%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n006.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 12:28:50 PM UTC 2026 % Result : Theorem 0.14s 0.39s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.03 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.08/0.34 % Computer : n006.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sat Sep 5 21:49:31 UTC 2026 % 0.08/0.34 % CPUTime : % 0.14/0.39 % SZS status Theorem % 0.14/0.39 % SZS output begin IncompleteProof % 0.14/0.39 cnf(c0, axiom, % 0.14/0.39 ~axiom_m2). % 0.14/0.39 cnf(c1, plain, % 0.14/0.39 ~axiom_m2, % 0.14/0.39 inference(start, [], [c0])). % 0.14/0.39 % 0.14/0.39 cnf(c2, axiom, % 0.14/0.39 axiom_m2 | ~is_a_theorem(strict_implies(and(sK78,sK79),sK78))). % 0.14/0.39 cnf(c3, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c1, c2])). % 0.14/0.39 cnf(c4, plain, % 0.14/0.39 ~is_a_theorem(strict_implies(and(sK78,sK79),sK78)), % 0.14/0.39 inference(strict_predicate_extension, [], [c1, c2])). % 0.14/0.39 % 0.14/0.39 cnf(c5, axiom, % 0.14/0.39 strict_implies(X0,X1) = necessarily(implies(X0,X1)) | ~op_strict_implies). % 0.14/0.39 cnf(a0, assumption, % 0.14/0.39 strict_implies(and(sK78,sK79),sK78) = strict_implies(X0,X1)). % 0.14/0.39 cnf(c6, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 0.14/0.39 cnf(c7, plain, % 0.14/0.39 ~op_strict_implies, % 0.14/0.39 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 0.14/0.39 cnf(c8, plain, % 0.14/0.39 X2 != necessarily(implies(X0,X1)) | ~is_a_theorem(X2), % 0.14/0.39 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 0.14/0.39 % 0.14/0.39 cnf(a1, assumption, % 0.14/0.39 X2 = necessarily(implies(X0,X1))). % 0.14/0.39 cnf(c9, plain, % 0.14/0.39 ~is_a_theorem(X2), % 0.14/0.39 inference(reflexivity, [assumptions([a1])], [c8])). % 0.14/0.39 % 0.14/0.39 cnf(c10, axiom, % 0.14/0.39 is_a_theorem(necessarily(X3)) | ~is_a_theorem(X3) | ~necessitation). % 0.14/0.39 cnf(a2, assumption, % 0.14/0.39 X2 = necessarily(X3)). % 0.14/0.39 cnf(c11, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [assumptions([a2])], [c9, c10])). % 0.14/0.39 cnf(c12, plain, % 0.14/0.39 ~is_a_theorem(X3) | ~necessitation, % 0.14/0.39 inference(strict_predicate_extension, [assumptions([a2])], [c9, c10])). % 0.14/0.39 % 0.14/0.39 cnf(c13, axiom, % 0.14/0.39 is_a_theorem(implies(and(X4,X5),X4)) | ~and_1). % 0.14/0.39 cnf(a3, assumption, % 0.14/0.39 X3 = implies(and(X4,X5),X4)). % 0.14/0.39 cnf(c14, plain, % 0.14/0.39 ~necessitation, % 0.14/0.39 inference(strict_predicate_extension, [assumptions([a3])], [c12, c13])). % 0.14/0.39 cnf(c15, plain, % 0.14/0.39 ~and_1, % 0.14/0.39 inference(strict_predicate_extension, [assumptions([a3])], [c12, c13])). % 0.14/0.39 % 0.14/0.39 cnf(c16, axiom, % 0.14/0.39 and_1). % 0.14/0.39 cnf(c17, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c15, c16])). % 0.14/0.39 cnf(c18, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c15, c16])). % 0.14/0.39 % 0.14/0.39 cnf(c19, axiom, % 0.14/0.39 necessitation). % 0.14/0.39 cnf(c20, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c14, c19])). % 0.14/0.39 cnf(c21, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c14, c19])). % 0.14/0.39 % 0.14/0.39 cnf(c22, axiom, % 0.14/0.39 op_strict_implies). % 0.14/0.39 cnf(c23, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c7, c22])). % 0.14/0.39 cnf(c24, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(strict_predicate_extension, [], [c7, c22])). % 0.14/0.39 % 0.14/0.39 cnf(c25, plain, % 0.14/0.39 $false, % 0.14/0.39 inference(constraint_solving, [ % 0.14/0.39 bind(X0, and(sK78,sK79)), % 0.14/0.39 bind(X1, sK78), % 0.14/0.39 bind(X2, necessarily(implies(X0,X1))), % 0.14/0.39 bind(X3, implies(X0,X1)), % 0.14/0.39 bind(X4, sK78), % 0.14/0.39 bind(X5, sK79) % 0.14/0.39 ], % 0.14/0.39 [a0, a1, a2, a3])). % 0.14/0.39 % 0.14/0.39 % SZS output end IncompleteProof %------------------------------------------------------------------------------