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.

Rules:
Proposition t0 is true if proposition t1 is true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition x8 is true if proposition x9 is not true. Proposition x3 is true if proposition x4 is not true. Proposition x1 is true if proposition x2 is not true. Proposition t6 is true if proposition t7 is true. Proposition g0_1 is true. Proposition btrue is true. Proposition x6 is true if proposition x7 is not true. Proposition x2 is true if proposition x3 is not true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true if proposition g1_0 is true. Proposition g1_0 is true. Proposition x9 is true if proposition x0 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition g0_0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_0 is true. Proposition g0_2 is true. Proposition x4 is true if proposition x5 is not true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition t4 is true if proposition t5 is true. Proposition x5 is true if proposition x6 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition g3_1 is true. Proposition g2_0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition t0 is true if proposition t1 is true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition x8 is true if proposition x9 is not true. Proposition x3 is true if proposition x4 is not true. Proposition x1 is true if proposition x2 is not true. Proposition t6 is true if proposition t7 is true. Proposition g0_1 is true. Proposition btrue is true. Proposition x6 is true if proposition x7 is not true. Proposition x2 is true if proposition x3 is not true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true if proposition g1_0 is true. Proposition g1_0 is true. Proposition x9 is true if proposition x0 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition g0_0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_0 is true. Proposition g0_2 is true. Proposition x4 is true if proposition x5 is not true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition t4 is true if proposition t5 is true. Proposition x5 is true if proposition x6 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition g3_1 is true. Proposition g2_0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition t0 is true if proposition t1 is true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition x8 is true if proposition x9 is not true. Proposition x3 is true if proposition x4 is not true. Proposition x1 is true if proposition x2 is not true. Proposition t6 is true if proposition t7 is true. Proposition g0_1 is true. Proposition btrue is true. Proposition x6 is true if proposition x7 is not true. Proposition x2 is true if proposition x3 is not true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true if proposition g1_0 is true. Proposition g1_0 is true. Proposition x9 is true if proposition x0 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition g0_0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_0 is true. Proposition g0_2 is true. Proposition x4 is true if proposition x5 is not true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition t4 is true if proposition t5 is true. Proposition x5 is true if proposition x6 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition g3_1 is true. Proposition g2_0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition t0 is true if proposition t1 is true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition x8 is true if proposition x9 is not true. Proposition x3 is true if proposition x4 is not true. Proposition x1 is true if proposition x2 is not true. Proposition t6 is true if proposition t7 is true. Proposition g0_1 is true. Proposition btrue is true. Proposition x6 is true if proposition x7 is not true. Proposition x2 is true if proposition x3 is not true. Proposition t1 is true if proposition t2 is true. Proposition s1 is true if proposition g1_0 is true. Proposition g1_0 is true. Proposition x9 is true if proposition x0 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition g0_0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_0 is true. Proposition g0_2 is true. Proposition x4 is true if proposition x5 is not true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition t4 is true if proposition t5 is true. Proposition x5 is true if proposition x6 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition g3_1 is true. Proposition g2_0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition etrue is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition t5 is true if proposition t6 is true. Proposition g1_2 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t0 is true if proposition t1 is true and proposition wide is true. Proposition g3_0 is true. Proposition g3_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t6 is true if proposition t7 is true and proposition cq is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition cq is true if proposition x0 is true. Proposition t7 is true if proposition btrue is true. Proposition p2 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 if proposition g0_0 is true. Proposition btrue is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true and proposition g1_3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition s3 is true. Proposition s2 is true if proposition g2_0 is true. Proposition g1_3 is true. Proposition g2_0 is true. Proposition q is true if proposition t0 is true. Proposition g0_0 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition g1_0 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition etrue is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition t5 is true if proposition t6 is true. Proposition g1_2 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t0 is true if proposition t1 is true and proposition wide is true. Proposition g3_0 is true. Proposition g3_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t6 is true if proposition t7 is true and proposition cq is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition cq is true if proposition x0 is true. Proposition t7 is true if proposition btrue is true. Proposition p2 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 if proposition g0_0 is true. Proposition btrue is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true and proposition g1_3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition s3 is true. Proposition s2 is true if proposition g2_0 is true. Proposition g1_3 is true. Proposition g2_0 is true. Proposition q is true if proposition t0 is true. Proposition g0_0 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition g1_0 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition t4 is true if proposition t5 is true. Proposition etrue is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition t5 is true if proposition t6 is true. Proposition g1_2 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t0 is true if proposition t1 is true