s2 is true. Proposition t3 is true if proposition t4 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition a2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i3-cred::cred", "rec_id": "hv3-decided_d2-i3", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78261}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition etrue is true. Proposition s1 is true. Proposition a0 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition t2 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition s2 is true. Proposition t3 is true if proposition t4 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition a2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i3-skept::skept", "rec_id": "hv3-decided_d2-i3", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78261}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition etrue is true. Proposition s1 is true. Proposition a0 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition t2 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition s2 is true. Proposition t3 is true if proposition t4 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition a2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i3-wfs::wfs", "rec_id": "hv3-decided_d2-i3", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78261}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition etrue is true. Proposition s1 is true. Proposition a0 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition t2 is true. Proposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition s2 is true. Proposition t3 is true if proposition t4 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition a2 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i4-none::none", "rec_id": "hv3-decided_d2-i4", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78262}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition t3 is true if proposition t4 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition s2 is true. Proposition t4 is true if proposition t5 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a2 is true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true. Proposition s1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i4-closed_world::closed_world", "rec_id": "hv3-decided_d2-i4", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78262}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition t3 is true if proposition t4 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition s2 is true. Proposition t4 is true if proposition t5 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a2 is true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true. Proposition s1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i4-cred::cred", "rec_id": "hv3-decided_d2-i4", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78262}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition t3 is true if proposition t4 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition s2 is true. Proposition t4 is true if proposition t5 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a2 is true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true. Proposition s1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i4-skept::skept", "rec_id": "hv3-decided_d2-i4", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78262}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition t3 is true if proposition t4 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition s2 is true. Proposition t4 is true if proposition t5 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a2 is true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true. Proposition s1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d2-i4-wfs::wfs", "rec_id": "hv3-decided_d2-i4", "axis": "decided", "difficulty": "decided_d2", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 2, "query": "q", "depth": 6, "width": 3, "variant_seed": 78262}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition t3 is true if proposition t4 is true. Proposition a2 is true if proposition a1 is not true. Proposition a1 is true if proposition a0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition s2 is true. Proposition t4 is true if proposition t5 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a2 is true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true. Proposition s1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i0-none::none", "rec_id": "hv3-decided_d3-i0", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81476}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition q is true if proposition a3 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i0-closed_world::closed_world", "rec_id": "hv3-decided_d3-i0", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81476}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition q is true if proposition a3 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i0-cred::cred", "rec_id": "hv3-decided_d3-i0", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81476}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition q is true if proposition a3 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i0-skept::skept", "rec_id": "hv3-decided_d3-i0", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81476}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition q is true if proposition a3 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i0-wfs::wfs", "rec_id": "hv3-decided_d3-i0", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81476}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition s0 is true. Proposition q is true if proposition a3 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i1-none::none", "rec_id": "hv3-decided_d3-i1", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 4, "variant_seed": 81477}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s3 is true. Proposition a3 is true if proposition a2 is not true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a3 is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i1-closed_world::closed_world", "rec_id": "hv3-decided_d3-i1", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 4, "variant_seed": 81477}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s3 is true. Proposition a3 is true if proposition a2 is not true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a3 is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i1-cred::cred", "rec_id": "hv3-decided_d3-i1", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 4, "variant_seed": 81477}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s3 is true. Proposition a3 is true if proposition a2 is not true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a3 is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i1-skept::skept", "rec_id": "hv3-decided_d3-i1", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 4, "variant_seed": 81477}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s3 is true. Proposition a3 is true if proposition a2 is not true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a3 is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i1-wfs::wfs", "rec_id": "hv3-decided_d3-i1", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 4, "variant_seed": 81477}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s3 is true. Proposition a3 is true if proposition a2 is not true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a3 is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i2-none::none", "rec_id": "hv3-decided_d3-i2", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 14, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 4, "width": 4, "variant_seed": 81478}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true. Proposition a2 is true if proposition a1 is not true. Proposition s3 is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i2-closed_world::closed_world", "rec_id": "hv3-decided_d3-i2", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 14, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 4, "width": 4, "variant_seed": 81478}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true. Proposition a2 is true if proposition a1 is not true. Proposition s3 is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i2-cred::cred", "rec_id": "hv3-decided_d3-i2", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 14, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 4, "width": 4, "variant_seed": 81478}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true. Proposition a2 is true if proposition a1 is not true. Proposition s3 is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i2-skept::skept", "rec_id": "hv3-decided_d3-i2", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 14, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 4, "width": 4, "variant_seed": 81478}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true. Proposition a2 is true if proposition a1 is not true. Proposition s3 is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i2-wfs::wfs", "rec_id": "hv3-decided_d3-i2", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 14, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 4, "width": 4, "variant_seed": 81478}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true. Proposition a2 is true if proposition a1 is not true. Proposition s3 is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition a3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i3-none::none", "rec_id": "hv3-decided_d3-i3", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81479}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a3 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i3-closed_world::closed_world", "rec_id": "hv3-decided_d3-i3", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81479}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a3 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i3-cred::cred", "rec_id": "hv3-decided_d3-i3", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81479}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a3 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i3-skept::skept", "rec_id": "hv3-decided_d3-i3", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81479}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a3 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i3-wfs::wfs", "rec_id": "hv3-decided_d3-i3", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 10, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 0, "width": 2, "variant_seed": 81479}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a3 is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition s1 is true. Proposition etrue is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i4-none::none", "rec_id": "hv3-decided_d3-i4", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 0, "variant_seed": 81480}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a3 is true. Proposition q is true if proposition t0 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i4-closed_world::closed_world", "rec_id": "hv3-decided_d3-i4", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 0, "variant_seed": 81480}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a3 is true. Proposition q is true if proposition t0 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i4-cred::cred", "rec_id": "hv3-decided_d3-i4", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 0, "variant_seed": 81480}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a3 is true. Proposition q is true if proposition t0 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i4-skept::skept", "rec_id": "hv3-decided_d3-i4", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 0, "variant_seed": 81480}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a3 is true. Proposition q is true if proposition t0 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d3-i4-wfs::wfs", "rec_id": "hv3-decided_d3-i4", "axis": "decided", "difficulty": "decided_d3", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 12, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 3, "query": "q", "depth": 2, "width": 0, "variant_seed": 81480}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a3 is true. Proposition q is true if proposition t0 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i0-none::none", "rec_id": "hv3-decided_d4-i0", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 22, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 4, "variant_seed": 37831}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition s2 is true. Proposition s1 is true. Proposition t3 is true if proposition t4 is true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i0-closed_world::closed_world", "rec_id": "hv3-decided_d4-i0", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 22, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 4, "variant_seed": 37831}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition s2 is true. Proposition s1 is true. Proposition t3 is true if proposition t4 is true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i0-cred::cred", "rec_id": "hv3-decided_d4-i0", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 22, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 4, "variant_seed": 37831}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition s2 is true. Proposition s1 is true. Proposition t3 is true if proposition t4 is true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i0-skept::skept", "rec_id": "hv3-decided_d4-i0", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 22, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 4, "variant_seed": 37831}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition s2 is true. Proposition s1 is true. Proposition t3 is true if proposition t4 is true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i0-wfs::wfs", "rec_id": "hv3-decided_d4-i0", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 22, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 4, "variant_seed": 37831}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a0 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition t0 is true if proposition t1 is true. Proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition s2 is true. Proposition s1 is true. Proposition t3 is true if proposition t4 is true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i1-none::none", "rec_id": "hv3-decided_d4-i1", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37832}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t5 is true if proposition a4 is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition a2 is true if proposition a1 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i1-closed_world::closed_world", "rec_id": "hv3-decided_d4-i1", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37832}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t5 is true if proposition a4 is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition a2 is true if proposition a1 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i1-cred::cred", "rec_id": "hv3-decided_d4-i1", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37832}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t5 is true if proposition a4 is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition a2 is true if proposition a1 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i1-skept::skept", "rec_id": "hv3-decided_d4-i1", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37832}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t5 is true if proposition a4 is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition a2 is true if proposition a1 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i1-wfs::wfs", "rec_id": "hv3-decided_d4-i1", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37832}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t5 is true if proposition a4 is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition a2 is true if proposition a1 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition a0 is true. Proposition q is true if proposition t0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i2-none::none", "rec_id": "hv3-decided_d4-i2", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 0, "width": 2, "variant_seed": 37833}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition a4 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition s0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i2-closed_world::closed_world", "rec_id": "hv3-decided_d4-i2", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 0, "width": 2, "variant_seed": 37833}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition a4 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition s0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i2-cred::cred", "rec_id": "hv3-decided_d4-i2", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 0, "width": 2, "variant_seed": 37833}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition a4 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition s0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i2-skept::skept", "rec_id": "hv3-decided_d4-i2", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 0, "width": 2, "variant_seed": 37833}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition a4 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition s0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i2-wfs::wfs", "rec_id": "hv3-decided_d4-i2", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 0, "width": 2, "variant_seed": 37833}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition a4 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s1 is true. Proposition s0 is true. Proposition a1 is true if proposition a0 is not true. Proposition a4 is true if proposition a3 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i3-none::none", "rec_id": "hv3-decided_d4-i3", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37834}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition t3 is true if proposition t4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i3-closed_world::closed_world", "rec_id": "hv3-decided_d4-i3", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37834}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition t3 is true if proposition t4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i3-cred::cred", "rec_id": "hv3-decided_d4-i3", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37834}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition t3 is true if proposition t4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i3-skept::skept", "rec_id": "hv3-decided_d4-i3", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37834}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition t3 is true if proposition t4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i3-wfs::wfs", "rec_id": "hv3-decided_d4-i3", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 18, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 6, "width": 0, "variant_seed": 37834}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true. Proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition t5 is true if proposition a4 is true. Proposition t3 is true if proposition t4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i4-none::none", "rec_id": "hv3-decided_d4-i4", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 2, "width": 2, "variant_seed": 37835}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a4 is true. Proposition etrue is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i4-closed_world::closed_world", "rec_id": "hv3-decided_d4-i4", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 2, "width": 2, "variant_seed": 37835}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a4 is true. Proposition etrue is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i4-cred::cred", "rec_id": "hv3-decided_d4-i4", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 2, "width": 2, "variant_seed": 37835}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a4 is true. Proposition etrue is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i4-skept::skept", "rec_id": "hv3-decided_d4-i4", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 2, "width": 2, "variant_seed": 37835}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a4 is true. Proposition etrue is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d4-i4-wfs::wfs", "rec_id": "hv3-decided_d4-i4", "axis": "decided", "difficulty": "decided_d4", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 17, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 4, "query": "q", "depth": 2, "width": 2, "variant_seed": 37835}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition t1 is true if proposition a4 is true. Proposition etrue is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a2 is true if proposition a1 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition a4 is true if proposition a3 is not true. Proposition s0 is true. Proposition a3 is true if proposition a2 is not true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i0-none::none", "rec_id": "hv3-decided_d5-i0", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38993}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition etrue is true. Proposition a0 is true. Proposition q is true if proposition a5 is true and proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i0-closed_world::closed_world", "rec_id": "hv3-decided_d5-i0", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38993}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition etrue is true. Proposition a0 is true. Proposition q is true if proposition a5 is true and proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i0-cred::cred", "rec_id": "hv3-decided_d5-i0", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38993}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition