%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL033-1 : 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 : n002.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 12:28:04 PM UTC 2026 % Result : Unsatisfiable 0.13s 0.45s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL033-1 : 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 % 0.07/0.35 % Computer : n002.cluster.edu % 0.07/0.35 % Model : x86_64 x86_64 % 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.35 % Memory : 8046.5625MB % 0.07/0.35 % OS : Linux 6.8.0-71-generic % 0.07/0.35 % CPULimit : 300 % 0.07/0.35 % WCLimit : 300 % 0.07/0.35 % DateTime : Fri Sep 4 18:52:20 UTC 2026 % 0.07/0.35 % CPUTime : % 0.13/0.45 % SZS status Unsatisfiable % 0.13/0.45 % SZS output begin IncompleteProof % 0.13/0.45 cnf(c0, axiom, % 0.13/0.45 ~is_a_theorem(implies(a,implies(b,a)))). % 0.13/0.45 cnf(c1, plain, % 0.13/0.45 ~is_a_theorem(implies(a,implies(b,a))), % 0.13/0.45 inference(start, [], [c0])). % 0.13/0.45 % 0.13/0.45 cnf(c2, axiom, % 0.13/0.45 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 0.13/0.45 cnf(a0, assumption, % 0.13/0.45 implies(a,implies(b,a)) = X0). % 0.13/0.45 cnf(c3, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.13/0.45 cnf(c4, plain, % 0.13/0.45 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.13/0.45 % 0.13/0.45 cnf(c5, axiom, % 0.13/0.45 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2))). % 0.13/0.45 cnf(a1, assumption, % 0.13/0.45 X1 = X2). % 0.13/0.45 cnf(c6, plain, % 0.13/0.45 ~is_a_theorem(implies(X1,X0)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.13/0.45 cnf(c7, plain, % 0.13/0.45 ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.13/0.45 % 0.13/0.45 cnf(c8, axiom, % 0.13/0.45 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4))). % 0.13/0.45 cnf(a2, assumption, % 0.13/0.45 X3 = X4). % 0.13/0.45 cnf(c9, plain, % 0.13/0.45 ~is_a_theorem(implies(X3,X2)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.13/0.45 cnf(c10, plain, % 0.13/0.45 ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.13/0.45 % 0.13/0.45 cnf(c11, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X6,X7),implies(X8,falsehood)),X9),X10),implies(implies(X10,X6),implies(X8,X6))))). % 0.13/0.45 cnf(a3, assumption, % 0.13/0.45 X5 = implies(implies(implies(implies(implies(X6,X7),implies(X8,falsehood)),X9),X10),implies(implies(X10,X6),implies(X8,X6)))). % 0.13/0.45 cnf(c12, plain, % 0.13/0.45 ~is_a_theorem(implies(X5,X4)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.13/0.45 cnf(c13, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.13/0.45 % 0.13/0.45 cnf(c14, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X11,X12),implies(X13,falsehood)),X14),X15),implies(implies(X15,X11),implies(X13,X11))))). % 0.13/0.45 cnf(a4, assumption, % 0.13/0.45 implies(X5,X4) = implies(implies(implies(implies(implies(X11,X12),implies(X13,falsehood)),X14),X15),implies(implies(X15,X11),implies(X13,X11)))). % 0.13/0.45 cnf(c15, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.13/0.45 cnf(c16, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.13/0.45 % 0.13/0.45 cnf(c17, axiom, % 0.13/0.45 is_a_theorem(X16) | ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16))). % 0.13/0.45 cnf(a5, assumption, % 0.13/0.45 implies(X3,X2) = X16). % 0.13/0.45 cnf(c18, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 0.13/0.45 cnf(c19, plain, % 0.13/0.45 ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 0.13/0.45 % 0.13/0.45 cnf(c20, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X18,X19),implies(X20,falsehood)),X21),X22),implies(implies(X22,X18),implies(X20,X18))))). % 0.13/0.45 cnf(a6, assumption, % 0.13/0.45 X17 = implies(implies(implies(implies(implies(X18,X19),implies(X20,falsehood)),X21),X22),implies(implies(X22,X18),implies(X20,X18)))). % 0.13/0.45 cnf(c21, plain, % 0.13/0.45 ~is_a_theorem(implies(X17,X16)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 0.13/0.45 cnf(c22, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 0.13/0.45 % 0.13/0.45 cnf(c23, axiom, % 0.13/0.45 is_a_theorem(X23) | ~is_a_theorem(X24) | ~is_a_theorem(implies(X24,X23))). % 0.13/0.45 cnf(a7, assumption, % 0.13/0.45 implies(X17,X16) = X23). % 0.13/0.45 cnf(c24, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 0.13/0.45 cnf(c25, plain, % 0.13/0.45 ~is_a_theorem(X24) | ~is_a_theorem(implies(X24,X23)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 0.13/0.45 % 0.13/0.45 cnf(c26, axiom, % 0.13/0.45 is_a_theorem(X25) | ~is_a_theorem(X26) | ~is_a_theorem(implies(X26,X25))). % 0.13/0.45 cnf(a8, assumption, % 0.13/0.45 X24 = X25). % 0.13/0.45 cnf(c27, plain, % 0.13/0.45 ~is_a_theorem(implies(X24,X23)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 0.13/0.45 cnf(c28, plain, % 0.13/0.45 ~is_a_theorem(X26) | ~is_a_theorem(implies(X26,X25)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 0.13/0.45 % 0.13/0.45 cnf(c29, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X27,X28),implies(X29,falsehood)),X30),X31),implies(implies(X31,X27),implies(X29,X27))))). % 0.13/0.45 cnf(a9, assumption, % 0.13/0.45 X26 = implies(implies(implies(implies(implies(X27,X28),implies(X29,falsehood)),X30),X31),implies(implies(X31,X27),implies(X29,X27)))). % 0.13/0.45 cnf(c30, plain, % 0.13/0.45 ~is_a_theorem(implies(X26,X25)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 0.13/0.45 cnf(c31, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 0.13/0.45 % 0.13/0.45 cnf(c32, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X32,X33),implies(X34,falsehood)),X35),X36),implies(implies(X36,X32),implies(X34,X32))))). % 0.13/0.45 cnf(a10, assumption, % 0.13/0.45 implies(X26,X25) = implies(implies(implies(implies(implies(X32,X33),implies(X34,falsehood)),X35),X36),implies(implies(X36,X32),implies(X34,X32)))). % 0.13/0.45 cnf(c33, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 0.13/0.45 cnf(c34, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 0.13/0.45 % 0.13/0.45 cnf(c35, axiom, % 0.13/0.45 is_a_theorem(implies(implies(implies(implies(implies(X37,X38),implies(X39,falsehood)),X40),X41),implies(implies(X41,X37),implies(X39,X37))))). % 0.13/0.45 cnf(a11, assumption, % 0.13/0.45 implies(X24,X23) = implies(implies(implies(implies(implies(X37,X38),implies(X39,falsehood)),X40),X41),implies(implies(X41,X37),implies(X39,X37)))). % 0.13/0.45 cnf(c36, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 0.13/0.45 cnf(c37, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 0.13/0.45 % 0.13/0.45 cnf(c38, axiom, % 0.13/0.45 is_a_theorem(X42) | ~is_a_theorem(X43) | ~is_a_theorem(implies(X43,X42))). % 0.13/0.45 cnf(a12, assumption, % 0.13/0.45 implies(X1,X0) = X42). % 0.13/0.45 cnf(c39, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a12])], [c6, c38])). % 0.13/0.45 cnf(c40, plain, % 0.13/0.45 ~is_a_theorem(X43) | ~is_a_theorem(implies(X43,X42)), % 0.13/0.45 inference(strict_predicate_extension, [assumptions([a12])], [c6, c38])). % 0.13/0.45 % 0.13/0.45 cnf(c41, plain, % 0.13/0.45 is_a_theorem(X1)). % 0.13/0.45 cnf(a13, assumption, % 0.13/0.45 X43 = X1). % 0.13/0.45 cnf(c42, plain, % 0.13/0.45 ~is_a_theorem(implies(X43,X42)), % 0.13/0.45 inference(predicate_reduction, [assumptions([a13])], [c40, c41])). % 0.13/0.45 % 0.13/0.45 cnf(c43, plain, % 0.13/0.45 is_a_theorem(X3)). % 0.13/0.45 cnf(a14, assumption, % 0.13/0.45 implies(X43,X42) = X3). % 0.13/0.45 cnf(c44, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(predicate_reduction, [assumptions([a14])], [c42, c43])). % 0.13/0.45 % 0.13/0.45 cnf(c45, plain, % 0.13/0.45 $false, % 0.13/0.45 inference(constraint_solving, [ % 0.13/0.45 bind(X0, implies(a,implies(b,a))), % 0.13/0.45 bind(X1, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X2, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X3, implies(implies(X15,X11),implies(X13,X11))), % 0.13/0.45 bind(X4, implies(implies(X15,X11),implies(X13,X11))), % 0.13/0.45 bind(X5, implies(implies(implies(implies(implies(X6,X7),implies(X8,falsehood)),X9),X10),implies(implies(X10,X6),implies(X8,X6)))), % 0.13/0.45 bind(X6, a), % 0.13/0.45 bind(X7, implies(X8,X6)), % 0.13/0.45 bind(X8, b), % 0.13/0.45 bind(X9, implies(X13,falsehood)), % 0.13/0.45 bind(X10, falsehood), % 0.13/0.45 bind(X11, implies(X6,X7)), % 0.13/0.45 bind(X12, implies(X8,falsehood)), % 0.13/0.45 bind(X13, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X14, falsehood), % 0.13/0.45 bind(X15, implies(implies(X10,X6),implies(X8,X6))), % 0.13/0.45 bind(X16, implies(X3,X2)), % 0.13/0.45 bind(X17, implies(implies(implies(implies(implies(X18,X19),implies(X20,falsehood)),X21),X22),implies(implies(X22,X18),implies(X20,X18)))), % 0.13/0.45 bind(X18, implies(X8,X6)), % 0.13/0.45 bind(X19, X19), % 0.13/0.45 bind(X20, a), % 0.13/0.45 bind(X21, X21), % 0.13/0.45 bind(X22, implies(X27,X28)), % 0.13/0.45 bind(X23, implies(X17,X16)), % 0.13/0.45 bind(X24, implies(implies(X36,X32),implies(X34,X32))), % 0.13/0.45 bind(X25, implies(implies(X36,X32),implies(X34,X32))), % 0.13/0.45 bind(X26, implies(implies(implies(implies(implies(X27,X28),implies(X29,falsehood)),X30),X31),implies(implies(X31,X27),implies(X29,X27)))), % 0.13/0.45 bind(X27, falsehood), % 0.13/0.45 bind(X28, a), % 0.13/0.45 bind(X29, implies(implies(X15,X11),implies(X13,X11))), % 0.13/0.45 bind(X30, implies(X34,falsehood)), % 0.13/0.45 bind(X31, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X32, implies(X27,X28)), % 0.13/0.45 bind(X33, implies(X29,falsehood)), % 0.13/0.45 bind(X34, implies(implies(implies(X18,X19),implies(X20,falsehood)),X21)), % 0.13/0.45 bind(X35, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X36, implies(implies(X31,X27),implies(X29,X27))), % 0.13/0.45 bind(X37, implies(implies(X22,X18),implies(X20,X18))), % 0.13/0.45 bind(X38, falsehood), % 0.13/0.45 bind(X39, implies(implies(X15,X11),implies(X13,X11))), % 0.13/0.45 bind(X40, implies(X27,X28)), % 0.13/0.45 bind(X41, implies(X34,X32)), % 0.13/0.45 bind(X42, implies(X1,X0)), % 0.13/0.45 bind(X43, implies(implies(X22,X18),implies(X20,X18))) % 0.13/0.45 ], % 0.13/0.45 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 0.13/0.45 % 0.13/0.45 % SZS output end IncompleteProof %------------------------------------------------------------------------------