and proposition wide is true. Proposition g3_0 is true. Proposition g3_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t6 is true if proposition t7 is true and proposition cq is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition cq is true if proposition x0 is true. Proposition t7 is true if proposition btrue is true. Proposition p2 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 if proposition g0_0 is true. Proposition btrue is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true and proposition g1_3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition s3 is true. Proposition s2 is true if proposition g2_0 is true. Proposition g1_3 is true. Proposition g2_0 is true. Proposition q is true if proposition t0 is true. Proposition g0_0 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition g1_0 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition t4 is true if proposition t5 is true. Proposition etrue is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition t5 is true if proposition t6 is true. Proposition g1_2 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t0 is true if proposition t1 is true and proposition wide is true. Proposition g3_0 is true. Proposition g3_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t6 is true if proposition t7 is true and proposition cq is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition cq is true if proposition x0 is true. Proposition t7 is true if proposition btrue is true. Proposition p2 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 if proposition g0_0 is true. Proposition btrue is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true and proposition g1_3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition s3 is true. Proposition s2 is true if proposition g2_0 is true. Proposition g1_3 is true. Proposition g2_0 is true. Proposition q is true if proposition t0 is true. Proposition g0_0 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition g1_0 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition etrue is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition t5 is true if proposition t6 is true. Proposition g1_2 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t2 is true if proposition t3 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t0 is true if proposition t1 is true and proposition wide is true. Proposition g3_0 is true. Proposition g3_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t6 is true if proposition t7 is true and proposition cq is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t1 is true if proposition t2 is true. Proposition t3 is true if proposition t4 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition cq is true if proposition x0 is true. Proposition t7 is true if proposition btrue is true. Proposition p2 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 if proposition g0_0 is true. Proposition btrue is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true and proposition g1_3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true. Proposition p1 is true if proposition s3 is true. Proposition s2 is true if proposition g2_0 is true. Proposition g1_3 is true. Proposition g2_0 is true. Proposition q is true if proposition t0 is true. Proposition g0_0 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition g1_0 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition g2_0 is true. Proposition g1_2 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition t0 is true if proposition t1 is true and proposition cq is true. Proposition g3_0 is true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition q is true if proposition t0 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition etrue is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t7 is true if proposition btrue is true. Proposition t1 is true if proposition t2 is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g0_1 is true. Proposition t6 is true if proposition t7 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition t5 is true if proposition t6 is true. Proposition t4 is true if proposition t5 is true and proposition wide is true. Proposition btrue is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition g2_1 is true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition p0 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 if proposition g0_0 is true and proposition g0_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition g2_0 is true. Proposition g1_2 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition t0 is true if proposition t1 is true and proposition cq is true. Proposition g3_0 is true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition q is true if proposition t0 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition etrue is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t7 is true if proposition btrue is true. Proposition t1 is true if proposition t2 is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g0_1 is true. Proposition t6 is true if proposition t7 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition t5 is true if proposition t6 is true. Proposition t4 is true if proposition t5 is true and proposition wide is true. Proposition btrue is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition g2_1 is true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition p0 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 if proposition g0_0 is true and proposition g0_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition g2_0 is true. Proposition g1_2 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition t0 is true if proposition t1 is true and proposition cq is true. Proposition g3_0 is true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition q is true if proposition t0 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition etrue is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t7 is true if proposition btrue is true. Proposition t1 is true if proposition t2 is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g0_1 is true. Proposition t6 is true if proposition t7 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition t5 is true if proposition t6 is true. Proposition t4 is true if proposition t5 is true and proposition wide is true. Proposition btrue is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition g2_1 is true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition p0 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 if proposition g0_0 is true and proposition g0_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition g2_0 is true. Proposition g1_2 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition t0 is true if proposition t1 is true and proposition cq is true. Proposition g3_0 is true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition q is true if proposition t0 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition etrue is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t7 is true if proposition btrue is true. Proposition t1 is true if proposition t2 is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g0_1 is true. Proposition t6 is true if proposition t7 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition t5 is true if proposition t6 is true. Proposition t4 is true if proposition t5 is true and proposition wide is true. Proposition btrue is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition g2_1 is true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition p0 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 if proposition g0_0 is true and proposition g0_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition g2_0 is true. Proposition g1_2 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true. Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition t0 is true if proposition t1 is true and proposition cq is true. Proposition g3_0 is true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition q is true if proposition t0 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition cq is true if proposition x0 is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition etrue is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition t7 is true if proposition btrue is true. Proposition t1 is true if proposition t2 is true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g0_1 is true. Proposition t6 is true if proposition t7 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition t5 is true if proposition t6 is true. Proposition t4 is true if proposition t5 is true and proposition wide is true. Proposition btrue is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition g2_1 is true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition p0 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 if proposition g0_0 is true and proposition g0_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x3 is true if proposition x4 is not true. Proposition g0_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t5 is true if proposition t6 is true. Proposition x7 is true if proposition x8 is not true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition g3_0 is true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition x2 is not true. Proposition x4 is true if proposition x5 is not true. Proposition g2_1 is true. Proposition x2 is true if proposition x3 is not true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_1 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition t7 is true if proposition btrue is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g1_2 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition s0 is true if proposition g0_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition cq is true if proposition x0 is true. Proposition x9 is true if proposition x0 is not true. Proposition q is true if proposition t0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition x5 is true if proposition x6 is not true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true and proposition wide is true. Proposition p2 is true if proposition s1 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition x0 is true if proposition x1 is not true. Proposition t6 is true if proposition t7 is true. Proposition x8 is true if proposition x9 is not true. Proposition btrue is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition x3 is true if proposition x4 is not true. Proposition g0_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t5 is true if proposition t6 is true. Proposition x7 is true if proposition x8 is not true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition g3_0 is true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition x2 is not true. Proposition x4 is true if proposition x5 is not true. Proposition g2_1 is true. Proposition x2 is true if proposition x3 is not true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_1 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition t7 is true if proposition btrue is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g1_2 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition s0 is true if proposition g0_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition cq is true if proposition x0 is true. Proposition x9 is true if proposition x0 is not true. Proposition q is true if proposition t0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition x5 is true if proposition x6 is not true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true and proposition wide is true. Proposition p2 is true if proposition s1 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition x0 is true if proposition x1 is not true. Proposition t6 is true if proposition t7 is true. Proposition x8 is true if proposition x9 is not true. Proposition btrue is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition x3 is true if proposition x4 is not true. Proposition g0_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t5 is true if proposition t6 is true. Proposition x7 is true if proposition x8 is not true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition g3_0 is true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition x2 is not true. Proposition x4 is true if proposition x5 is not true. Proposition g2_1 is true. Proposition x2 is true if proposition x3 is not true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_1 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition t7 is true if proposition btrue is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g1_2 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition s0 is true if proposition g0_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition cq is true if proposition x0 is true. Proposition x9 is true if proposition x0 is not true. Proposition q is true if proposition t0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition x5 is true if proposition x6 is not true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true and proposition wide is true. Proposition p2 is true if proposition s1 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition x0 is true if proposition x1 is not true. Proposition t6 is true if proposition t7 is true. Proposition x8 is true if proposition x9 is not true. Proposition btrue is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition x3 is true if proposition x4 is not true. Proposition g0_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t5 is true if proposition t6 is true. Proposition x7 is true if proposition x8 is not true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition g3_0 is true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition x2 is not true. Proposition x4 is true if proposition x5 is not true. Proposition g2_1 is true. Proposition x2 is true if proposition x3 is not true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_1 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition t7 is true