etrue is true. Proposition a0 is true. Proposition q is true if proposition a5 is true and proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i0-skept::skept", "rec_id": "hv3-decided_d5-i0", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38993}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition etrue is true. Proposition a0 is true. Proposition q is true if proposition a5 is true and proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i0-wfs::wfs", "rec_id": "hv3-decided_d5-i0", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38993}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition etrue is true. Proposition a0 is true. Proposition q is true if proposition a5 is true and proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i1-none::none", "rec_id": "hv3-decided_d5-i1", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38994}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition q is true if proposition a5 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i1-closed_world::closed_world", "rec_id": "hv3-decided_d5-i1", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38994}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition q is true if proposition a5 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i1-cred::cred", "rec_id": "hv3-decided_d5-i1", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38994}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition q is true if proposition a5 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i1-skept::skept", "rec_id": "hv3-decided_d5-i1", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38994}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition q is true if proposition a5 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i1-wfs::wfs", "rec_id": "hv3-decided_d5-i1", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 0, "variant_seed": 38994}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition a0 is true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition q is true if proposition a5 is true. Proposition a3 is true if proposition a2 is not true. Proposition a2 is true if proposition a1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i2-none::none", "rec_id": "hv3-decided_d5-i2", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 2, "width": 0, "variant_seed": 38995}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a5 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i2-closed_world::closed_world", "rec_id": "hv3-decided_d5-i2", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 2, "width": 0, "variant_seed": 38995}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a5 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i2-cred::cred", "rec_id": "hv3-decided_d5-i2", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 2, "width": 0, "variant_seed": 38995}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a5 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i2-skept::skept", "rec_id": "hv3-decided_d5-i2", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 2, "width": 0, "variant_seed": 38995}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a5 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i2-wfs::wfs", "rec_id": "hv3-decided_d5-i2", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 2, "width": 0, "variant_seed": 38995}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition t1 is true if proposition a5 is true. Proposition a1 is true if proposition a0 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a4 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i3-none::none", "rec_id": "hv3-decided_d5-i3", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 6, "width": 4, "variant_seed": 38996}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a1 is true if proposition a0 is not true. Proposition s2 is true. Proposition t5 is true if proposition a5 is true. Proposition t3 is true if proposition t4 is true. Proposition s3 is true. Proposition s1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition a4 is true if proposition a3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i3-closed_world::closed_world", "rec_id": "hv3-decided_d5-i3", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 6, "width": 4, "variant_seed": 38996}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a1 is true if proposition a0 is not true. Proposition s2 is true. Proposition t5 is true if proposition a5 is true. Proposition t3 is true if proposition t4 is true. Proposition s3 is true. Proposition s1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition a4 is true if proposition a3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i3-cred::cred", "rec_id": "hv3-decided_d5-i3", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 6, "width": 4, "variant_seed": 38996}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a1 is true if proposition a0 is not true. Proposition s2 is true. Proposition t5 is true if proposition a5 is true. Proposition t3 is true if proposition t4 is true. Proposition s3 is true. Proposition s1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition a4 is true if proposition a3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i3-skept::skept", "rec_id": "hv3-decided_d5-i3", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 6, "width": 4, "variant_seed": 38996}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a1 is true if proposition a0 is not true. Proposition s2 is true. Proposition t5 is true if proposition a5 is true. Proposition t3 is true if proposition t4 is true. Proposition s3 is true. Proposition s1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition a4 is true if proposition a3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i3-wfs::wfs", "rec_id": "hv3-decided_d5-i3", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 6, "width": 4, "variant_seed": 38996}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a1 is true if proposition a0 is not true. Proposition s2 is true. Proposition t5 is true if proposition a5 is true. Proposition t3 is true if proposition t4 is true. Proposition s3 is true. Proposition s1 is true. Proposition s0 is true. Proposition t1 is true if proposition t2 is true. Proposition a4 is true if proposition a3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition a2 is true if proposition a1 is not true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i4-none::none", "rec_id": "hv3-decided_d5-i4", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 2, "variant_seed": 38997}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition a5 is true and proposition wide is true. Proposition a4 is true if proposition a3 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i4-closed_world::closed_world", "rec_id": "hv3-decided_d5-i4", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "closed_world", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 2, "variant_seed": 38997}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition a5 is true and proposition wide is true. Proposition a4 is true if proposition a3 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i4-cred::cred", "rec_id": "hv3-decided_d5-i4", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 2, "variant_seed": 38997}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition a5 is true and proposition wide is true. Proposition a4 is true if proposition a3 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i4-skept::skept", "rec_id": "hv3-decided_d5-i4", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 2, "variant_seed": 38997}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition a5 is true and proposition wide is true. Proposition a4 is true if proposition a3 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d5-i4-wfs::wfs", "rec_id": "hv3-decided_d5-i4", "axis": "decided", "difficulty": "decided_d5", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_FFFF", "signature": "FFFF", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "F"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 13, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 5, "query": "q", "depth": 0, "width": 2, "variant_seed": 38997}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a2 is true if proposition a1 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition a5 is true and proposition wide is true. Proposition a4 is true if proposition a3 is not true. Proposition a0 is true. Proposition a3 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i0-none::none", "rec_id": "hv3-decided_d6-i0", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 0, "variant_seed": 53003}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition q is true if proposition a6 is true and proposition etrue is true. Proposition a0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a2 is true if proposition a1 is not true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i0-closed_world::closed_world", "rec_id": "hv3-decided_d6-i0", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 0, "variant_seed": 53003}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition q is true if proposition a6 is true and proposition etrue is true. Proposition a0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a2 is true if proposition a1 is not true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i0-cred::cred", "rec_id": "hv3-decided_d6-i0", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 0, "variant_seed": 53003}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition q is true if proposition a6 is true and proposition etrue is true. Proposition a0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a2 is true if proposition a1 is not true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i0-skept::skept", "rec_id": "hv3-decided_d6-i0", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 0, "variant_seed": 53003}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition q is true if proposition a6 is true and proposition etrue is true. Proposition a0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a2 is true if proposition a1 is not true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i0-wfs::wfs", "rec_id": "hv3-decided_d6-i0", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 15, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 0, "variant_seed": 53003}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition q is true if proposition a6 is true and proposition etrue is true. Proposition a0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a2 is true if proposition a1 is not true. Proposition etrue is true. Proposition a3 is true if proposition a2 is not true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i1-none::none", "rec_id": "hv3-decided_d6-i1", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 4, "variant_seed": 53004}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a6 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a6 is true if proposition a5 is not true. Proposition etrue is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i1-closed_world::closed_world", "rec_id": "hv3-decided_d6-i1", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 4, "variant_seed": 53004}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a6 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a6 is true if proposition a5 is not true. Proposition etrue is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i1-cred::cred", "rec_id": "hv3-decided_d6-i1", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 4, "variant_seed": 53004}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a6 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a6 is true if proposition a5 is not true. Proposition etrue is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i1-skept::skept", "rec_id": "hv3-decided_d6-i1", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 4, "variant_seed": 53004}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a6 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a6 is true if proposition a5 is not true. Proposition etrue is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i1-wfs::wfs", "rec_id": "hv3-decided_d6-i1", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 0, "width": 4, "variant_seed": 53004}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a1 is true if proposition a0 is not true. Proposition q is true if proposition a6 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition s1 is true. Proposition a0 is true. Proposition s0 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a6 is true if proposition a5 is not true. Proposition etrue is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i2-none::none", "rec_id": "hv3-decided_d6-i2", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53005}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a0 is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a6 is true if proposition a5 is not true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i2-closed_world::closed_world", "rec_id": "hv3-decided_d6-i2", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53005}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a0 is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a6 is true if proposition a5 is not true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i2-cred::cred", "rec_id": "hv3-decided_d6-i2", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53005}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a0 is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a6 is true if proposition a5 is not true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i2-skept::skept", "rec_id": "hv3-decided_d6-i2", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53005}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a0 is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a6 is true if proposition a5 is not true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i2-wfs::wfs", "rec_id": "hv3-decided_d6-i2", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 19, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53005}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a0 is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s1 is true. Proposition a2 is true if proposition a1 is not true. Proposition a4 is true if proposition a3 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a3 is true if proposition a2 is not true. Proposition a6 is true if proposition a5 is not true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t0 is true if proposition t1 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i3-none::none", "rec_id": "hv3-decided_d6-i3", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 23, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 6, "width": 2, "variant_seed": 53006}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition s0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t5 is true if proposition a6 is true. Proposition a2 is true if proposition a1 is not true. Proposition s1 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i3-closed_world::closed_world", "rec_id": "hv3-decided_d6-i3", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 23, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 6, "width": 2, "variant_seed": 53006}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition s0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t5 is true if proposition a6 is true. Proposition a2 is true if proposition a1 is not true. Proposition s1 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i3-cred::cred", "rec_id": "hv3-decided_d6-i3", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 23, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 6, "width": 2, "variant_seed": 53006}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition s0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t5 is true if proposition a6 is true. Proposition a2 is true if proposition a1 is not true. Proposition s1 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i3-skept::skept", "rec_id": "hv3-decided_d6-i3", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 23, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 6, "width": 2, "variant_seed": 53006}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition s0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t5 is true if proposition a6 is true. Proposition a2 is true if proposition a1 is not true. Proposition s1 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i3-wfs::wfs", "rec_id": "hv3-decided_d6-i3", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 23, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 6, "width": 2, "variant_seed": 53006}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition t0 is true and proposition wide is true. Proposition t2 is true if proposition t3 is true. Proposition a4 is true if proposition a3 is not true. Proposition t4 is true if proposition t5 is true. Proposition t0 is true if proposition t1 is true. Proposition a5 is true if proposition a4 is not true. Proposition s0 is true. Proposition a6 is true if proposition a5 is not true. Proposition a3 is true if proposition a2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition t5 is true if proposition a6 is true. Proposition a2 is true if proposition a1 is not true. Proposition s1 is true. Proposition a0 is true. Proposition a1 is true if proposition a0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i4-none::none", "rec_id": "hv3-decided_d6-i4", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53007}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition a6 is true if proposition a5 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition s0 is true. Proposition a0 is true. Proposition a4 is true if proposition a3 is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i4-closed_world::closed_world", "rec_id": "hv3-decided_d6-i4", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "closed_world", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53007}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition a6 is true if proposition a5 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition s0 is true. Proposition a0 is true. Proposition a4 is true if proposition a3 is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i4-cred::cred", "rec_id": "hv3-decided_d6-i4", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53007}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition a6 is true if proposition a5 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition s0 is true. Proposition a0 is true. Proposition a4 is true if proposition a3 is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i4-skept::skept", "rec_id": "hv3-decided_d6-i4", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53007}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition a6 is true if proposition a5 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition s0 is true. Proposition a0 is true. Proposition a4 is true if proposition a3 is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-decided_d6-i4-wfs::wfs", "rec_id": "hv3-decided_d6-i4", "axis": "decided", "difficulty": "decided_d6", "hardness_kind": "definite", "n_stable_models": 1, "divergence_bin": "sig_TTTT", "signature": "TTTT", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "T"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": 20, "n_stable_models": 1}, "meta": {"family": "decided", "stack_depth": 6, "query": "q", "depth": 2, "width": 2, "variant_seed": 53007}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition a6 is true if proposition a5 is not true. Proposition t0 is true if proposition t1 is true. Proposition a3 is true if proposition a2 is not true. Proposition a5 is true if proposition a4 is not true. Proposition a2 is true if proposition a1 is not true. Proposition s0 is true. Proposition a0 is true. Proposition a4 is true if proposition a3 is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t1 is true if proposition a6 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a1 is true if proposition a0 is not true. Proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i0-none::none", "rec_id": "hv3-loopy_d1-i0", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 20243}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i0-closed_world::closed_world", "rec_id": "hv3-loopy_d1-i0", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 20243}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i0-cred::cred", "rec_id": "hv3-loopy_d1-i0", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 20243}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i0-skept::skept", "rec_id": "hv3-loopy_d1-i0", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 20243}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i0-wfs::wfs", "rec_id": "hv3-loopy_d1-i0", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 20243}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i1-none::none", "rec_id": "hv3-loopy_d1-i1", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 20244}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s1 is true. Proposition s2 is true. Proposition s0 is true. Proposition p1 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i1-closed_world::closed_world", "rec_id": "hv3-loopy_d1-i1", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 20244}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s1 is true. Proposition s2 is true. Proposition s0 is true. Proposition p1 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i1-cred::cred", "rec_id": "hv3-loopy_d1-i1", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 20244}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s1 is true. Proposition s2 is true. Proposition s0 is true. Proposition p1 