%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:28:07 PM UTC 2026 % Result : Unsatisfiable 0.14s 0.43s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0. % 0.00/0.04 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.09/0.35 % Computer : n018.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 16:33:04 UTC 2026 % 0.09/0.36 % CPUTime : % 0.14/0.43 % SZS status Unsatisfiable % 0.14/0.43 % SZS output begin IncompleteProof % 0.14/0.43 cnf(c0, axiom, % 0.14/0.43 ~is_a_theorem(implies(a,implies(b,a)))). % 0.14/0.43 cnf(c1, plain, % 0.14/0.43 ~is_a_theorem(implies(a,implies(b,a))), % 0.14/0.43 inference(start, [], [c0])). % 0.14/0.43 % 0.14/0.43 cnf(c2, axiom, % 0.14/0.43 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 0.14/0.43 cnf(a0, assumption, % 0.14/0.43 implies(a,implies(b,a)) = X0). % 0.14/0.43 cnf(c3, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.14/0.43 cnf(c4, plain, % 0.14/0.43 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.14/0.43 % 0.14/0.43 cnf(c5, axiom, % 0.14/0.43 is_a_theorem(implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2))))). % 0.14/0.43 cnf(a1, assumption, % 0.14/0.43 X1 = implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))). % 0.14/0.43 cnf(c6, plain, % 0.14/0.43 ~is_a_theorem(implies(X1,X0)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.14/0.43 cnf(c7, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.14/0.43 % 0.14/0.43 cnf(c8, axiom, % 0.14/0.43 is_a_theorem(X6) | ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6))). % 0.14/0.43 cnf(a2, assumption, % 0.14/0.43 implies(X1,X0) = X6). % 0.14/0.43 cnf(c9, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 0.14/0.43 cnf(c10, plain, % 0.14/0.43 ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 0.14/0.43 % 0.14/0.43 cnf(c11, axiom, % 0.14/0.43 is_a_theorem(X8) | ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8))). % 0.14/0.43 cnf(a3, assumption, % 0.14/0.43 X7 = X8). % 0.14/0.43 cnf(c12, plain, % 0.14/0.43 ~is_a_theorem(implies(X7,X6)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.14/0.43 cnf(c13, plain, % 0.14/0.43 ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.14/0.43 % 0.14/0.43 cnf(c14, axiom, % 0.14/0.43 is_a_theorem(implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10))))). % 0.14/0.43 cnf(a4, assumption, % 0.14/0.43 X9 = implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))). % 0.14/0.43 cnf(c15, plain, % 0.14/0.43 ~is_a_theorem(implies(X9,X8)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 0.14/0.43 cnf(c16, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 0.14/0.43 % 0.14/0.43 cnf(c17, axiom, % 0.14/0.43 is_a_theorem(X14) | ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14))). % 0.14/0.43 cnf(a5, assumption, % 0.14/0.43 implies(X9,X8) = X14). % 0.14/0.43 cnf(c18, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a5])], [c15, c17])). % 0.14/0.43 cnf(c19, plain, % 0.14/0.43 ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14)), % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a5])], [c15, c17])). % 0.14/0.43 % 0.14/0.43 cnf(c20, plain, % 0.14/0.43 is_a_theorem(X1)). % 0.14/0.43 cnf(a6, assumption, % 0.14/0.43 X15 = X1). % 0.14/0.43 cnf(c21, plain, % 0.14/0.43 ~is_a_theorem(implies(X15,X14)), % 0.14/0.43 inference(predicate_reduction, [assumptions([a6])], [c19, c20])). % 0.14/0.43 % 0.14/0.43 cnf(c22, axiom, % 0.14/0.43 is_a_theorem(X16) | ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16))). % 0.14/0.43 cnf(a7, assumption, % 0.14/0.43 implies(X15,X14) = X16). % 0.14/0.43 cnf(c23, plain, % 0.14/0.43 $false, % 0.14/0.43 inference(strict_predicate_extension, [assumptions([a7])], [c21, c22])). % 0.14/0.43 cnf(c24, plain, % 0.14/0.43 ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16)), % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a7])], [c21, c22])). % 0.14/0.44 % 0.14/0.44 cnf(c25, axiom, % 0.14/0.44 is_a_theorem(X18) | ~is_a_theorem(X19) | ~is_a_theorem(implies(X19,X18))). % 0.14/0.44 cnf(a8, assumption, % 0.14/0.44 X17 = X18). % 0.14/0.44 cnf(c26, plain, % 0.14/0.44 ~is_a_theorem(implies(X17,X16)), % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 0.14/0.44 cnf(c27, plain, % 0.14/0.44 ~is_a_theorem(X19) | ~is_a_theorem(implies(X19,X18)), % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 0.14/0.44 % 0.14/0.44 cnf(c28, plain, % 0.14/0.44 is_a_theorem(X1)). % 0.14/0.44 cnf(a9, assumption, % 0.14/0.44 X19 = X1). % 0.14/0.44 cnf(c29, plain, % 