if proposition btrue is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g1_2 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition s0 is true if proposition g0_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition cq is true if proposition x0 is true. Proposition x9 is true if proposition x0 is not true. Proposition q is true if proposition t0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition x5 is true if proposition x6 is not true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true and proposition wide is true. Proposition p2 is true if proposition s1 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition x0 is true if proposition x1 is not true. Proposition t6 is true if proposition t7 is true. Proposition x8 is true if proposition x9 is not true. Proposition btrue is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition x3 is true if proposition x4 is not true. Proposition g0_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true and proposition p3 is true. Proposition t5 is true if proposition t6 is true. Proposition x7 is true if proposition x8 is not true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition g3_0 is true. Proposition p3 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition x2 is not true. Proposition x4 is true if proposition x5 is not true. Proposition g2_1 is true. Proposition x2 is true if proposition x3 is not true. Proposition g1_0 is true. Proposition g1_1 is true. Proposition t3 is true if proposition t4 is true. Proposition g3_1 is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition t7 is true if proposition btrue is true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g1_2 is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true and proposition g1_2 is true. Proposition s0 is true if proposition g0_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition cq is true if proposition x0 is true. Proposition x9 is true if proposition x0 is not true. Proposition q is true if proposition t0 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition x5 is true if proposition x6 is not true. Proposition t0 is true if proposition t1 is true. Proposition t2 is true if proposition t3 is true and proposition wide is true. Proposition p2 is true if proposition s1 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition x0 is true if proposition x1 is not true. Proposition t6 is true if proposition t7 is true. Proposition x8 is true if proposition x9 is not true. Proposition btrue is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x2 is true if proposition x3 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition x8 is true if proposition x9 is not true. Proposition q is true if proposition t0 is true. Proposition g1_0 is true. Proposition t7 is true if proposition btrue is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition x4 is true if proposition x5 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition t6 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t6 is true if proposition t7 is true and proposition wide is true. Proposition cq is true if proposition x0 is true. Proposition x0 is true if proposition x1 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition g0_1 is true. Proposition p0 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 g1_1 is true. Proposition x1 is true if proposition x2 is not true. Proposition t0 is true if proposition t1 is true. Proposition x9 is true if proposition x0 is not true. Proposition g2_0 is true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition x6 is true if proposition x7 is not true. Proposition g3_1 is true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g0_0 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition btrue is true. Proposition g3_0 is true. Proposition x5 is true if proposition x6 is not true. Proposition g2_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition x2 is true if proposition x3 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition x8 is true if proposition x9 is not true. Proposition q is true if proposition t0 is true. Proposition g1_0 is true. Proposition t7 is true if proposition btrue is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition x4 is true if proposition x5 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition t6 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t6 is true if proposition t7 is true and proposition wide is true. Proposition cq is true if proposition x0 is true. Proposition x0 is true if proposition x1 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition g0_1 is true. Proposition p0 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 g1_1 is true. Proposition x1 is true if proposition x2 is not true. Proposition t0 is true if proposition t1 is true. Proposition x9 is true if proposition x0 is not true. Proposition g2_0 is true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition x6 is true if proposition x7 is not true. Proposition g3_1 is true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g0_0 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition btrue is true. Proposition g3_0 is true. Proposition x5 is true if proposition x6 is not true. Proposition g2_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition x2 is true if proposition x3 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition x8 is true if proposition x9 is not true. Proposition q is true if proposition t0 is true. Proposition g1_0 is true. Proposition t7 is true if proposition btrue is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition x4 is true if proposition x5 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition t6 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t6 is true if proposition t7 is true and proposition wide is true. Proposition cq is true if proposition x0 is true. Proposition x0 is true if proposition x1 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition g0_1 is true. Proposition p0 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 g1_1 is true. Proposition x1 is true if proposition x2 is not true. Proposition t0 is true if proposition t1 is true. Proposition x9 is true if proposition x0 is not true. Proposition g2_0 is true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition x6 is true if proposition x7 is not true. Proposition g3_1 is true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g0_0 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition btrue is true. Proposition g3_0 is true. Proposition x5 is true if proposition x6 is not true. Proposition g2_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition x2 is true if proposition x3 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition x8 is true if proposition x9 is not true. Proposition q is true if proposition t0 is true. Proposition g1_0 is true. Proposition t7 is true if proposition btrue is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition x4 