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i1-skept::skept", "rec_id": "hv3-loopy_d1-i1", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 20244}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s1 is true. Proposition s2 is true. Proposition s0 is true. Proposition p1 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i1-wfs::wfs", "rec_id": "hv3-loopy_d1-i1", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 20244}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s1 is true. Proposition s2 is true. Proposition s0 is true. Proposition p1 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i2-none::none", "rec_id": "hv3-loopy_d1-i2", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 20245}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition wide is true and proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i2-closed_world::closed_world", "rec_id": "hv3-loopy_d1-i2", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 20245}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition wide is true and proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i2-cred::cred", "rec_id": "hv3-loopy_d1-i2", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 20245}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition wide is true and proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i2-skept::skept", "rec_id": "hv3-loopy_d1-i2", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 20245}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition wide is true and proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i2-wfs::wfs", "rec_id": "hv3-loopy_d1-i2", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 20245}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition wide is true and proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p1 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i3-none::none", "rec_id": "hv3-loopy_d1-i3", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 20246}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i3-closed_world::closed_world", "rec_id": "hv3-loopy_d1-i3", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 20246}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i3-cred::cred", "rec_id": "hv3-loopy_d1-i3", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 20246}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i3-skept::skept", "rec_id": "hv3-loopy_d1-i3", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 20246}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i3-wfs::wfs", "rec_id": "hv3-loopy_d1-i3", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 20246}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i4-none::none", "rec_id": "hv3-loopy_d1-i4", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 20248}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p1 is true if proposition p1 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i4-closed_world::closed_world", "rec_id": "hv3-loopy_d1-i4", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 20248}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p1 is true if proposition p1 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i4-cred::cred", "rec_id": "hv3-loopy_d1-i4", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 20248}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p1 is true if proposition p1 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i4-skept::skept", "rec_id": "hv3-loopy_d1-i4", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 20248}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p1 is true if proposition p1 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d1-i4-wfs::wfs", "rec_id": "hv3-loopy_d1-i4", "axis": "loopy", "difficulty": "loopy_d1", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 1, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 20248}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p1 is true if proposition p1 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition s0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i0-none::none", "rec_id": "hv3-loopy_d2-i0", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 70569}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i0-closed_world::closed_world", "rec_id": "hv3-loopy_d2-i0", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 70569}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i0-cred::cred", "rec_id": "hv3-loopy_d2-i0", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 70569}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i0-skept::skept", "rec_id": "hv3-loopy_d2-i0", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 70569}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i0-wfs::wfs", "rec_id": "hv3-loopy_d2-i0", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 70569}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p0 is true if proposition p1 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true. Proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i1-none::none", "rec_id": "hv3-loopy_d2-i1", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 70570}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i1-closed_world::closed_world", "rec_id": "hv3-loopy_d2-i1", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 70570}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i1-cred::cred", "rec_id": "hv3-loopy_d2-i1", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 70570}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i1-skept::skept", "rec_id": "hv3-loopy_d2-i1", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 70570}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i1-wfs::wfs", "rec_id": "hv3-loopy_d2-i1", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 70570}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition p0 is true if proposition p1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i2-none::none", "rec_id": "hv3-loopy_d2-i2", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 70571}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i2-closed_world::closed_world", "rec_id": "hv3-loopy_d2-i2", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 70571}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i2-cred::cred", "rec_id": "hv3-loopy_d2-i2", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 70571}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i2-skept::skept", "rec_id": "hv3-loopy_d2-i2", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 70571}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i2-wfs::wfs", "rec_id": "hv3-loopy_d2-i2", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 70571}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i3-none::none", "rec_id": "hv3-loopy_d2-i3", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 70572}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition p1 is true if proposition p2 is true. Proposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i3-closed_world::closed_world", "rec_id": "hv3-loopy_d2-i3", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 70572}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition p1 is true if proposition p2 is true. Proposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i3-cred::cred", "rec_id": "hv3-loopy_d2-i3", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 70572}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition p1 is true if proposition p2 is true. Proposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i3-skept::skept", "rec_id": "hv3-loopy_d2-i3", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 70572}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition p1 is true if proposition p2 is true. Proposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i3-wfs::wfs", "rec_id": "hv3-loopy_d2-i3", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 70572}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p2 is true if proposition p2 is true. Proposition p1 is true if proposition p2 is true. Proposition p0 is true if proposition p1 is true. Proposition q is true if proposition p0 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i4-none::none", "rec_id": "hv3-loopy_d2-i4", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 70576}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i4-closed_world::closed_world", "rec_id": "hv3-loopy_d2-i4", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 70576}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i4-cred::cred", "rec_id": "hv3-loopy_d2-i4", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 70576}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i4-skept::skept", "rec_id": "hv3-loopy_d2-i4", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 70576}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d2-i4-wfs::wfs", "rec_id": "hv3-loopy_d2-i4", "axis": "loopy", "difficulty": "loopy_d2", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 2, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 70576}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition s0 is true. Proposition p2 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i0-none::none", "rec_id": "hv3-loopy_d3-i0", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 51967}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s0 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p3 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i0-closed_world::closed_world", "rec_id": "hv3-loopy_d3-i0", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 51967}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s0 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p3 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i0-cred::cred", "rec_id": "hv3-loopy_d3-i0", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 51967}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s0 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p3 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i0-skept::skept", "rec_id": "hv3-loopy_d3-i0", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 51967}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s0 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p3 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i0-wfs::wfs", "rec_id": "hv3-loopy_d3-i0", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 51967}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition s0 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition p1 is true if proposition p2 is true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p3 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i1-none::none", "rec_id": "hv3-loopy_d3-i1", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 51968}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p2 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i1-closed_world::closed_world", "rec_id": "hv3-loopy_d3-i1", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 51968}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p2 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i1-cred::cred", "rec_id": "hv3-loopy_d3-i1", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 51968}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p2 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i1-skept::skept", "rec_id": "hv3-loopy_d3-i1", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 51968}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p2 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i1-wfs::wfs", "rec_id": "hv3-loopy_d3-i1", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 51968}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s2 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition p2 is true if proposition p3 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i2-none::none", "rec_id": "hv3-loopy_d3-i2", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 51969}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition p3 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p3 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i2-closed_world::closed_world", "rec_id": "hv3-loopy_d3-i2", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 51969}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition p3 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p3 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i2-cred::cred", "rec_id": "hv3-loopy_d3-i2", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 51969}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition p3 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p3 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i2-skept::skept", "rec_id": "hv3-loopy_d3-i2", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 51969}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition p3 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p3 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i2-wfs::wfs", "rec_id": "hv3-loopy_d3-i2", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 3, "variant_seed": 51969}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition p3 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition p2 is true if proposition p3 is true. Proposition s1 is true. Proposition q is true if proposition wide is true and proposition p0 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i3-none::none", "rec_id": "hv3-loopy_d3-i3", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 51970}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p3 is true if proposition p3 is true. Proposition p2 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i3-closed_world::closed_world", "rec_id": "hv3-loopy_d3-i3", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 51970}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p3 is true if proposition p3 is true. Proposition p2 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i3-cred::cred", "rec_id": "hv3-loopy_d3-i3", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 51970}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p3 is true if proposition p3 is true. Proposition p2 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i3-skept::skept", "rec_id": "hv3-loopy_d3-i3", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 51970}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p3 is true if proposition p3 is true. Proposition p2 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i3-wfs::wfs", "rec_id": "hv3-loopy_d3-i3", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 51970}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p3 is true if proposition p3 is true. Proposition p2 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i4-none::none", "rec_id": "hv3-loopy_d3-i4", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 51975}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i4-closed_world::closed_world", "rec_id": "hv3-loopy_d3-i4", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 51975}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i4-cred::cred", "rec_id": "hv3-loopy_d3-i4", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 51975}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i4-skept::skept", "rec_id": "hv3-loopy_d3-i4", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 51975}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d3-i4-wfs::wfs", "rec_id": "hv3-loopy_d3-i4", "axis": "loopy", "difficulty": "loopy_d3", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 3, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 51975}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p3 is true if proposition p3 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i0-none::none", "rec_id": "hv3-loopy_d4-i0", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 65564}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p4 is true if proposition p4 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition p3 is true if proposition p4 is true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i0-closed_world::closed_world", "rec_id": "hv3-loopy_d4-i0", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 65564}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p4 is true if proposition p4 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition p3 is true if proposition p4 is true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i0-cred::cred", "rec_id": "hv3-loopy_d4-i0", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 65564}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p4 is true if proposition p4 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition p3 is true if proposition p4 is true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i0-skept::skept", "rec_id": "hv3-loopy_d4-i0", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 65564}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p4 is true if proposition p4 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition p3 is true if proposition p4 is true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i0-wfs::wfs", "rec_id": "hv3-loopy_d4-i0", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 3, "variant_seed": 65564}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p4 is true if proposition p4 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true. Proposition p0 is true if proposition p1 is true. Proposition p3 is true if proposition p4 is true. Proposition s1 is true. Proposition s0 is true. Proposition s2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i1-none::none", "rec_id": "hv3-loopy_d4-i1", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 65565}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i1-closed_world::closed_world", "rec_id": "hv3-loopy_d4-i1", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 65565}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i1-cred::cred", "rec_id": "hv3-loopy_d4-i1", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 65565}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i1-skept::skept", "rec_id": "hv3-loopy_d4-i1", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 65565}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i1-wfs::wfs", "rec_id": "hv3-loopy_d4-i1", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 0, "variant_seed": 65565}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition q is true if proposition p0 is not true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i2-none::none", "rec_id": "hv3-loopy_d4-i2", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 65566}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i2-closed_world::closed_world", "rec_id": "hv3-loopy_d4-i2", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 65566}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i2-cred::cred", "rec_id": "hv3-loopy_d4-i2", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 65566}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i2-skept::skept", "rec_id": "hv3-loopy_d4-i2", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 65566}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i2-wfs::wfs", "rec_id": "hv3-loopy_d4-i2", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 2, "variant_seed": 65566}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition s1 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition p2 is true if proposition p3 is true. Proposition p1 is true if proposition p2 is true. Proposition q is true if proposition p0 is true and proposition wide is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i3-none::none", "rec_id": "hv3-loopy_d4-i3", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 65567}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i3-closed_world::closed_world", "rec_id": "hv3-loopy_d4-i3", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 65567}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i3-cred::cred", "rec_id": "hv3-loopy_d4-i3", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 65567}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i3-skept::skept", "rec_id": "hv3-loopy_d4-i3", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "skept", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 65567}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i3-wfs::wfs", "rec_id": "hv3-loopy_d4-i3", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_TTTloop", "signature": "TTTloop", "cond": "wfs", "gold": "A", "labels": {"cred": "T", "skept": "T", "wfs": "T", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "neg", "width": 2, "variant_seed": 65567}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s1 is true. Proposition s0 is true. Proposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition p3 is true if proposition p4 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition q is true if proposition wide is true and proposition p0 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i4-none::none", "rec_id": "hv3-loopy_d4-i4", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "none", "gold": null, "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 65568}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition p0 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i4-closed_world::closed_world", "rec_id": "hv3-loopy_d4-i4", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 65568}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition p0 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i4-cred::cred", "rec_id": "hv3-loopy_d4-i4", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "cred", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 65568}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition p0 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i4-skept::skept", "rec_id": "hv3-loopy_d4-i4", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "skept", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 65568}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition p0 