| {"id": "P01", "role": "sanity", "premises": ["a", "b"], "goal": "AND(a, b)", "provable": true, "reference_proof": "PROOF\npremises: a, b\ngoal: AND(a, b)\n1. a [premise]\n2. b [premise]\n3. AND(a, b) [AND_I 1, 2]\nEND", "naive_proof": null, "side_conditions": [], "min_proof_steps": 3} |
| {"id": "P02", "role": "single_rule", "premises": ["r", "IMPL(r, t)"], "goal": "t", "provable": true, "reference_proof": "PROOF\npremises: r, IMPL(r, t)\ngoal: t\n1. r [premise]\n2. IMPL(r, t) [premise]\n3. t [IMPL_E 2, 1]\nEND", "naive_proof": "PROOF\npremises: r, IMPL(r, t)\ngoal: t\n1. r [premise]\n2. IMPL(r, t) [premise]\n3. t [IMPL_E 1, 2]\nEND", "side_conditions": ["IMPL_E_MAJOR_FIRST"], "min_proof_steps": 3} |
| {"id": "P03", "role": "single_rule", "premises": ["NOT(p)"], "goal": "IMPL(p, q)", "provable": true, "reference_proof": "PROOF\npremises: NOT(p)\ngoal: IMPL(p, q)\n1. NOT(p) [premise]\n2. | p [assume]\n3. | | NOT(q) [assume]\n4. | | BOT [NOT_E 2, 1]\n5. | NOT(NOT(q)) [NOT_I 3-4]\n6. | q [DNE 5]\n7. IMPL(p, q) [IMPL_I 2-6]\nEND", "naive_proof": "PROOF\npremises: NOT(p)\ngoal: IMPL(p, q)\n1. NOT(p) [premise]\n2. | p [assume]\n3. | BOT [NOT_E 2, 1]\n4. | q [BOT_E 3]\n5. IMPL(p, q) [IMPL_I 2-4]\nEND", "side_conditions": ["BOT_E_TOP_LEVEL_ONLY"], "min_proof_steps": 7} |
| {"id": "P04", "role": "two_rule", "premises": ["AND(s, t)", "IMPL(s, t)"], "goal": "t", "provable": true, "reference_proof": "PROOF\npremises: AND(s, t), IMPL(s, t)\ngoal: t\n1. AND(s, t) [premise]\n2. IMPL(s, t) [premise]\n3. s [AND_E1 1]\n4. t [IMPL_E 2, 3]\nEND", "naive_proof": "PROOF\npremises: AND(s, t), IMPL(s, t)\ngoal: t\n1. AND(s, t) [premise]\n2. IMPL(s, t) [premise]\n3. t [AND_E2 1]\nEND", "side_conditions": ["AND_E_LEFT_ONLY", "IMPL_E_MAJOR_FIRST"], "min_proof_steps": 4} |
| {"id": "U01", "role": "unprovable", "premises": ["AND(p, q)"], "goal": "q", "provable": false, "reference_proof": null, "naive_proof": "PROOF\npremises: AND(p, q)\ngoal: q\n1. AND(p, q) [premise]\n2. q [AND_E2 1]\nEND", "side_conditions": ["AND_E_LEFT_ONLY"], "min_proof_steps": 0} |
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