%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL081-1 : 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 : n012.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 45.44s 6.04s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL081-1 : TPTP v9.3.1. Released v1.0.0. % 0.00/0.02 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.03/0.30 % Computer : n012.cluster.edu % 0.03/0.30 % Model : x86_64 x86_64 % 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.03/0.30 % Memory : 8046.5625MB % 0.03/0.30 % OS : Linux 6.8.0-71-generic % 0.03/0.30 % CPULimit : 300 % 0.03/0.30 % WCLimit : 300 % 0.03/0.30 % DateTime : Sat Sep 5 12:56:42 UTC 2026 % 0.03/0.30 % CPUTime : % 45.44/6.04 % SZS status Unsatisfiable % 45.44/6.04 % SZS output begin IncompleteProof % 45.44/6.04 cnf(c0, axiom, % 45.44/6.04 ~is_a_theorem(implies(a,a))). % 45.44/6.04 cnf(c1, plain, % 45.44/6.04 ~is_a_theorem(implies(a,a)), % 45.44/6.04 inference(start, [], [c0])). % 45.44/6.04 % 45.44/6.04 cnf(c2, axiom, % 45.44/6.04 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 45.44/6.04 cnf(a0, assumption, % 45.44/6.04 implies(a,a) = X0). % 45.44/6.04 cnf(c3, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 45.44/6.04 cnf(c4, plain, % 45.44/6.04 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 45.44/6.04 % 45.44/6.04 cnf(c5, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2))))). % 45.44/6.04 cnf(a1, assumption, % 45.44/6.04 X1 = implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))). % 45.44/6.04 cnf(c6, plain, % 45.44/6.04 ~is_a_theorem(implies(X1,X0)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 45.44/6.04 cnf(c7, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 45.44/6.04 % 45.44/6.04 cnf(c8, axiom, % 45.44/6.04 is_a_theorem(X6) | ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6))). % 45.44/6.04 cnf(a2, assumption, % 45.44/6.04 implies(X1,X0) = X6). % 45.44/6.04 cnf(c9, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 45.44/6.04 cnf(c10, plain, % 45.44/6.04 ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 45.44/6.04 % 45.44/6.04 cnf(c11, axiom, % 45.44/6.04 is_a_theorem(X8) | ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8))). % 45.44/6.04 cnf(a3, assumption, % 45.44/6.04 X7 = X8). % 45.44/6.04 cnf(c12, plain, % 45.44/6.04 ~is_a_theorem(implies(X7,X6)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 45.44/6.04 cnf(c13, plain, % 45.44/6.04 ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 45.44/6.04 % 45.44/6.04 cnf(c14, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10))))). % 45.44/6.04 cnf(a4, assumption, % 45.44/6.04 X9 = implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))). % 45.44/6.04 cnf(c15, plain, % 45.44/6.04 ~is_a_theorem(implies(X9,X8)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 45.44/6.04 cnf(c16, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 45.44/6.04 % 45.44/6.04 cnf(c17, axiom, % 45.44/6.04 is_a_theorem(X14) | ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14))). % 45.44/6.04 cnf(a5, assumption, % 45.44/6.04 implies(X9,X8) = X14). % 45.44/6.04 cnf(c18, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a5])], [c15, c17])). % 45.44/6.04 cnf(c19, plain, % 45.44/6.04 ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a5])], [c15, c17])). % 45.44/6.04 % 45.44/6.04 cnf(c20, axiom, % 45.44/6.04 is_a_theorem(X16) | ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16))). % 45.44/6.04 cnf(a6, assumption, % 45.44/6.04 X15 = X16). % 45.44/6.04 cnf(c21, plain, % 45.44/6.04 ~is_a_theorem(implies(X15,X14)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 45.44/6.04 cnf(c22, plain, % 45.44/6.04 ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 45.44/6.04 % 45.44/6.04 cnf(c23, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X18,X19),X20),implies(implies(X20,X18),implies(X21,X18))))). % 45.44/6.04 cnf(a7, assumption, % 45.44/6.04 X17 = implies(implies(implies(X18,X19),X20),implies(implies(X20,X18),implies(X21,X18)))). % 45.44/6.04 cnf(c24, plain, % 45.44/6.04 ~is_a_theorem(implies(X17,X16)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 45.44/6.04 cnf(c25, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 45.44/6.04 % 45.44/6.04 cnf(c26, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X22,X23),X24),implies(implies(X24,X22),implies(X25,X22))))). % 45.44/6.04 cnf(a8, assumption, % 45.44/6.04 implies(X17,X16) = implies(implies(implies(X22,X23),X24),implies(implies(X24,X22),implies(X25,X22)))). % 45.44/6.04 cnf(c27, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a8])], [c24, c26])). % 45.44/6.04 cnf(c28, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a8])], [c24, c26])). % 45.44/6.04 % 45.44/6.04 cnf(c29, axiom, % 45.44/6.04 is_a_theorem(X26) | ~is_a_theorem(X27) | ~is_a_theorem(implies(X27,X26))). % 45.44/6.04 cnf(a9, assumption, % 45.44/6.04 implies(X15,X14) = X26). % 45.44/6.04 cnf(c30, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a9])], [c21, c29])). % 45.44/6.04 cnf(c31, plain, % 45.44/6.04 ~is_a_theorem(X27) | ~is_a_theorem(implies(X27,X26)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a9])], [c21, c29])). % 45.44/6.04 % 45.44/6.04 cnf(c32, axiom, % 45.44/6.04 is_a_theorem(X28) | ~is_a_theorem(X29) | ~is_a_theorem(implies(X29,X28))). % 45.44/6.04 cnf(a10, assumption, % 45.44/6.04 X27 = X28). % 45.44/6.04 cnf(c33, plain, % 45.44/6.04 ~is_a_theorem(implies(X27,X26)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 45.44/6.04 cnf(c34, plain, % 45.44/6.04 ~is_a_theorem(X29) | ~is_a_theorem(implies(X29,X28)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 45.44/6.04 % 45.44/6.04 cnf(c35, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X30,X31),X32),implies(implies(X32,X30),implies(X33,X30))))). % 45.44/6.04 cnf(a11, assumption, % 45.44/6.04 X29 = implies(implies(implies(X30,X31),X32),implies(implies(X32,X30),implies(X33,X30)))). % 45.44/6.04 cnf(c36, plain, % 45.44/6.04 ~is_a_theorem(implies(X29,X28)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a11])], [c34, c35])). % 45.44/6.04 cnf(c37, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a11])], [c34, c35])). % 45.44/6.04 % 45.44/6.04 cnf(c38, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X34,X35),X36),implies(implies(X36,X34),implies(X37,X34))))). % 45.44/6.04 cnf(a12, assumption, % 45.44/6.04 implies(X29,X28) = implies(implies(implies(X34,X35),X36),implies(implies(X36,X34),implies(X37,X34)))). % 45.44/6.04 cnf(c39, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a12])], [c36, c38])). % 45.44/6.04 cnf(c40, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a12])], [c36, c38])). % 45.44/6.04 % 45.44/6.04 cnf(c41, plain, % 45.44/6.04 is_a_theorem(X1)). % 45.44/6.04 cnf(a13, assumption, % 45.44/6.04 implies(X27,X26) = X1). % 45.44/6.04 cnf(c42, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(predicate_reduction, [assumptions([a13])], [c33, c41])). % 45.44/6.04 % 45.44/6.04 cnf(c43, axiom, % 45.44/6.04 is_a_theorem(X38) | ~is_a_theorem(X39) | ~is_a_theorem(implies(X39,X38))). % 45.44/6.04 cnf(a14, assumption, % 45.44/6.04 implies(X7,X6) = X38). % 45.44/6.04 cnf(c44, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a14])], [c12, c43])). % 45.44/6.04 cnf(c45, plain, % 45.44/6.04 ~is_a_theorem(X39) | ~is_a_theorem(implies(X39,X38)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a14])], [c12, c43])). % 45.44/6.04 % 45.44/6.04 cnf(c46, axiom, % 45.44/6.04 is_a_theorem(X40) | ~is_a_theorem(X41) | ~is_a_theorem(implies(X41,X40))). % 45.44/6.04 cnf(a15, assumption, % 45.44/6.04 X39 = X40). % 45.44/6.04 cnf(c47, plain, % 45.44/6.04 ~is_a_theorem(implies(X39,X38)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a15])], [c45, c46])). % 45.44/6.04 cnf(c48, plain, % 45.44/6.04 ~is_a_theorem(X41) | ~is_a_theorem(implies(X41,X40)), % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a15])], [c45, c46])). % 