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-loopy_d4-i4-wfs::wfs", "rec_id": "hv3-loopy_d4-i4", "axis": "loopy", "difficulty": "loopy_d4", "hardness_kind": "divergence", "n_stable_models": 1, "divergence_bin": "sig_FFFloop", "signature": "FFFloop", "cond": "wfs", "gold": "B", "labels": {"cred": "F", "skept": "F", "wfs": "F", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 0, "prolog_inferences": null, "n_stable_models": 1}, "meta": {"family": "loopy", "loop_depth": 4, "query": "q", "polarity": "pos", "width": 0, "variant_seed": 65568}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition p0 is true if proposition p1 is true. Proposition p2 is true if proposition p3 is true. Proposition q is true if proposition p0 is true. Proposition p1 is true if proposition p2 is true. Proposition p4 is true if proposition p4 is true. Proposition p3 is true if proposition p4 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i0-none::none", "rec_id": "hv3-control_n8-i0", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 51, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 50, "prolog_inferences": null, "n_stable_models": 51}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 0, "query_sign": true, "depth": 4, "width": 4, "n_filler": 9, "variant_seed": 41398}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition f5 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition s0 is true. Proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v3 is true if proposition w3 is not true. Proposition f8 is true. Proposition g3 is true if proposition f3 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition g8 is true if proposition f8 is true. Proposition t3 is true if proposition v0 is true. Proposition f4 is true. Proposition w4 is true if proposition v4 is not true. Proposition g0 is true if proposition f0 is true. Proposition v0 is true if proposition w0 is not true. Proposition f1 is true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition f6 is true. Proposition w0 is true if proposition v0 is not true. Proposition f0 is true. Proposition v5 is true if proposition w5 is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition f7 is true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g6 is true if proposition f6 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g1 is true if proposition f1 is true. Proposition g2 is true if proposition f2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i0-closed_world::closed_world", "rec_id": "hv3-control_n8-i0", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 51, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 50, "prolog_inferences": null, "n_stable_models": 51}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 0, "query_sign": true, "depth": 4, "width": 4, "n_filler": 9, "variant_seed": 41398}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition f5 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition s0 is true. Proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v3 is true if proposition w3 is not true. Proposition f8 is true. Proposition g3 is true if proposition f3 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition g8 is true if proposition f8 is true. Proposition t3 is true if proposition v0 is true. Proposition f4 is true. Proposition w4 is true if proposition v4 is not true. Proposition g0 is true if proposition f0 is true. Proposition v0 is true if proposition w0 is not true. Proposition f1 is true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition f6 is true. Proposition w0 is true if proposition v0 is not true. Proposition f0 is true. Proposition v5 is true if proposition w5 is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition f7 is true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g6 is true if proposition f6 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g1 is true if proposition f1 is true. Proposition g2 is true if proposition f2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i0-cred::cred", "rec_id": "hv3-control_n8-i0", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 51, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 50, "prolog_inferences": null, "n_stable_models": 51}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 0, "query_sign": true, "depth": 4, "width": 4, "n_filler": 9, "variant_seed": 41398}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition f5 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition s0 is true. Proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v3 is true if proposition w3 is not true. Proposition f8 is true. Proposition g3 is true if proposition f3 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition g8 is true if proposition f8 is true. Proposition t3 is true if proposition v0 is true. Proposition f4 is true. Proposition w4 is true if proposition v4 is not true. Proposition g0 is true if proposition f0 is true. Proposition v0 is true if proposition w0 is not true. Proposition f1 is true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition f6 is true. Proposition w0 is true if proposition v0 is not true. Proposition f0 is true. Proposition v5 is true if proposition w5 is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition f7 is true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g6 is true if proposition f6 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g1 is true if proposition f1 is true. Proposition g2 is true if proposition f2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i0-skept::skept", "rec_id": "hv3-control_n8-i0", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 51, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 50, "prolog_inferences": null, "n_stable_models": 51}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 0, "query_sign": true, "depth": 4, "width": 4, "n_filler": 9, "variant_seed": 41398}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition f5 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition s0 is true. Proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v3 is true if proposition w3 is not true. Proposition f8 is true. Proposition g3 is true if proposition f3 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition g8 is true if proposition f8 is true. Proposition t3 is true if proposition v0 is true. Proposition f4 is true. Proposition w4 is true if proposition v4 is not true. Proposition g0 is true if proposition f0 is true. Proposition v0 is true if proposition w0 is not true. Proposition f1 is true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition f6 is true. Proposition w0 is true if proposition v0 is not true. Proposition f0 is true. Proposition v5 is true if proposition w5 is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition f7 is true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g6 is true if proposition f6 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g1 is true if proposition f1 is true. Proposition g2 is true if proposition f2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i0-wfs::wfs", "rec_id": "hv3-control_n8-i0", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 51, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 50, "prolog_inferences": null, "n_stable_models": 51}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 0, "query_sign": true, "depth": 4, "width": 4, "n_filler": 9, "variant_seed": 41398}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition f5 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition w5 is true and proposition v6 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w1 is true and proposition v0 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition s0 is true. Proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition w5 is true and proposition w4 is true and proposition bad is not true. Proposition s1 is true. Proposition v3 is true if proposition w3 is not true. Proposition f8 is true. Proposition g3 is true if proposition f3 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition w5 is true and proposition v1 is true and proposition w3 is true and proposition bad is not true. Proposition g8 is true if proposition f8 is true. Proposition t3 is true if proposition v0 is true. Proposition f4 is true. Proposition w4 is true if proposition v4 is not true. Proposition g0 is true if proposition f0 is true. Proposition v0 is true if proposition w0 is not true. Proposition f1 is true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition f6 is true. Proposition w0 is true if proposition v0 is not true. Proposition f0 is true. Proposition v5 is true if proposition w5 is not true. Proposition etrue is true. Proposition w5 is true if proposition v5 is not true. Proposition f7 is true. Proposition bad is true if proposition w3 is true and proposition v1 is true and proposition v4 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g6 is true if proposition f6 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v1 is true and proposition w3 is true and proposition w4 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g1 is true if proposition f1 is true. Proposition g2 is true if proposition f2 is true. Proposition w3 is true if proposition v3 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition v1 is true and proposition w2 is true and proposition bad is not true. Proposition v6 is true if proposition w6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition w0 is true and proposition w3 is true and proposition w5 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition v4 is true if proposition w4 is not true. Proposition t0 is true if proposition t1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition s2 is true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition v5 is true and proposition v4 is true and proposition w6 is true and proposition bad is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i1-none::none", "rec_id": "hv3-control_n8-i1", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 49, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 48, "prolog_inferences": null, "n_stable_models": 49}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 2, "n_filler": 9, "variant_seed": 41399}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition f3 is true. Proposition f7 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition f8 is true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition v5 is true if proposition w5 is not true. Proposition g0 is true if proposition f0 is true. Proposition t1 is true if proposition t2 is true. Proposition v7 is true if proposition w7 is not true. Proposition g5 is true if proposition f5 is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition g8 is true if proposition f8 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition f2 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition f6 is true. Proposition f5 is true. Proposition v6 is true if proposition w6 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g1 is true if proposition f1 is true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition f4 is true. Proposition t2 is true if proposition t3 is true. Proposition f0 is true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition g4 is true if proposition f4 is true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v1 is true if proposition w1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i1-closed_world::closed_world", "rec_id": "hv3-control_n8-i1", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 49, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 48, "prolog_inferences": null, "n_stable_models": 49}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 2, "n_filler": 9, "variant_seed": 41399}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition f3 is true. Proposition f7 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition f8 is true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition v5 is true if proposition w5 is not true. Proposition g0 is true if proposition f0 is true. Proposition t1 is true if proposition t2 is true. Proposition v7 is true if proposition w7 is not true. Proposition g5 is true if proposition f5 is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition g8 is true if proposition f8 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition f2 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition f6 is true. Proposition f5 is true. Proposition v6 is true if proposition w6 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g1 is true if proposition f1 is true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition f4 is true. Proposition t2 is true if proposition t3 is true. Proposition f0 is true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition g4 is true if proposition f4 is true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v1 is true if proposition w1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i1-cred::cred", "rec_id": "hv3-control_n8-i1", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 49, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 48, "prolog_inferences": null, "n_stable_models": 49}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 2, "n_filler": 9, "variant_seed": 41399}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition f3 is true. Proposition f7 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition f8 is true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition v5 is true if proposition w5 is not true. Proposition g0 is true if proposition f0 is true. Proposition t1 is true if proposition t2 is true. Proposition v7 is true if proposition w7 is not true. Proposition g5 is true if proposition f5 is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition g8 is true if proposition f8 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition f2 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition f6 is true. Proposition f5 is true. Proposition v6 is true if proposition w6 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g1 is true if proposition f1 is true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition f4 is true. Proposition t2 is true if proposition t3 is true. Proposition f0 is true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition g4 is true if proposition f4 is true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v1 is true if proposition w1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i1-skept::skept", "rec_id": "hv3-control_n8-i1", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 49, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 48, "prolog_inferences": null, "n_stable_models": 49}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 2, "n_filler": 9, "variant_seed": 41399}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition f3 is true. Proposition f7 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition f8 is true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition v5 is true if proposition w5 is not true. Proposition g0 is true if proposition f0 is true. Proposition t1 is true if proposition t2 is true. Proposition v7 is true if proposition w7 is not true. Proposition g5 is true if proposition f5 is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition g8 is true if proposition f8 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition f2 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition f6 is true. Proposition f5 is true. Proposition v6 is true if proposition w6 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g1 is true if proposition f1 is true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition f4 is true. Proposition t2 is true if proposition t3 is true. Proposition f0 is true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition g4 is true if proposition f4 is true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v1 is true if proposition w1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n8-i1-wfs::wfs", "rec_id": "hv3-control_n8-i1", "axis": "easy_pad", "difficulty": "control_n8", "hardness_kind": "control", "n_stable_models": 49, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 48, "prolog_inferences": null, "n_stable_models": 49}, "meta": {"family": "easy_pad", "n_vars": 8, "n_clauses": 14, "ratio": 1.8, "query": "q", "query_var": 7, "query_sign": true, "depth": 6, "width": 2, "n_filler": 9, "variant_seed": 41399}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition t4 is true if proposition t5 is true. Proposition bad is true if proposition w0 is true and proposition w4 is true and proposition v3 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition w7 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v2 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition f3 is true. Proposition f7 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v6 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition bad is true if proposition w6 is true and proposition w2 is true and proposition v5 is true and proposition bad is not true. Proposition t5 is true if proposition v7 is true. Proposition f8 is true. Proposition bad is true if proposition v3 is true and proposition w5 is true and proposition w0 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition v5 is true if proposition w5 is not true. Proposition g0 is true if proposition f0 is true. Proposition t1 is true if proposition t2 is true. Proposition v7 is true if proposition w7 is not true. Proposition g5 is true if proposition f5 is true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition w4 is true and proposition v3 is true and proposition w6 is true and proposition bad is not true. Proposition s1 is true. Proposition g8 is true if proposition f8 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition f2 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v4 is true and proposition w7 is true and proposition v2 is true and proposition bad is not true. Proposition f6 is true. Proposition f5 is true. Proposition v6 is true if proposition w6 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g1 is true if proposition f1 is true. Proposition bad is true if proposition w1 is true and proposition v2 is true and proposition v3 is true and proposition bad is not true. Proposition bad is true if proposition v4 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition bad is true if proposition v3 is true and proposition w7 is true and proposition v4 is true and proposition bad is not true. Proposition f4 is true. Proposition t2 is true if proposition t3 is true. Proposition f0 is true. Proposition t3 is true if proposition t4 is true. Proposition bad is true if proposition v5 is true and proposition w4 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition w5 is true if proposition v5 is not true. Proposition v0 is true if proposition w0 is not true. Proposition g4 is true if proposition f4 is true. Proposition w1 is true if proposition v1 is not true. Proposition bad is true if proposition v5 is true and proposition w7 is true and proposition v3 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v1 is true if proposition w1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i0-none::none", "rec_id": "hv3-control_n14-i0", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 704, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 703, "prolog_inferences": null, "n_stable_models": 704}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 8, "query_sign": true, "depth": 0, "width": 3, "n_filler": 16, "variant_seed": 55795}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition s1 is true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition f0 is true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition f14 is true. Proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition v9 is true and proposition bad is not true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition g2 is true if proposition f2 is true. Proposition w7 is true if proposition v7 is not true. Proposition f13 is true. Proposition w6 is true if proposition v6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition g10 is true if proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition f4 is true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition s2 is true. Proposition w12 is true if proposition v12 is not true. Proposition f8 is true. Proposition g9 is true if proposition f9 is true. Proposition g11 is true if proposition f11 is true. Proposition f3 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition g1 is true if proposition f1 is true. Proposition w8 is true if proposition v8 is not true. Proposition f9 is true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition f12 is true. Proposition f1 is true. Proposition s0 is true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition f2 is true. Proposition f7 is true. Proposition bad is true if proposition v13 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition f15 is true. Proposition w13 is true if proposition v13 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v4 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition f11 is true. Proposition g8 is true if proposition f8 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition q is true if proposition v8 is true and proposition wide is true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition f6 is true. Proposition g7 is true if proposition f7 is true. Proposition g13 is true if proposition f13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v3 is true and proposition bad is not true. Proposition f10 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i0-closed_world::closed_world", "rec_id": "hv3-control_n14-i0", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 704, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 703, "prolog_inferences": null, "n_stable_models": 