is true if proposition x5 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition t6 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t6 is true if proposition t7 is true and proposition wide is true. Proposition cq is true if proposition x0 is true. Proposition x0 is true if proposition x1 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition g0_1 is true. Proposition p0 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 g1_1 is true. Proposition x1 is true if proposition x2 is not true. Proposition t0 is true if proposition t1 is true. Proposition x9 is true if proposition x0 is not true. Proposition g2_0 is true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition x6 is true if proposition x7 is not true. Proposition g3_1 is true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g0_0 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition btrue is true. Proposition g3_0 is true. Proposition x5 is true if proposition x6 is not true. Proposition g2_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition x2 is true if proposition x3 is not true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition x7 is true if proposition x8 is not true. Proposition x8 is true if proposition x9 is not true. Proposition q is true if proposition t0 is true. Proposition g1_0 is true. Proposition t7 is true if proposition btrue is true. Proposition wide is true if proposition p0 is true and proposition p1 is true. Proposition x4 is true if proposition x5 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition t6 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true. Proposition t6 is true if proposition t7 is true and proposition wide is true. Proposition cq is true if proposition x0 is true. Proposition x0 is true if proposition x1 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition g0_1 is true. Proposition p0 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 g1_1 is true. Proposition x1 is true if proposition x2 is not true. Proposition t0 is true if proposition t1 is true. Proposition x9 is true if proposition x0 is not true. Proposition g2_0 is true. Proposition t1 is true if proposition t2 is true and proposition cq is true. Proposition x6 is true if proposition x7 is not true. Proposition g3_1 is true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition g0_0 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition btrue is true. Proposition g3_0 is true. Proposition x5 is true if proposition x6 is not true. Proposition g2_1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition cq is true if proposition x0 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition p1 is true if proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true. Proposition g1_1 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition t6 is true if proposition t7 is true. Proposition s2 is true if proposition g2_0 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true and proposition g3_2 is true. Proposition t1 is true if proposition t2 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition t7 is true if proposition btrue is true and proposition cq is true. Proposition t5 is true if proposition t6 is true. Proposition btrue is true. Proposition g3_1 is true. Proposition g1_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition t4 is true if proposition t5 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g3_0 is true. Proposition t0 is true if proposition t1 is true. Proposition g3_2 is true. Proposition t3 is true if proposition t4 is true and proposition wide is true. Proposition g0_1 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition cq is true if proposition x0 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition p1 is true if proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true. Proposition g1_1 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition t6 is true if proposition t7 is true. Proposition s2 is true if proposition g2_0 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true and proposition g3_2 is true. Proposition t1 is true if proposition t2 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition t7 is true if proposition btrue is true and proposition cq is true. Proposition t5 is true if proposition t6 is true. Proposition btrue is true. Proposition g3_1 is true. Proposition g1_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition t4 is true if proposition t5 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g3_0 is true. Proposition t0 is true if proposition t1 is true. Proposition g3_2 is true. Proposition t3 is true if proposition t4 is true and proposition wide is true. Proposition g0_1 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition cq is true if proposition x0 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition p1 is true if proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true. Proposition g1_1 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition t6 is true if proposition t7 is true. Proposition s2 is true if proposition g2_0 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true and proposition g3_2 is true. Proposition t1 is true if proposition t2 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition t7 is true if proposition btrue is true and proposition cq is true. Proposition t5 is true if proposition t6 is true. Proposition btrue is true. Proposition g3_1 is true. Proposition g1_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition t4 is true if proposition t5 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g3_0 is true. Proposition t0 is true if proposition t1 is true. Proposition g3_2 is true. Proposition t3 is true if proposition t4 is true and proposition wide is true. Proposition g0_1 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.'

Rules:
Proposition cq is true if proposition x0 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition p1 is true if proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true. Proposition g1_1 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition t6 is true if proposition t7 is true. Proposition s2 is true if proposition g2_0 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true and proposition g3_2 is true. Proposition t1 is true if proposition t2 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition t7 is true if proposition btrue is true and proposition cq is true. Proposition t5 is true if proposition t6 is true. Proposition btrue is true. Proposition g3_1 is true. Proposition g1_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition t4 is true if proposition t5 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g3_0 is true. Proposition t0 is true if proposition t1 is true. Proposition g3_2 is true. Proposition t3 is true if proposition t4 is true and proposition wide is true. Proposition g0_1 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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'.