0.14/0.44 ~is_a_theorem(implies(X19,X18)), % 0.14/0.44 inference(predicate_reduction, [assumptions([a9])], [c27, c28])). % 0.14/0.44 % 0.14/0.44 cnf(c30, axiom, % 0.14/0.44 is_a_theorem(implies(implies(implies(X20,X21),X22),implies(implies(X22,X20),implies(X23,X20))))). % 0.14/0.44 cnf(a10, assumption, % 0.14/0.44 implies(X19,X18) = implies(implies(implies(X20,X21),X22),implies(implies(X22,X20),implies(X23,X20)))). % 0.14/0.44 cnf(c31, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a10])], [c29, c30])). % 0.14/0.44 cnf(c32, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a10])], [c29, c30])). % 0.14/0.44 % 0.14/0.44 cnf(c33, axiom, % 0.14/0.44 is_a_theorem(implies(implies(implies(X24,X25),X26),implies(implies(X26,X24),implies(X27,X24))))). % 0.14/0.44 cnf(a11, assumption, % 0.14/0.44 implies(X17,X16) = implies(implies(implies(X24,X25),X26),implies(implies(X26,X24),implies(X27,X24)))). % 0.14/0.44 cnf(c34, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a11])], [c26, c33])). % 0.14/0.44 cnf(c35, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a11])], [c26, c33])). % 0.14/0.44 % 0.14/0.44 cnf(c36, axiom, % 0.14/0.44 is_a_theorem(X28) | ~is_a_theorem(X29) | ~is_a_theorem(implies(X29,X28))). % 0.14/0.44 cnf(a12, assumption, % 0.14/0.44 implies(X7,X6) = X28). % 0.14/0.44 cnf(c37, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a12])], [c12, c36])). % 0.14/0.44 cnf(c38, plain, % 0.14/0.44 ~is_a_theorem(X29) | ~is_a_theorem(implies(X29,X28)), % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a12])], [c12, c36])). % 0.14/0.44 % 0.14/0.44 cnf(c39, plain, % 0.14/0.44 is_a_theorem(X9)). % 0.14/0.44 cnf(a13, assumption, % 0.14/0.44 X29 = X9). % 0.14/0.44 cnf(c40, plain, % 0.14/0.44 ~is_a_theorem(implies(X29,X28)), % 0.14/0.44 inference(predicate_reduction, [assumptions([a13])], [c38, c39])). % 0.14/0.44 % 0.14/0.44 cnf(c41, axiom, % 0.14/0.44 is_a_theorem(implies(implies(implies(X30,X31),X32),implies(implies(X32,X30),implies(X33,X30))))). % 0.14/0.44 cnf(a14, assumption, % 0.14/0.44 implies(X29,X28) = implies(implies(implies(X30,X31),X32),implies(implies(X32,X30),implies(X33,X30)))). % 0.14/0.44 cnf(c42, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a14])], [c40, c41])). % 0.14/0.44 cnf(c43, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(strict_predicate_extension, [assumptions([a14])], [c40, c41])). % 0.14/0.44 % 0.14/0.44 cnf(c44, plain, % 0.14/0.44 $false, % 0.14/0.44 inference(constraint_solving, [ % 0.14/0.44 bind(X0, implies(a,implies(b,a))), % 0.14/0.44 bind(X1, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))), % 0.14/0.44 bind(X2, implies(X13,X10)), % 0.14/0.44 bind(X3, a), % 0.14/0.44 bind(X4, implies(X2,X3)), % 0.14/0.44 bind(X5, a), % 0.14/0.44 bind(X6, implies(X1,X0)), % 0.14/0.44 bind(X7, implies(implies(X4,X2),implies(X5,X2))), % 0.14/0.44 bind(X8, implies(implies(X4,X2),implies(X5,X2))), % 0.14/0.44 bind(X9, implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))), % 0.14/0.44 bind(X10, a), % 0.14/0.44 bind(X11, implies(X13,X10)), % 0.14/0.44 bind(X12, implies(X13,X10)), % 0.14/0.44 bind(X13, b), % 0.14/0.44 bind(X14, implies(X9,X8)), % 0.14/0.44 bind(X15, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))), % 0.14/0.44 bind(X16, implies(X15,X14)), % 0.14/0.44 bind(X17, implies(implies(X22,X20),implies(X23,X20))), % 0.14/0.44 bind(X18, implies(implies(X22,X20),implies(X23,X20))), % 0.14/0.44 bind(X19, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))), % 0.14/0.44 bind(X20, implies(X2,X3)), % 0.14/0.44 bind(X21, implies(X2,X3)), % 0.14/0.44 bind(X22, implies(implies(X4,X2),implies(X5,X2))), % 0.14/0.44 bind(X23, implies(X2,X3)), % 0.14/0.44 bind(X24, implies(implies(X4,X2),implies(X5,X2))), % 0.14/0.44 bind(X25, implies(X2,X3)), % 0.14/0.44 bind(X26, implies(X23,X20)), % 0.14/0.44 bind(X27, implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))), % 0.14/0.44 bind(X28, implies(X7,X6)), % 0.14/0.44 bind(X29, implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))), % 0.14/0.44 bind(X30, implies(X10,X11)), % 0.14/0.44 bind(X31, implies(X13,X10)), % 0.14/0.44 bind(X32, implies(implies(X12,X10),implies(X13,X10))), % 0.14/0.44 bind(X33, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))) % 0.14/0.44 ], % 0.14/0.44 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 0.14/0.44 % 0.14/0.44 % SZS output end IncompleteProof %------------------------------------------------------------------------------