704}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 8, "query_sign": true, "depth": 0, "width": 3, "n_filler": 16, "variant_seed": 55795}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition s1 is true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition f0 is true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition f14 is true. Proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition v9 is true and proposition bad is not true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition g2 is true if proposition f2 is true. Proposition w7 is true if proposition v7 is not true. Proposition f13 is true. Proposition w6 is true if proposition v6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition g10 is true if proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition f4 is true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition s2 is true. Proposition w12 is true if proposition v12 is not true. Proposition f8 is true. Proposition g9 is true if proposition f9 is true. Proposition g11 is true if proposition f11 is true. Proposition f3 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition g1 is true if proposition f1 is true. Proposition w8 is true if proposition v8 is not true. Proposition f9 is true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition f12 is true. Proposition f1 is true. Proposition s0 is true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition f2 is true. Proposition f7 is true. Proposition bad is true if proposition v13 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition f15 is true. Proposition w13 is true if proposition v13 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v4 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition f11 is true. Proposition g8 is true if proposition f8 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition q is true if proposition v8 is true and proposition wide is true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition f6 is true. Proposition g7 is true if proposition f7 is true. Proposition g13 is true if proposition f13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v3 is true and proposition bad is not true. Proposition f10 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i0-cred::cred", "rec_id": "hv3-control_n14-i0", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 704, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 703, "prolog_inferences": null, "n_stable_models": 704}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 8, "query_sign": true, "depth": 0, "width": 3, "n_filler": 16, "variant_seed": 55795}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition s1 is true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition f0 is true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition f14 is true. Proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition v9 is true and proposition bad is not true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition g2 is true if proposition f2 is true. Proposition w7 is true if proposition v7 is not true. Proposition f13 is true. Proposition w6 is true if proposition v6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition g10 is true if proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition f4 is true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition s2 is true. Proposition w12 is true if proposition v12 is not true. Proposition f8 is true. Proposition g9 is true if proposition f9 is true. Proposition g11 is true if proposition f11 is true. Proposition f3 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition g1 is true if proposition f1 is true. Proposition w8 is true if proposition v8 is not true. Proposition f9 is true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition f12 is true. Proposition f1 is true. Proposition s0 is true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition f2 is true. Proposition f7 is true. Proposition bad is true if proposition v13 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition f15 is true. Proposition w13 is true if proposition v13 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v4 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition f11 is true. Proposition g8 is true if proposition f8 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition q is true if proposition v8 is true and proposition wide is true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition f6 is true. Proposition g7 is true if proposition f7 is true. Proposition g13 is true if proposition f13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v3 is true and proposition bad is not true. Proposition f10 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i0-skept::skept", "rec_id": "hv3-control_n14-i0", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 704, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 703, "prolog_inferences": null, "n_stable_models": 704}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 8, "query_sign": true, "depth": 0, "width": 3, "n_filler": 16, "variant_seed": 55795}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition s1 is true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition f0 is true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition f14 is true. Proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition v9 is true and proposition bad is not true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition g2 is true if proposition f2 is true. Proposition w7 is true if proposition v7 is not true. Proposition f13 is true. Proposition w6 is true if proposition v6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition g10 is true if proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition f4 is true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition s2 is true. Proposition w12 is true if proposition v12 is not true. Proposition f8 is true. Proposition g9 is true if proposition f9 is true. Proposition g11 is true if proposition f11 is true. Proposition f3 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition g1 is true if proposition f1 is true. Proposition w8 is true if proposition v8 is not true. Proposition f9 is true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition f12 is true. Proposition f1 is true. Proposition s0 is true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition f2 is true. Proposition f7 is true. Proposition bad is true if proposition v13 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition f15 is true. Proposition w13 is true if proposition v13 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v4 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition f11 is true. Proposition g8 is true if proposition f8 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition q is true if proposition v8 is true and proposition wide is true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition f6 is true. Proposition g7 is true if proposition f7 is true. Proposition g13 is true if proposition f13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v3 is true and proposition bad is not true. Proposition f10 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i0-wfs::wfs", "rec_id": "hv3-control_n14-i0", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 704, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 703, "prolog_inferences": null, "n_stable_models": 704}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 8, "query_sign": true, "depth": 0, "width": 3, "n_filler": 16, "variant_seed": 55795}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition s1 is true. Proposition bad is true if proposition v11 is true and proposition v3 is true and proposition w7 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition v7 is true and proposition v0 is true and proposition bad is not true. Proposition f0 is true. Proposition bad is true if proposition w7 is true and proposition w5 is true and proposition w9 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v3 is true and proposition v0 is true and proposition w11 is true and proposition bad is not true. Proposition bad is true if proposition w3 is true and proposition w7 is true and proposition w13 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition f14 is true. Proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition v6 is true and proposition v11 is true and proposition bad is not true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition v7 is true and proposition w1 is true and proposition w4 is true and proposition bad is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w11 is true and proposition w1 is true and proposition v9 is true and proposition bad is not true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition g2 is true if proposition f2 is true. Proposition w7 is true if proposition v7 is not true. Proposition f13 is true. Proposition w6 is true if proposition v6 is not true. Proposition w2 is true if proposition v2 is not true. Proposition g10 is true if proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition f4 is true. Proposition bad is true if proposition v4 is true and proposition v6 is true and proposition v10 is true and proposition bad is not true. Proposition bad is true if proposition v11 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition v0 is true and proposition w12 is true and proposition v1 is true and proposition bad is not true. Proposition w9 is true if proposition v9 is not true. Proposition s2 is true. Proposition w12 is true if proposition v12 is not true. Proposition f8 is true. Proposition g9 is true if proposition f9 is true. Proposition g11 is true if proposition f11 is true. Proposition f3 is true. Proposition w4 is true if proposition v4 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w8 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition g1 is true if proposition f1 is true. Proposition w8 is true if proposition v8 is not true. Proposition f9 is true. Proposition bad is true if proposition v12 is true and proposition w0 is true and proposition v5 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition bad is true if proposition v2 is true and proposition v6 is true and proposition v13 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition f12 is true. Proposition f1 is true. Proposition s0 is true. Proposition v11 is true if proposition w11 is not true. Proposition v10 is true if proposition w10 is not true. Proposition f2 is true. Proposition f7 is true. Proposition bad is true if proposition v13 is true and proposition v9 is true and proposition v12 is true and proposition bad is not true. Proposition w1 is true if proposition v1 is not true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w4 is true and proposition bad is not true. Proposition v13 is true if proposition w13 is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition w4 is true and proposition w12 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v11 is true and proposition bad is not true. Proposition f15 is true. Proposition w13 is true if proposition v13 is not true. Proposition v2 is true if proposition w2 is not true. Proposition bad is true if proposition v4 is true and proposition w13 is true and proposition v0 is true and proposition bad is not true. Proposition v5 is true if proposition w5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition bad is true if proposition w10 is true and proposition v6 is true and proposition w7 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition f11 is true. Proposition g8 is true if proposition f8 is true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition v5 is true and proposition w13 is true and proposition w1 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition q is true if proposition v8 is true and proposition wide is true. Proposition bad is true if proposition v12 is true and proposition w4 is true and proposition w7 is true and proposition bad is not true. Proposition f6 is true. Proposition g7 is true if proposition f7 is true. Proposition g13 is true if proposition f13 is true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v8 is true and proposition v2 is true and proposition v11 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v12 is true if proposition w12 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v5 is true and proposition w8 is true and proposition v3 is true and proposition bad is not true. Proposition f10 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i1-none::none", "rec_id": "hv3-control_n14-i1", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 987, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 986, "prolog_inferences": null, "n_stable_models": 987}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 0, "n_filler": 16, "variant_seed": 55798}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition g1 is true if proposition f1 is true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition f9 is true. Proposition t1 is true if proposition w9 is true. Proposition f7 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition f2 is true. Proposition f15 is true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition f3 is true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v1 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition f0 is true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition g2 is true if proposition f2 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition f10 is true. Proposition w13 is true if proposition v13 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition f6 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v1 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition f13 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition w5 is true and proposition bad is not true. Proposition f5 is true. Proposition f8 is true. Proposition g12 is true if proposition f12 is true. Proposition g3 is true if proposition f3 is true. Proposition v12 is true if proposition w12 is not true. Proposition f14 is true. Proposition f12 is true. Proposition v7 is true if proposition w7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v9 is true if proposition w9 is not true. Proposition g11 is true if proposition f11 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w11 is true and proposition bad is not true. Proposition f11 is true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition f4 is true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition g13 is true if proposition f13 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition f1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i1-closed_world::closed_world", "rec_id": "hv3-control_n14-i1", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 987, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 986, "prolog_inferences": null, "n_stable_models": 987}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 0, "n_filler": 16, "variant_seed": 55798}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition g1 is true if proposition f1 is true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition f9 is true. Proposition t1 is true if proposition w9 is true. Proposition f7 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition f2 is true. Proposition f15 is true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition f3 is true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v1 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition f0 is true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition g2 is true if proposition f2 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition f10 is true. Proposition w13 is true if proposition v13 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition f6 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v1 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition f13 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition w5 is true and proposition bad is not true. Proposition f5 is true. Proposition f8 is true. Proposition g12 is true if proposition f12 is true. Proposition g3 is true if proposition f3 is true. Proposition v12 is true if proposition w12 is not true. Proposition f14 is true. Proposition f12 is true. Proposition v7 is true if proposition w7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v9 is true if proposition w9 is not true. Proposition g11 is true if proposition f11 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w11 is true and proposition bad is not true. Proposition f11 is true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition f4 is true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition g13 is true if proposition f13 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition f1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i1-cred::cred", "rec_id": "hv3-control_n14-i1", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 987, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 986, "prolog_inferences": null, "n_stable_models": 987}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 0, "n_filler": 16, "variant_seed": 55798}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition g1 is true if proposition f1 is true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition f9 is true. Proposition t1 is true if proposition w9 is true. Proposition f7 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition f2 is true. Proposition f15 is true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition f3 is true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v1 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition f0 is true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition g2 is true if proposition f2 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition f10 is true. Proposition w13 is true if proposition v13 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition f6 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v1 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition f13 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition w5 is true and proposition bad is not true. Proposition f5 is true. Proposition f8 is true. Proposition g12 is true if proposition f12 is true. Proposition g3 is true if proposition f3 is true. Proposition v12 is true if proposition w12 is not true. Proposition f14 is true. Proposition f12 is true. Proposition v7 is true if proposition w7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v9 is true if proposition w9 is not true. Proposition g11 is true if proposition f11 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w11 is true and proposition bad is not true. Proposition f11 is true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition f4 is true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition g13 is true if proposition f13 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition f1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i1-skept::skept", "rec_id": "hv3-control_n14-i1", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 987, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 986, "prolog_inferences": null, "n_stable_models": 987}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 0, "n_filler": 16, "variant_seed": 55798}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition g1 is true if proposition f1 is true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition f9 is true. Proposition t1 is true if proposition w9 is true. Proposition f7 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition f2 is true. Proposition f15 is true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition f3 is true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v1 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition f0 is true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition g2 is true if proposition f2 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition f10 is true. Proposition w13 is true if proposition v13 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition f6 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v1 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition f13 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition w5 is true and proposition bad is not true. Proposition f5 is true. Proposition f8 is true. Proposition g12 is true if proposition f12 is true. Proposition g3 is true if proposition f3 is true. Proposition v12 is true if proposition w12 is not true. Proposition f14 is true. Proposition f12 is true. Proposition v7 is true if proposition w7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v9 is true if proposition w9 is not true. Proposition g11 is true if proposition f11 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w11 is true and proposition bad is not true. Proposition f11 is true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition f4 is true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition g13 is true if proposition f13 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition f1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n14-i1-wfs::wfs", "rec_id": "hv3-control_n14-i1", "axis": "easy_pad", "difficulty": "control_n14", "hardness_kind": "control", "n_stable_models": 987, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 986, "prolog_inferences": null, "n_stable_models": 987}, "meta": {"family": "easy_pad", "n_vars": 14, "n_clauses": 25, "ratio": 1.8, "query": "q", "query_var": 9, "query_sign": false, "depth": 2, "width": 0, "n_filler": 16, "variant_seed": 55798}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition v4 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition w7 is true if proposition v7 is not true. Proposition g1 is true if proposition f1 is true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v11 