Rules:
Proposition cq is true if proposition x0 is true. Proposition x3 is true if proposition etrue is true and proposition x4 is not true. Proposition p1 is true if proposition s2 is true and proposition s3 is true. Proposition g2_0 is true. Proposition g0_0 is true. Proposition t2 is true if proposition t3 is true. Proposition x4 is true if proposition etrue is true and proposition x5 is not true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true. Proposition etrue is true. Proposition q is true if proposition t0 is true. Proposition g1_1 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition t6 is true if proposition t7 is true. Proposition s2 is true if proposition g2_0 is true. Proposition x8 is true if proposition etrue is true and proposition x9 is not true. Proposition x5 is true if proposition etrue is true and proposition x6 is not true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition s3 is true if proposition g3_0 is true and proposition g3_1 is true and proposition g3_2 is true. Proposition t1 is true if proposition t2 is true. Proposition x9 is true if proposition etrue is true and proposition x0 is not true. Proposition t7 is true if proposition btrue is true and proposition cq is true. Proposition t5 is true if proposition t6 is true. Proposition btrue is true. Proposition g3_1 is true. Proposition g1_0 is true. Proposition p0 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition x1 is true if proposition etrue is true and proposition x2 is not true. Proposition t4 is true if proposition t5 is true. Proposition x2 is true if proposition etrue is true and proposition x3 is not true. Proposition x7 is true if proposition etrue is true and proposition x8 is not true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition x6 is true if proposition etrue is true and proposition x7 is not true. Proposition g3_0 is true. Proposition t0 is true if proposition t1 is true. Proposition g3_2 is true. Proposition t3 is true if proposition t4 is true and proposition wide is true. Proposition g0_1 is true. Proposition x0 is true if proposition etrue is true and proposition x1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition x5 is true if proposition x6 is not true. Proposition g1_0 is true. Proposition g3_0 is true. Proposition x4 is true if proposition x5 is not true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition t4 is true if proposition t5 is true. Proposition x9 is true if proposition x0 is not true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t2 is true if proposition t3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition x7 is true if proposition x8 is not true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition x2 is true if proposition x3 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t0 is true if proposition t1 is true. Proposition x1 is true if proposition x2 is not true. Proposition x8 is true if proposition x9 is not true. Proposition g0_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition g0_0 is true. Proposition g0_2 is true. Proposition t1 is true if proposition t2 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g1_1 is true. Proposition btrue is true. Proposition g2_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition t6 is true if proposition t7 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


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.

Rules:
Proposition s3 is true if proposition g3_0 is true. Proposition t3 is true if proposition t4 is true. Proposition x5 is true if proposition x6 is not true. Proposition g1_0 is true. Proposition g3_0 is true. Proposition x4 is true if proposition x5 is not true. Proposition t7 is true if proposition btrue is true and proposition wide is true. Proposition s1 is true if proposition g1_0 is true and proposition g1_1 is true. Proposition s0 is true if proposition g0_0 is true and proposition g0_1 is true and proposition g0_2 is true. Proposition t4 is true if proposition t5 is true. Proposition x9 is true if proposition x0 is not true. Proposition x3 is true if proposition x4 is not true. Proposition s2 is true if proposition g2_0 is true and proposition g2_1 is true. Proposition t2 is true if proposition t3 is true. Proposition p0 is true if proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g2_1 is true. Proposition x7 is true if proposition x8 is not true. Proposition cq is true if proposition x0 is true. Proposition q is true if proposition t0 is true. Proposition t5 is true if proposition t6 is true and proposition cq is true. Proposition p1 is true if proposition s0 is true and proposition s1 is true and proposition s3 is true. Proposition x2 is true if proposition x3 is not true. Proposition x0 is true if proposition x1 is not true. Proposition t0 is true if proposition t1 is true. Proposition x1 is true if proposition x2 is not true. Proposition x8 is true if proposition x9 is not true. Proposition g0_1 is true. Proposition wide is true if proposition p0 is true and proposition p1 is true and proposition p2 is true. Proposition g0_0 is true. Proposition g0_2 is true. Proposition t1 is true if proposition t2 is true. Proposition p2 is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition g1_1 is true. Proposition btrue is true. Proposition g2_0 is true. Proposition x6 is true if proposition x7 is not true. Proposition t6 is true if proposition t7 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.