45.44/6.04 % 45.44/6.04 cnf(c49, plain, % 45.44/6.04 is_a_theorem(X7)). % 45.44/6.04 cnf(a16, assumption, % 45.44/6.04 X41 = X7). % 45.44/6.04 cnf(c50, plain, % 45.44/6.04 ~is_a_theorem(implies(X41,X40)), % 45.44/6.04 inference(predicate_reduction, [assumptions([a16])], [c48, c49])). % 45.44/6.04 % 45.44/6.04 cnf(c51, plain, % 45.44/6.04 is_a_theorem(X17)). % 45.44/6.04 cnf(a17, assumption, % 45.44/6.04 implies(X41,X40) = X17). % 45.44/6.04 cnf(c52, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(predicate_reduction, [assumptions([a17])], [c50, c51])). % 45.44/6.04 % 45.44/6.04 cnf(c53, axiom, % 45.44/6.04 is_a_theorem(implies(implies(implies(X42,X43),X44),implies(implies(X44,X42),implies(X45,X42))))). % 45.44/6.04 cnf(a18, assumption, % 45.44/6.04 implies(X39,X38) = implies(implies(implies(X42,X43),X44),implies(implies(X44,X42),implies(X45,X42)))). % 45.44/6.04 cnf(c54, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a18])], [c47, c53])). % 45.44/6.04 cnf(c55, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(strict_predicate_extension, [assumptions([a18])], [c47, c53])). % 45.44/6.04 % 45.44/6.04 cnf(c56, plain, % 45.44/6.04 $false, % 45.44/6.04 inference(constraint_solving, [ % 45.44/6.04 bind(X0, implies(a,a)), % 45.44/6.04 bind(X1, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))), % 45.44/6.04 bind(X2, implies(implies(X32,X30),implies(X33,X30))), % 45.44/6.04 bind(X3, implies(X30,X31)), % 45.44/6.04 bind(X4, implies(X37,X34)), % 45.44/6.04 bind(X5, implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))), % 45.44/6.04 bind(X6, implies(X1,X0)), % 45.44/6.04 bind(X7, implies(implies(X32,X30),implies(X33,X30))), % 45.44/6.04 bind(X8, implies(implies(X32,X30),implies(X33,X30))), % 45.44/6.04 bind(X9, implies(implies(implies(X10,X11),X12),implies(implies(X12,X10),implies(X13,X10)))), % 45.44/6.04 bind(X10, X10), % 45.44/6.04 bind(X11, X11), % 45.44/6.04 bind(X12, X12), % 45.44/6.04 bind(X13, X13), % 45.44/6.04 bind(X14, implies(X9,X8)), % 45.44/6.04 bind(X15, implies(implies(X24,X22),implies(X25,X22))), % 45.44/6.04 bind(X16, implies(implies(X24,X22),implies(X25,X22))), % 45.44/6.04 bind(X17, implies(implies(implies(X18,X19),X20),implies(implies(X20,X18),implies(X21,X18)))), % 45.44/6.04 bind(X18, a), % 45.44/6.04 bind(X19, a), % 45.44/6.04 bind(X20, implies(X33,X30)), % 45.44/6.04 bind(X21, a), % 45.44/6.04 bind(X22, implies(X18,X19)), % 45.44/6.04 bind(X23, implies(X33,X30)), % 45.44/6.04 bind(X24, implies(implies(X20,X18),implies(X21,X18))), % 45.44/6.04 bind(X25, implies(X32,X30)), % 45.44/6.04 bind(X26, implies(X15,X14)), % 45.44/6.04 bind(X27, implies(implies(X36,X34),implies(X37,X34))), % 45.44/6.04 bind(X28, implies(implies(X36,X34),implies(X37,X34))), % 45.44/6.04 bind(X29, implies(implies(implies(X30,X31),X32),implies(implies(X32,X30),implies(X33,X30)))), % 45.44/6.04 bind(X30, a), % 45.44/6.04 bind(X31, a), % 45.44/6.04 bind(X32, a), % 45.44/6.04 bind(X33, a), % 45.44/6.04 bind(X34, implies(X30,X31)), % 45.44/6.04 bind(X35, a), % 45.44/6.04 bind(X36, implies(implies(X32,X30),implies(X33,X30))), % 45.44/6.04 bind(X37, implies(implies(X20,X18),implies(X21,X18))), % 45.44/6.04 bind(X38, implies(X7,X6)), % 45.44/6.04 bind(X39, implies(implies(X20,X18),implies(X21,X18))), % 45.44/6.04 bind(X40, implies(implies(X20,X18),implies(X21,X18))), % 45.44/6.04 bind(X41, implies(implies(X32,X30),implies(X33,X30))), % 45.44/6.04 bind(X42, implies(X33,X30)), % 45.44/6.04 bind(X43, a), % 45.44/6.04 bind(X44, implies(X21,X18)), % 45.44/6.04 bind(X45, implies(implies(implies(X2,X3),X4),implies(implies(X4,X2),implies(X5,X2)))) % 45.44/6.04 ], % 45.44/6.04 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18])). % 45.44/6.04 % 45.44/6.04 % SZS output end IncompleteProof %------------------------------------------------------------------------------