is true and proposition v9 is true and proposition v4 is true and proposition bad is not true. Proposition f9 is true. Proposition t1 is true if proposition w9 is true. Proposition f7 is true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition v8 is true and proposition w7 is true and proposition w4 is true and proposition bad is not true. Proposition f2 is true. Proposition f15 is true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition v6 is true and proposition v7 is true and proposition w3 is true and proposition bad is not true. Proposition f3 is true. Proposition bad is true if proposition w12 is true and proposition w13 is true and proposition w10 is true and proposition bad is not true. Proposition v2 is true if proposition w2 is not true. Proposition g0 is true if proposition f0 is true. Proposition bad is true if proposition w4 is true and proposition w13 is true and proposition v8 is true and proposition bad is not true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition v1 is true and proposition v9 is true and proposition w0 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition w3 is true and proposition w6 is true and proposition v4 is true and proposition bad is not true. Proposition w5 is true if proposition v5 is not true. Proposition w8 is true if proposition v8 is not true. Proposition f0 is true. Proposition bad is true if proposition w3 is true and proposition v8 is true and proposition v7 is true and proposition bad is not true. Proposition g7 is true if proposition f7 is true. Proposition bad is true if proposition w5 is true and proposition w8 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w10 is true and proposition w8 is true and proposition w11 is true and proposition bad is not true. Proposition g15 is true if proposition f15 is true. Proposition g4 is true if proposition f4 is true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w2 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition v8 is true and proposition v12 is true and proposition w6 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition g2 is true if proposition f2 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w10 is true and proposition w12 is true and proposition v11 is true and proposition bad is not true. Proposition f10 is true. Proposition w13 is true if proposition v13 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v9 is true and proposition v5 is true and proposition v3 is true and proposition bad is not true. Proposition f6 is true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition v1 is true and proposition w2 is true and proposition w6 is true and proposition bad is not true. Proposition etrue is true. Proposition f13 is true. Proposition v8 is true if proposition w8 is not true. Proposition bad is true if proposition w13 is true and proposition w6 is true and proposition w9 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w1 is true and proposition w5 is true and proposition bad is not true. Proposition f5 is true. Proposition f8 is true. Proposition g12 is true if proposition f12 is true. Proposition g3 is true if proposition f3 is true. Proposition v12 is true if proposition w12 is not true. Proposition f14 is true. Proposition f12 is true. Proposition v7 is true if proposition w7 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v13 is true if proposition w13 is not true. Proposition v9 is true if proposition w9 is not true. Proposition g11 is true if proposition f11 is true. Proposition v5 is true if proposition w5 is not true. Proposition bad is true if proposition v7 is true and proposition v12 is true and proposition w11 is true and proposition bad is not true. Proposition f11 is true. Proposition bad is true if proposition w3 is true and proposition v11 is true and proposition w4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w7 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g14 is true if proposition f14 is true. Proposition w10 is true if proposition v10 is not true. Proposition w3 is true if proposition v3 is not true. Proposition g5 is true if proposition f5 is true. Proposition f4 is true. Proposition bad is true if proposition v12 is true and proposition w11 is true and proposition w5 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition bad is true if proposition w10 is true and proposition w6 is true and proposition v5 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition g13 is true if proposition f13 is true. Proposition bad is true if proposition w6 is true and proposition v5 is true and proposition w0 is true and proposition bad is not true. Proposition w6 is true if proposition v6 is not true. Proposition v4 is true if proposition w4 is not true. Proposition bad is true if proposition w8 is true and proposition w11 is true and proposition v6 is true and proposition bad is not true. Proposition f1 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i0-none::none", "rec_id": "hv3-control_n22-i0", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 18484, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 18483, "prolog_inferences": null, "n_stable_models": 18484}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 15, "query_sign": true, "depth": 2, "width": 3, "n_filler": 25, "variant_seed": 88073}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition f15 is true. Proposition v6 is true if proposition w6 is not true. Proposition w9 is true if proposition v9 is not true. Proposition f5 is true. Proposition g23 is true if proposition f23 is true. Proposition g21 is true if proposition f21 is true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition f18 is true. Proposition f12 is true. Proposition f20 is true. Proposition w8 is true if proposition v8 is not true. Proposition g19 is true if proposition f19 is true. Proposition f0 is true. Proposition f17 is true. Proposition g20 is true if proposition f20 is true. Proposition f14 is true. Proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition g22 is true if proposition f22 is true. Proposition g7 is true if proposition f7 is true. Proposition f22 is true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition w21 is true and proposition bad is not true. Proposition f3 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition f21 is true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v14 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v17 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w17 is true and proposition v13 is true and proposition bad is not true. Proposition f9 is true. Proposition v21 is true if proposition w21 is not true. Proposition w11 is true if proposition v11 is not true. Proposition g3 is true if proposition f3 is true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v12 is true if proposition w12 is not true. Proposition g14 is true if proposition f14 is true. Proposition v16 is true if proposition w16 is not true. Proposition w14 is true if proposition v14 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w20 is true and proposition w13 is true and proposition v21 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition w12 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition s2 is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w19 is true and proposition w15 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition f19 is true. Proposition g5 is true if proposition f5 is true. Proposition v20 is true if proposition w20 is not true. Proposition v18 is true if proposition w18 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v21 is true and proposition w19 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v7 is true and proposition bad is not true. Proposition f4 is true. Proposition s0 is true. Proposition f2 is true. Proposition w20 is true if proposition v20 is not true. Proposition g1 is true if proposition f1 is true. Proposition f11 is true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition t1 is true if proposition v15 is true. Proposition w17 is true if proposition v17 is not true. Proposition g0 is true if proposition f0 is true. Proposition f23 is true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition w10 is true if proposition v10 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition w9 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g16 is true if proposition f16 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v12 is true and proposition v14 is true and proposition w7 is true and proposition bad is not true. Proposition f24 is true. Proposition v2 is true if proposition w2 is not true. Proposition f7 is true. Proposition f13 is true. Proposition bad is true if proposition w11 is true and proposition w9 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition g17 is true if proposition f17 is true. Proposition g4 is true if proposition f4 is true. Proposition f8 is true. Proposition w12 is true if proposition v12 is not true. Proposition f16 is true. Proposition f6 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v21 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition v11 is true and proposition v16 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w19 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v16 is true and proposition v13 is true and proposition v3 is true and proposition bad is not true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition w18 is true and proposition w14 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition g13 is true if proposition f13 is true. Proposition w1 is true if proposition v1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i0-closed_world::closed_world", "rec_id": "hv3-control_n22-i0", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 18484, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 18483, "prolog_inferences": null, "n_stable_models": 18484}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 15, "query_sign": true, "depth": 2, "width": 3, "n_filler": 25, "variant_seed": 88073}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition f15 is true. Proposition v6 is true if proposition w6 is not true. Proposition w9 is true if proposition v9 is not true. Proposition f5 is true. Proposition g23 is true if proposition f23 is true. Proposition g21 is true if proposition f21 is true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition f18 is true. Proposition f12 is true. Proposition f20 is true. Proposition w8 is true if proposition v8 is not true. Proposition g19 is true if proposition f19 is true. Proposition f0 is true. Proposition f17 is true. Proposition g20 is true if proposition f20 is true. Proposition f14 is true. Proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition g22 is true if proposition f22 is true. Proposition g7 is true if proposition f7 is true. Proposition f22 is true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition w21 is true and proposition bad is not true. Proposition f3 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition f21 is true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v14 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v17 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w17 is true and proposition v13 is true and proposition bad is not true. Proposition f9 is true. Proposition v21 is true if proposition w21 is not true. Proposition w11 is true if proposition v11 is not true. Proposition g3 is true if proposition f3 is true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v12 is true if proposition w12 is not true. Proposition g14 is true if proposition f14 is true. Proposition v16 is true if proposition w16 is not true. Proposition w14 is true if proposition v14 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w20 is true and proposition w13 is true and proposition v21 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition w12 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition s2 is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w19 is true and proposition w15 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition f19 is true. Proposition g5 is true if proposition f5 is true. Proposition v20 is true if proposition w20 is not true. Proposition v18 is true if proposition w18 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v21 is true and proposition w19 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v7 is true and proposition bad is not true. Proposition f4 is true. Proposition s0 is true. Proposition f2 is true. Proposition w20 is true if proposition v20 is not true. Proposition g1 is true if proposition f1 is true. Proposition f11 is true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition t1 is true if proposition v15 is true. Proposition w17 is true if proposition v17 is not true. Proposition g0 is true if proposition f0 is true. Proposition f23 is true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition w10 is true if proposition v10 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition w9 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g16 is true if proposition f16 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v12 is true and proposition v14 is true and proposition w7 is true and proposition bad is not true. Proposition f24 is true. Proposition v2 is true if proposition w2 is not true. Proposition f7 is true. Proposition f13 is true. Proposition bad is true if proposition w11 is true and proposition w9 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition g17 is true if proposition f17 is true. Proposition g4 is true if proposition f4 is true. Proposition f8 is true. Proposition w12 is true if proposition v12 is not true. Proposition f16 is true. Proposition f6 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v21 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition v11 is true and proposition v16 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w19 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v16 is true and proposition v13 is true and proposition v3 is true and proposition bad is not true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition w18 is true and proposition w14 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition g13 is true if proposition f13 is true. Proposition w1 is true if proposition v1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i0-cred::cred", "rec_id": "hv3-control_n22-i0", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 18484, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 18483, "prolog_inferences": null, "n_stable_models": 18484}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 15, "query_sign": true, "depth": 2, "width": 3, "n_filler": 25, "variant_seed": 88073}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition f15 is true. Proposition v6 is true if proposition w6 is not true. Proposition w9 is true if proposition v9 is not true. Proposition f5 is true. Proposition g23 is true if proposition f23 is true. Proposition g21 is true if proposition f21 is true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition f18 is true. Proposition f12 is true. Proposition f20 is true. Proposition w8 is true if proposition v8 is not true. Proposition g19 is true if proposition f19 is true. Proposition f0 is true. Proposition f17 is true. Proposition g20 is true if proposition f20 is true. Proposition f14 is true. Proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition g22 is true if proposition f22 is true. Proposition g7 is true if proposition f7 is true. Proposition f22 is true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition w21 is true and proposition bad is not true. Proposition f3 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition f21 is true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v14 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v17 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w17 is true and proposition v13 is true and proposition bad is not true. Proposition f9 is true. Proposition v21 is true if proposition w21 is not true. Proposition w11 is true if proposition v11 is not true. Proposition g3 is true if proposition f3 is true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v12 is true if proposition w12 is not true. Proposition g14 is true if proposition f14 is true. Proposition v16 is true if proposition w16 is not true. Proposition w14 is true if proposition v14 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w20 is true and proposition w13 is true and proposition v21 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition w12 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition s2 is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w19 is true and proposition w15 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition f19 is true. Proposition g5 is true if proposition f5 is true. Proposition v20 is true if proposition w20 is not true. Proposition v18 is true if proposition w18 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v21 is true and proposition w19 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v7 is true and proposition bad is not true. Proposition f4 is true. Proposition s0 is true. Proposition f2 is true. Proposition w20 is true if proposition v20 is not true. Proposition g1 is true if proposition f1 is true. Proposition f11 is true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition t1 is true if proposition v15 is true. Proposition w17 is true if proposition v17 is not true. Proposition g0 is true if proposition f0 is true. Proposition f23 is true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition w10 is true if proposition v10 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition w9 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g16 is true if proposition f16 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v12 is true and proposition v14 is true and proposition w7 is true and proposition bad is not true. Proposition f24 is true. Proposition v2 is true if proposition w2 is not true. Proposition f7 is true. Proposition f13 is true. Proposition bad is true if proposition w11 is true and proposition w9 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition g17 is true if proposition f17 is true. Proposition g4 is true if proposition f4 is true. Proposition f8 is true. Proposition w12 is true if proposition v12 is not true. Proposition f16 is true. Proposition f6 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v21 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition v11 is true and proposition v16 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w19 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v16 is true and proposition v13 is true and proposition v3 is true and proposition bad is not true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition w18 is true and proposition w14 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition g13 is true if proposition f13 is true. Proposition w1 is true if proposition v1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i0-skept::skept", "rec_id": "hv3-control_n22-i0", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 18484, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 18483, "prolog_inferences": null, "n_stable_models": 18484}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 15, "query_sign": true, "depth": 2, "width": 3, "n_filler": 25, "variant_seed": 88073}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition f15 is true. Proposition v6 is true if proposition w6 is not true. Proposition w9 is true if proposition v9 is not true. Proposition f5 is true. Proposition g23 is true if proposition f23 is true. Proposition g21 is true if proposition f21 is true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition f18 is true. Proposition f12 is true. Proposition f20 is true. Proposition w8 is true if proposition v8 is not true. Proposition g19 is true if proposition f19 is true. Proposition f0 is true. Proposition f17 is true. Proposition g20 is true if proposition f20 is true. Proposition f14 is true. Proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition g22 is true if proposition f22 is true. Proposition g7 is true if proposition f7 is true. Proposition f22 is true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition w21 is true and proposition bad is not true. Proposition f3 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition f21 is true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v14 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v17 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w17 is true and proposition v13 is true and proposition bad is not true. Proposition f9 is true. Proposition v21 is true if proposition w21 is not true. Proposition w11 is true if proposition v11 is not true. Proposition g3 is true if proposition f3 is true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v12 is true if proposition w12 is not true. Proposition g14 is true if proposition f14 is true. Proposition v16 is true if proposition w16 is not true. Proposition w14 is true if proposition v14 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w20 is true and proposition w13 is true and proposition v21 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition w12 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition s2 is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w19 is true and proposition w15 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition f19 is true. Proposition g5 is true if proposition f5 is true. Proposition v20 is true if proposition w20 is not true. Proposition v18 is true if proposition w18 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v21 is true and proposition w19 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v7 is true and proposition bad is not true. Proposition f4 is true. Proposition s0 is true. Proposition f2 is true. Proposition w20 is true if proposition v20 is not true. Proposition g1 is true if proposition f1 is true. Proposition f11 is true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition t1 is true if proposition v15 is true. Proposition w17 is true if proposition v17 is not true. Proposition g0 is true if proposition f0 is true. Proposition f23 is true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition w10 is true if proposition v10 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition w9 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g16 is true if proposition f16 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v12 is true and proposition v14 is true and proposition w7 is true and proposition bad is not true. Proposition f24 is true. Proposition v2 is true if proposition w2 is not true. Proposition f7 is true. Proposition f13 is true. Proposition bad is true if proposition w11 is true and proposition w9 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition g17 is true if proposition f17 is true. Proposition g4 is true if proposition f4 is true. Proposition f8 is true. Proposition w12 is true if proposition v12 is not true. Proposition f16 is true. Proposition f6 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v21 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition v11 is true and proposition v16 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w19 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v16 is true and proposition v13 is true and proposition v3 is true and proposition bad is not true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition w18 is true and proposition w14 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition g13 is true if proposition f13 is true. Proposition w1 is true if proposition v1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i0-wfs::wfs", "rec_id": "hv3-control_n22-i0", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 18484, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 18483, "prolog_inferences": null, "n_stable_models": 18484}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 15, "query_sign": true, "depth": 2, "width": 3, "n_filler": 25, "variant_seed": 88073}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition f15 is true. Proposition v6 is true if proposition w6 is not true. Proposition w9 is true if proposition v9 is not true. Proposition f5 is true. Proposition g23 is true if proposition f23 is true. Proposition g21 is true if proposition f21 is true. Proposition v7 is true if proposition w7 is not true. Proposition w16 is true if proposition v16 is not true. Proposition bad is true if proposition w6 is true and proposition w21 is true and proposition v13 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition w20 is true and proposition v18 is true and proposition bad is not true. Proposition w4 is true if proposition v4 is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v1 is true and proposition bad is not true. Proposition w2 is true if proposition v2 is not true. Proposition f18 is true. Proposition f12 is true. Proposition f20 is true. Proposition w8 is true if proposition v8 is not true. Proposition g19 is true if proposition f19 is true. Proposition f0 is true. Proposition f17 is true. Proposition g20 is true if proposition f20 is true. Proposition f14 is true. Proposition f10 is true. Proposition g12 is true if proposition f12 is true. Proposition g22 is true if proposition f22 is true. Proposition g7 is true if proposition f7 is true. Proposition f22 is true. Proposition w19 is true if proposition v19 is not true. Proposition bad is true if proposition w16 is true and proposition v2 is true and proposition w21 is true and proposition bad is not true. Proposition f3 is true. Proposition v0 is true if proposition w0 is not true. Proposition bad is true if proposition w15 is true and proposition v17 is true and proposition w16 is true and proposition bad is not true. Proposition bad is true if proposition w15 is true and proposition v10 is true and proposition v5 is true and proposition bad is not true. Proposition bad is true if proposition w4 is true and proposition v11 is true and proposition v10 is true and proposition bad is not true. Proposition f21 is true. Proposition bad is true if proposition w13 is true and proposition w12 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition v14 is true and proposition w10 is true and proposition bad is not true. Proposition bad is true if proposition w0 is true and proposition w7 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition v3 is true and proposition w15 is true and proposition bad is not true. Proposition bad is true if proposition w5 is true and proposition w13 is true and proposition v17 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition v5 is true if proposition w5 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v7 is true and proposition v6 is true and proposition w1 is true and proposition bad is not true. Proposition bad is true if proposition w14 is true and proposition w17 is true and proposition v13 is true and proposition bad is not true. Proposition f9 is true. Proposition v21 is true if proposition w21 is not true. Proposition w11 is true if proposition v11 is not true. Proposition g3 is true if proposition f3 is true. Proposition g15 is true if proposition f15 is true. Proposition bad is true if proposition v4 is true and proposition w5 is true and proposition v12 is true and proposition bad is not true. Proposition v15 is true if proposition w15 is not true. Proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition w14 is true and proposition v6 is true and proposition bad is not true. Proposition bad is true if proposition w13 is true and proposition w2 is true and proposition w21 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition bad is true if proposition v7 is true and proposition v2 is true and proposition v17 is true and proposition bad is not true. Proposition t0 is true if proposition t1 is true. Proposition v12 is true if proposition w12 is not true. Proposition g14 is true if proposition f14 is true. Proposition v16 is true if proposition w16 is not true. Proposition w14 is true if proposition v14 is not true. Proposition v17 is true if proposition w17 is not true. Proposition v10 is true if proposition w10 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition g6 is true if proposition f6 is true. Proposition bad is true if proposition w12 is true and proposition w18 is true and proposition v20 is true and proposition bad is not true. Proposition f1 is true. Proposition bad is true if proposition w20 is true and proposition w13 is true and proposition v21 is true and proposition bad is not true. Proposition v4 is true if proposition w4 is not true. Proposition v13 is true if proposition w13 is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition w12 is true and proposition w1 is true and proposition w8 is true and proposition bad is not true. Proposition v8 is true if proposition w8 is not true. Proposition s2 is true. Proposition bad is true if proposition v1 is true and proposition v4 is true and proposition w20 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition w18 is true if proposition v18 is not true. Proposition bad is true if proposition w16 is true and proposition w19 is true and proposition w15 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition v14 is true if proposition w14 is not true. Proposition f19 is true. Proposition g5 is true if proposition f5 is true. Proposition v20 is true if proposition w20 is not true. Proposition v18 is true if proposition w18 is not true. Proposition g8 is true if proposition f8 is true. Proposition bad is true if proposition v21 is true and proposition w19 is true and proposition v18 is true and proposition bad is not true. Proposition w0 is true if proposition v0 is not true. Proposition bad is true if proposition v11 is true and proposition w21 is true and proposition v7 is true and proposition bad is not true. Proposition f4 is true. Proposition s0 is true. Proposition f2 is true. Proposition w20 is true if proposition v20 is not true. Proposition g1 is true if proposition f1 is true. Proposition f11 is true. Proposition bad is true if proposition w6 is true and proposition w11 is true and proposition v3 is true and proposition bad is not true. Proposition t1 is true if proposition v15 is true. Proposition w17 is true if proposition v17 is not true. Proposition g0 is true if proposition f0 is true. Proposition f23 is true. Proposition bad is true if proposition w16 is true and proposition w17 is true and proposition w7 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition w10 is true if proposition v10 is not true. Proposition v9 is true if proposition w9 is not true. Proposition bad is true if proposition v9 is true and proposition v6 is true and proposition w18 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition v14 is true and proposition w9 is true and proposition bad is not true. Proposition g9 is true if proposition f9 is true. Proposition g16 is true if proposition f16 is true. Proposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition v12 is true and proposition v14 is true and proposition w7 is true and proposition bad is not true. Proposition f24 is true. Proposition v2 is true if proposition w2 is not true. Proposition f7 is true. Proposition f13 is true. Proposition bad is true if proposition w11 is true and proposition w9 is true and proposition v2 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition g17 is true if proposition f17 is true. Proposition g4 is true if proposition f4 is true. Proposition f8 is true. Proposition w12 is true if proposition v12 is not true. Proposition f16 is true. Proposition f6 is true. Proposition w6 is true if proposition v6 is not true. Proposition bad is true if proposition v2 is true and proposition v1 is true and proposition v21 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition bad is true if proposition v1 is true and proposition v11 is true and proposition w5 is true and proposition bad is not true. Proposition v11 is true if proposition w11 is not true. Proposition v19 is true if proposition w19 is not true. Proposition bad is true if proposition v6 is true and proposition v11 is true and proposition v16 is true and proposition bad is not true. Proposition s1 is true. Proposition bad is true if proposition v17 is true and proposition w4 is true and proposition w19 is true and proposition bad is not true. Proposition v1 is true if proposition w1 is not true. Proposition bad is true if proposition w13 is true and proposition w5 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition v2 is true and proposition v15 is true and proposition w0 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition bad is true if proposition v16 is true and proposition v13 is true and proposition v3 is true and proposition bad is not true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition w18 is true and proposition w14 is true and proposition v21 is true and proposition bad is not true. Proposition bad is true if proposition w21 is true and proposition v0 is true and proposition w14 is true and proposition bad is not true. Proposition g13 is true if proposition f13 is true. Proposition w1 is true if proposition v1 is not true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i1-none::none", "rec_id": "hv3-control_n22-i1", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 33287, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "none", "gold": null, "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 33286, "prolog_inferences": null, "n_stable_models": 33287}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 25, "variant_seed": 88092}, "prompt": "Answer using ordinary commonsense reasoning about the rules below.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition f19 is true. Proposition g9 is true if proposition f9 is true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w19 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition g16 is true if proposition f16 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition v20 is true if proposition w20 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w21 is true and proposition v16 is true and proposition w15 is true and proposition bad is not true. Proposition f8 is true. Proposition v14 is true if proposition w14 is not true. Proposition f3 is true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v15 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w4 is true if proposition v4 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w17 is true and proposition w14 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition g1 is true if proposition f1 is true. Proposition w14 is true if proposition v14 is not true. Proposition v18 is true if proposition w18 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v1 is true and proposition w19 is true and proposition w13 is true and proposition bad is not true. Proposition g19 is true if proposition f19 is true. Proposition bad is true if proposition w8 is true and proposition w16 is true and proposition w9 is true and proposition bad is not true. Proposition f22 is true. Proposition g0 is true if proposition f0 is true. Proposition g17 is true if proposition f17 is true. Proposition f17 is true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition v16 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition v0 is true if proposition w0 is not true. Proposition f15 is true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v15 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition f4 is true. Proposition w6 is true if proposition v6 is not true. Proposition t1 is true if proposition t2 is true. Proposition w2 is true if proposition v2 is not true. Proposition v12 is true if proposition w12 is not true. Proposition f12 is true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition v9 is true if proposition w9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v18 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g14 is true if proposition f14 is true. Proposition f20 is true. Proposition g12 is true if proposition f12 is true. Proposition v21 is true if proposition w21 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w20 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition g20 is true if proposition f20 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v9 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition f5 is true. Proposition f10 is true. Proposition f21 is true. Proposition g7 is true if proposition f7 is true. Proposition v1 is true if proposition w1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w10 is true if proposition v10 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition v10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition f0 is true. Proposition s1 is true. Proposition w18 is true if proposition v18 is not true. Proposition g21 is true if proposition f21 is true. Proposition f13 is true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition f6 is true. Proposition f24 is true. Proposition v13 is true if proposition w13 is not true. Proposition f11 is true. Proposition w19 is true if proposition v19 is not true. Proposition f16 is true. Proposition w1 is true if proposition v1 is not true. Proposition g13 is true if proposition f13 is true. Proposition f7 is true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition v12 is true and proposition bad is not true. Proposition f23 is true. Proposition g8 is true if proposition f8 is true. Proposition f14 is true. Proposition v2 is true if proposition w2 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w10 is true and proposition w16 is true and proposition bad is not true. Proposition g22 is true if proposition f22 is true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition g23 is true if proposition f23 is true. Proposition bad is true if proposition w18 is true and proposition w5 is true and proposition w8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition f18 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w16 is true and proposition v20 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w17 is true if proposition v17 is not true. Proposition g15 is true if proposition f15 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v14 is true and proposition v5 is true and proposition w21 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition f9 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition v11 is true if proposition w11 is not true. Proposition g6 is true if proposition f6 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i1-closed_world::closed_world", "rec_id": "hv3-control_n22-i1", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 33287, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "closed_world", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 33286, "prolog_inferences": null, "n_stable_models": 33287}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 25, "variant_seed": 88092}, "prompt": "Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition f19 is true. Proposition g9 is true if proposition f9 is true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w19 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition g16 is true if proposition f16 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition v20 is true if proposition w20 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w21 is true and proposition v16 is true and proposition w15 is true and proposition bad is not true. Proposition f8 is true. Proposition v14 is true if proposition w14 is not true. Proposition f3 is true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v15 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w4 is true if proposition v4 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w17 is true and proposition w14 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition g1 is true if proposition f1 is true. Proposition w14 is true if proposition v14 is not true. Proposition v18 is true if proposition w18 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v1 is true and proposition w19 is true and proposition w13 is true and proposition bad is not true. Proposition g19 is true if proposition f19 is true. Proposition bad is true if proposition w8 is true and proposition w16 is true and proposition w9 is true and proposition bad is not true. Proposition f22 is true. Proposition g0 is true if proposition f0 is true. Proposition g17 is true if proposition f17 is true. Proposition f17 is true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition v16 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition v0 is true if proposition w0 is not true. Proposition f15 is true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v15 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition f4 is true. Proposition w6 is true if proposition v6 is not true. Proposition t1 is true if proposition t2 is true. Proposition w2 is true if proposition v2 is not true. Proposition v12 is true if proposition w12 is not true. Proposition f12 is true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition v9 is true if proposition w9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v18 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g14 is true if proposition f14 is true. Proposition f20 is true. Proposition g12 is true if proposition f12 is true. Proposition v21 is true if proposition w21 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w20 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition g20 is true if proposition f20 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v9 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition f5 is true. Proposition f10 is true. Proposition f21 is true. Proposition g7 is true if proposition f7 is true. Proposition v1 is true if proposition w1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w10 is true if proposition v10 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition v10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition f0 is true. Proposition s1 is true. Proposition w18 is true if proposition v18 is not true. Proposition g21 is true if proposition f21 is true. Proposition f13 is true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition f6 is true. Proposition f24 is true. Proposition v13 is true if proposition w13 is not true. Proposition f11 is true. Proposition w19 is true if proposition v19 is not true. Proposition f16 is true. Proposition w1 is true if proposition v1 is not true. Proposition g13 is true if proposition f13 is true. Proposition f7 is true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition v12 is true and proposition bad is not true. Proposition f23 is true. Proposition g8 is true if proposition f8 is true. Proposition f14 is true. Proposition v2 is true if proposition w2 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w10 is true and proposition w16 is true and proposition bad is not true. Proposition g22 is true if proposition f22 is true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition g23 is true if proposition f23 is true. Proposition bad is true if proposition w18 is true and proposition w5 is true and proposition w8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition f18 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w16 is true and proposition v20 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w17 is true if proposition v17 is not true. Proposition g15 is true if proposition f15 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v14 is true and proposition v5 is true and proposition w21 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition f9 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition v11 is true if proposition w11 is not true. Proposition g6 is true if proposition f6 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i1-cred::cred", "rec_id": "hv3-control_n22-i1", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 33287, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "cred", "gold": "A", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 33286, "prolog_inferences": null, "n_stable_models": 33287}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 25, "variant_seed": 88092}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition f19 is true. Proposition g9 is true if proposition f9 is true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w19 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition g16 is true if proposition f16 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition v20 is true if proposition w20 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w21 is true and proposition v16 is true and proposition w15 is true and proposition bad is not true. Proposition f8 is true. Proposition v14 is true if proposition w14 is not true. Proposition f3 is true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v15 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w4 is true if proposition v4 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w17 is true and proposition w14 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition g1 is true if proposition f1 is true. Proposition w14 is true if proposition v14 is not true. Proposition v18 is true if proposition w18 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v1 is true and proposition w19 is true and proposition w13 is true and proposition bad is not true. Proposition g19 is true if proposition f19 is true. Proposition bad is true if proposition w8 is true and proposition w16 is true and proposition w9 is true and proposition bad is not true. Proposition f22 is true. Proposition g0 is true if proposition f0 is true. Proposition g17 is true if proposition f17 is true. Proposition f17 is true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition v16 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition v0 is true if proposition w0 is not true. Proposition f15 is true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v15 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition f4 is true. Proposition w6 is true if proposition v6 is not true. Proposition t1 is true if proposition t2 is true. Proposition w2 is true if proposition v2 is not true. Proposition v12 is true if proposition w12 is not true. Proposition f12 is true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition v9 is true if proposition w9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v18 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g14 is true if proposition f14 is true. Proposition f20 is true. Proposition g12 is true if proposition f12 is true. Proposition v21 is true if proposition w21 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w20 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition g20 is true if proposition f20 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v9 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition f5 is true. Proposition f10 is true. Proposition f21 is true. Proposition g7 is true if proposition f7 is true. Proposition v1 is true if proposition w1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w10 is true if proposition v10 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition v10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition f0 is true. Proposition s1 is true. Proposition w18 is true if proposition v18 is not true. Proposition g21 is true if proposition f21 is true. Proposition f13 is true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition f6 is true. Proposition f24 is true. Proposition v13 is true if proposition w13 is not true. Proposition f11 is true. Proposition w19 is true if proposition v19 is not true. Proposition f16 is true. Proposition w1 is true if proposition v1 is not true. Proposition g13 is true if proposition f13 is true. Proposition f7 is true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition v12 is true and proposition bad is not true. Proposition f23 is true. Proposition g8 is true if proposition f8 is true. Proposition f14 is true. Proposition v2 is true if proposition w2 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w10 is true and proposition w16 is true and proposition bad is not true. Proposition g22 is true if proposition f22 is true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition g23 is true if proposition f23 is true. Proposition bad is true if proposition w18 is true and proposition w5 is true and proposition w8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition f18 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w16 is true and proposition v20 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w17 is true if proposition v17 is not true. Proposition g15 is true if proposition f15 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v14 is true and proposition v5 is true and proposition w21 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition f9 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition v11 is true if proposition w11 is not true. Proposition g6 is true if proposition f6 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i1-skept::skept", "rec_id": "hv3-control_n22-i1", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 33287, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "skept", "gold": "B", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 33286, "prolog_inferences": null, "n_stable_models": 33287}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 25, "variant_seed": 88092}, "prompt": "Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition f19 is true. Proposition g9 is true if proposition f9 is true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w19 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition g16 is true if proposition f16 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition v20 is true if proposition w20 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w21 is true and proposition v16 is true and proposition w15 is true and proposition bad is not true. Proposition f8 is true. Proposition v14 is true if proposition w14 is not true. Proposition f3 is true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v15 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w4 is true if proposition v4 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w17 is true and proposition w14 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition g1 is true if proposition f1 is true. Proposition w14 is true if proposition v14 is not true. Proposition v18 is true if proposition w18 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v1 is true and proposition w19 is true and proposition w13 is true and proposition bad is not true. Proposition g19 is true if proposition f19 is true. Proposition bad is true if proposition w8 is true and proposition w16 is true and proposition w9 is true and proposition bad is not true. Proposition f22 is true. Proposition g0 is true if proposition f0 is true. Proposition g17 is true if proposition f17 is true. Proposition f17 is true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition v16 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition v0 is true if proposition w0 is not true. Proposition f15 is true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v15 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition f4 is true. Proposition w6 is true if proposition v6 is not true. Proposition t1 is true if proposition t2 is true. Proposition w2 is true if proposition v2 is not true. Proposition v12 is true if proposition w12 is not true. Proposition f12 is true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition v9 is true if proposition w9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v18 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g14 is true if proposition f14 is true. Proposition f20 is true. Proposition g12 is true if proposition f12 is true. Proposition v21 is true if proposition w21 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w20 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition g20 is true if proposition f20 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v9 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition f5 is true. Proposition f10 is true. Proposition f21 is true. Proposition g7 is true if proposition f7 is true. Proposition v1 is true if proposition w1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w10 is true if proposition v10 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition v10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition f0 is true. Proposition s1 is true. Proposition w18 is true if proposition v18 is not true. Proposition g21 is true if proposition f21 is true. Proposition f13 is true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition f6 is true. Proposition f24 is true. Proposition v13 is true if proposition w13 is not true. Proposition f11 is true. Proposition w19 is true if proposition v19 is not true. Proposition f16 is true. Proposition w1 is true if proposition v1 is not true. Proposition g13 is true if proposition f13 is true. Proposition f7 is true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition v12 is true and proposition bad is not true. Proposition f23 is true. Proposition g8 is true if proposition f8 is true. Proposition f14 is true. Proposition v2 is true if proposition w2 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w10 is true and proposition w16 is true and proposition bad is not true. Proposition g22 is true if proposition f22 is true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition g23 is true if proposition f23 is true. Proposition bad is true if proposition w18 is true and proposition w5 is true and proposition w8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition f18 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w16 is true and proposition v20 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w17 is true if proposition v17 is not true. Proposition g15 is true if proposition f15 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v14 is true and proposition v5 is true and proposition w21 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition f9 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition v11 is true if proposition w11 is not true. Proposition g6 is true if proposition f6 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}
{"id": "hv3-control_n22-i1-wfs::wfs", "rec_id": "hv3-control_n22-i1", "axis": "easy_pad", "difficulty": "control_n22", "hardness_kind": "control", "n_stable_models": 33287, "divergence_bin": "sig_TFuloop", "signature": "TFuloop", "cond": "wfs", "gold": "C", "labels": {"cred": "T", "skept": "F", "wfs": "u", "sldnf": "loop"}, "metrics": {"clingo_conflicts": 0, "clingo_choices": 33286, "prolog_inferences": null, "n_stable_models": 33287}, "meta": {"family": "easy_pad", "n_vars": 22, "n_clauses": 40, "ratio": 1.8, "query": "q", "query_var": 1, "query_sign": false, "depth": 4, "width": 2, "n_filler": 25, "variant_seed": 88092}, "prompt": "Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.\n\nRules:\nProposition w5 is true if proposition v5 is not true. Proposition bad is true if proposition w13 is true and proposition v0 is true and proposition w10 is true and proposition bad is not true. Proposition f19 is true. Proposition g9 is true if proposition f9 is true. Proposition bad is true if proposition v1 is true and proposition v6 is true and proposition w12 is true and proposition bad is not true. Proposition v7 is true if proposition w7 is not true. Proposition bad is true if proposition w19 is true and proposition w13 is true and proposition w2 is true and proposition bad is not true. Proposition bad is true if proposition w2 is true and proposition w15 is true and proposition w21 is true and proposition bad is not true. Proposition g11 is true if proposition f11 is true. Proposition g16 is true if proposition f16 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition v20 is true if proposition w20 is not true. Proposition w0 is true if proposition v0 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v16 is true if proposition w16 is not true. Proposition bad is true if proposition w21 is true and proposition v16 is true and proposition w15 is true and proposition bad is not true. Proposition f8 is true. Proposition v14 is true if proposition w14 is not true. Proposition f3 is true. Proposition bad is true if proposition w6 is true and proposition w7 is true and proposition w11 is true and proposition bad is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition bad is true if proposition v15 is true and proposition w10 is true and proposition v1 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition w17 is true and proposition v4 is true and proposition bad is not true. Proposition bad is true if proposition w6 is true and proposition w17 is true and proposition w11 is true and proposition bad is not true. Proposition v17 is true if proposition w17 is not true. Proposition w4 is true if proposition v4 is not true. Proposition v8 is true if proposition w8 is not true. Proposition v6 is true if proposition w6 is not true. Proposition bad is true if proposition w17 is true and proposition w14 is true and proposition v3 is true and proposition bad is not true. Proposition t3 is true if proposition w1 is true. Proposition g1 is true if proposition f1 is true. Proposition w14 is true if proposition v14 is not true. Proposition v18 is true if proposition w18 is not true. Proposition v10 is true if proposition w10 is not true. Proposition bad is true if proposition v1 is true and proposition w19 is true and proposition w13 is true and proposition bad is not true. Proposition g19 is true if proposition f19 is true. Proposition bad is true if proposition w8 is true and proposition w16 is true and proposition w9 is true and proposition bad is not true. Proposition f22 is true. Proposition g0 is true if proposition f0 is true. Proposition g17 is true if proposition f17 is true. Proposition f17 is true. Proposition bad is true if proposition w20 is true and proposition w7 is true and proposition v1 is true and proposition bad is not true. Proposition w13 is true if proposition v13 is not true. Proposition bad is true if proposition v10 is true and proposition v17 is true and proposition v16 is true and proposition bad is not true. Proposition g3 is true if proposition f3 is true. Proposition bad is true if proposition v6 is true and proposition v9 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w4 is true and proposition w17 is true and proposition bad is not true. Proposition bad is true if proposition v1 is true and proposition w10 is true and proposition v4 is true and proposition bad is not true. Proposition v19 is true if proposition w19 is not true. Proposition v0 is true if proposition w0 is not true. Proposition f15 is true. Proposition bad is true if proposition v6 is true and proposition w16 is true and proposition v15 is true and proposition bad is not true. Proposition g10 is true if proposition f10 is true. Proposition f4 is true. Proposition w6 is true if proposition v6 is not true. Proposition t1 is true if proposition t2 is true. Proposition w2 is true if proposition v2 is not true. Proposition v12 is true if proposition w12 is not true. Proposition f12 is true. Proposition bad is true if proposition v9 is true and proposition w18 is true and proposition w3 is true and proposition bad is not true. Proposition f1 is true. Proposition v9 is true if proposition w9 is not true. Proposition v4 is true if proposition w4 is not true. Proposition v15 is true if proposition w15 is not true. Proposition bad is true if proposition v18 is true and proposition w6 is true and proposition w5 is true and proposition bad is not true. Proposition f2 is true. Proposition g14 is true if proposition f14 is true. Proposition f20 is true. Proposition g12 is true if proposition f12 is true. Proposition v21 is true if proposition w21 is not true. Proposition w8 is true if proposition v8 is not true. Proposition bad is true if proposition w20 is true and proposition w8 is true and proposition v4 is true and proposition bad is not true. Proposition w3 is true if proposition v3 is not true. Proposition bad is true if proposition w6 is true and proposition v18 is true and proposition w13 is true and proposition bad is not true. Proposition g20 is true if proposition f20 is true. Proposition g4 is true if proposition f4 is true. Proposition bad is true if proposition v9 is true and proposition w15 is true and proposition w10 is true and proposition bad is not true. Proposition f5 is true. Proposition f10 is true. Proposition f21 is true. Proposition g7 is true if proposition f7 is true. Proposition v1 is true if proposition w1 is not true. Proposition t0 is true if proposition t1 is true. Proposition w10 is true if proposition v10 is not true. Proposition w20 is true if proposition v20 is not true. Proposition w9 is true if proposition v9 is not true. Proposition bad is true if proposition w2 is true and proposition v0 is true and proposition w4 is true and proposition bad is not true. Proposition g2 is true if proposition f2 is true. Proposition bad is true if proposition v10 is true and proposition v19 is true and proposition w0 is true and proposition bad is not true. Proposition w15 is true if proposition v15 is not true. Proposition f0 is true. Proposition s1 is true. Proposition w18 is true if proposition v18 is not true. Proposition g21 is true if proposition f21 is true. Proposition f13 is true. Proposition g24 is true if proposition f24 is true. Proposition bad is true if proposition v0 is true and proposition w6 is true and proposition v12 is true and proposition bad is not true. Proposition bad is true if proposition w8 is true and proposition w2 is true and proposition w17 is true and proposition bad is not true. Proposition w7 is true if proposition v7 is not true. Proposition f6 is true. Proposition f24 is true. Proposition v13 is true if proposition w13 is not true. Proposition f11 is true. Proposition w19 is true if proposition v19 is not true. Proposition f16 is true. Proposition w1 is true if proposition v1 is not true. Proposition g13 is true if proposition f13 is true. Proposition f7 is true. Proposition bad is true if proposition v20 is true and proposition v16 is true and proposition v12 is true and proposition bad is not true. Proposition f23 is true. Proposition g8 is true if proposition f8 is true. Proposition f14 is true. Proposition v2 is true if proposition w2 is not true. Proposition g18 is true if proposition f18 is true. Proposition bad is true if proposition v19 is true and proposition v17 is true and proposition v20 is true and proposition bad is not true. Proposition bad is true if proposition w7 is true and proposition v11 is true and proposition w13 is true and proposition bad is not true. Proposition bad is true if proposition v21 is true and proposition w10 is true and proposition w16 is true and proposition bad is not true. Proposition g22 is true if proposition f22 is true. Proposition bad is true if proposition v0 is true and proposition w13 is true and proposition v9 is true and proposition bad is not true. Proposition g23 is true if proposition f23 is true. Proposition bad is true if proposition w18 is true and proposition w5 is true and proposition w8 is true and proposition bad is not true. Proposition v3 is true if proposition w3 is not true. Proposition bad is true if proposition w5 is true and proposition v7 is true and proposition w12 is true and proposition bad is not true. Proposition f18 is true. Proposition g5 is true if proposition f5 is true. Proposition bad is true if proposition v20 is true and proposition v17 is true and proposition v11 is true and proposition bad is not true. Proposition w12 is true if proposition v12 is not true. Proposition bad is true if proposition w2 is true and proposition w1 is true and proposition w20 is true and proposition bad is not true. Proposition bad is true if proposition v19 is true and proposition w16 is true and proposition v20 is true and proposition bad is not true. Proposition w11 is true if proposition v11 is not true. Proposition w17 is true if proposition v17 is not true. Proposition g15 is true if proposition f15 is true. Proposition t2 is true if proposition t3 is true. Proposition bad is true if proposition v14 is true and proposition v5 is true and proposition w21 is true and proposition bad is not true. Proposition w21 is true if proposition v21 is not true. Proposition f9 is true. Proposition bad is true if proposition v9 is true and proposition w1 is true and proposition w14 is true and proposition bad is not true. Proposition bad is true if proposition w11 is true and proposition w6 is true and proposition w0 is true and proposition bad is not true. Proposition w16 is true if proposition v16 is not true. Proposition v11 is true if proposition w11 is not true. Proposition g6 is true if proposition f6 is true.\n\nQuestion: Is proposition q true?\n\nChoose exactly one:\n  A. Definitely yes\n  B. Definitely no\n  C. Cannot be determined\n\nThink step by step, then end with a line 'ANSWER: X' where X is A, B, or C."}