%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL544+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 : n007.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 73.77s 9.80s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.04 % Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.06 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.14/0.41 % Computer : n007.cluster.edu % 0.14/0.41 % Model : x86_64 x86_64 % 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.41 % Memory : 8046.5625MB % 0.14/0.41 % OS : Linux 6.8.0-71-generic % 0.14/0.41 % CPULimit : 300 % 0.14/0.41 % WCLimit : 300 % 0.14/0.41 % DateTime : Sat Sep 5 20:11:39 UTC 2026 % 0.14/0.41 % CPUTime : % 73.77/9.80 % SZS status Theorem % 73.77/9.80 % SZS output begin IncompleteProof % 73.77/9.80 cnf(c0, axiom, % 73.77/9.80 ~axiom_m4). % 73.77/9.80 cnf(c1, plain, % 73.77/9.80 ~axiom_m4, % 73.77/9.80 inference(start, [], [c0])). % 73.77/9.80 % 73.77/9.80 cnf(c2, axiom, % 73.77/9.80 axiom_m4 | ~is_a_theorem(strict_implies(sK83,and(sK83,sK83)))). % 73.77/9.80 cnf(c3, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c1, c2])). % 73.77/9.80 cnf(c4, plain, % 73.77/9.80 ~is_a_theorem(strict_implies(sK83,and(sK83,sK83))), % 73.77/9.80 inference(strict_predicate_extension, [], [c1, c2])). % 73.77/9.80 % 73.77/9.80 cnf(c5, axiom, % 73.77/9.80 strict_implies(X0,X1) = necessarily(implies(X0,X1)) | ~op_strict_implies). % 73.77/9.80 cnf(a0, assumption, % 73.77/9.80 strict_implies(sK83,and(sK83,sK83)) = strict_implies(X0,X1)). % 73.77/9.80 cnf(c6, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 73.77/9.80 cnf(c7, plain, % 73.77/9.80 ~op_strict_implies, % 73.77/9.80 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 73.77/9.80 cnf(c8, plain, % 73.77/9.80 X2 != necessarily(implies(X0,X1)) | ~is_a_theorem(X2), % 73.77/9.80 inference(strict_function_extension, [assumptions([a0])], [c4, c5])). % 73.77/9.80 % 73.77/9.80 cnf(a1, assumption, % 73.77/9.80 X2 = necessarily(implies(X0,X1))). % 73.77/9.80 cnf(c9, plain, % 73.77/9.80 ~is_a_theorem(X2), % 73.77/9.80 inference(reflexivity, [assumptions([a1])], [c8])). % 73.77/9.80 % 73.77/9.80 cnf(c10, axiom, % 73.77/9.80 is_a_theorem(necessarily(X3)) | ~is_a_theorem(X3) | ~necessitation). % 73.77/9.80 cnf(a2, assumption, % 73.77/9.80 X2 = necessarily(X3)). % 73.77/9.80 cnf(c11, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a2])], [c9, c10])). % 73.77/9.80 cnf(c12, plain, % 73.77/9.80 ~is_a_theorem(X3) | ~necessitation, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a2])], [c9, c10])). % 73.77/9.80 % 73.77/9.80 cnf(c13, axiom, % 73.77/9.80 is_a_theorem(X4) | ~is_a_theorem(implies(X5,X4)) | ~is_a_theorem(X5) | ~modus_ponens). % 73.77/9.80 cnf(a3, assumption, % 73.77/9.80 X3 = X4). % 73.77/9.80 cnf(c14, plain, % 73.77/9.80 ~necessitation, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a3])], [c12, c13])). % 73.77/9.80 cnf(c15, plain, % 73.77/9.80 ~is_a_theorem(implies(X5,X4)) | ~is_a_theorem(X5) | ~modus_ponens, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a3])], [c12, c13])). % 73.77/9.80 % 73.77/9.80 cnf(c16, axiom, % 73.77/9.80 is_a_theorem(implies(implies(X6,implies(X6,X7)),implies(X6,X7))) | ~implies_2). % 73.77/9.80 cnf(a4, assumption, % 73.77/9.80 implies(X5,X4) = implies(implies(X6,implies(X6,X7)),implies(X6,X7))). % 73.77/9.80 cnf(c17, plain, % 73.77/9.80 ~is_a_theorem(X5) | ~modus_ponens, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a4])], [c15, c16])). % 73.77/9.80 cnf(c18, plain, % 73.77/9.80 ~implies_2, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a4])], [c15, c16])). % 73.77/9.80 % 73.77/9.80 cnf(c19, axiom, % 73.77/9.80 implies_2). % 73.77/9.80 cnf(c20, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c18, c19])). % 73.77/9.80 cnf(c21, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c18, c19])). % 73.77/9.80 % 73.77/9.80 cnf(c22, axiom, % 73.77/9.80 is_a_theorem(implies(X8,implies(X9,and(X8,X9)))) | ~and_3). % 73.77/9.80 cnf(a5, assumption, % 73.77/9.80 X5 = implies(X8,implies(X9,and(X8,X9)))). % 73.77/9.80 cnf(c23, plain, % 73.77/9.80 ~modus_ponens, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a5])], [c17, c22])). % 73.77/9.80 cnf(c24, plain, % 73.77/9.80 ~and_3, % 73.77/9.80 inference(strict_predicate_extension, [assumptions([a5])], [c17, c22])). % 73.77/9.80 % 73.77/9.80 cnf(c25, axiom, % 73.77/9.80 and_3). % 73.77/9.80 cnf(c26, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c24, c25])). % 73.77/9.80 cnf(c27, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c24, c25])). % 73.77/9.80 % 73.77/9.80 cnf(c28, axiom, % 73.77/9.80 modus_ponens). % 73.77/9.80 cnf(c29, plain, % 73.77/9.80 $false, % 73.77/9.80 inference(strict_predicate_extension, [], [c23, c28])). % 73.77/9.81 cnf(c30, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(strict_predicate_extension, [], [c23, c28])). % 73.77/9.81 % 73.77/9.81 cnf(c31, axiom, % 73.77/9.81 necessitation). % 73.77/9.81 cnf(c32, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(strict_predicate_extension, [], [c14, c31])). % 73.77/9.81 cnf(c33, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(strict_predicate_extension, [], [c14, c31])). % 73.77/9.81 % 73.77/9.81 cnf(c34, axiom, % 73.77/9.81 op_strict_implies). % 73.77/9.81 cnf(c35, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(strict_predicate_extension, [], [c7, c34])). % 73.77/9.81 cnf(c36, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(strict_predicate_extension, [], [c7, c34])). % 73.77/9.81 % 73.77/9.81 cnf(c37, plain, % 73.77/9.81 $false, % 73.77/9.81 inference(constraint_solving, [ % 73.77/9.81 bind(X0, sK83), % 73.77/9.81 bind(X1, and(sK83,sK83)), % 73.77/9.81 bind(X2, necessarily(implies(X0,X1))), % 73.77/9.81 bind(X3, implies(X0,X1)), % 73.77/9.81 bind(X4, implies(X0,X1)), % 73.77/9.81 bind(X5, implies(X6,implies(X6,X7))), % 73.77/9.81 bind(X6, sK83), % 73.77/9.81 bind(X7, and(sK83,sK83)), % 73.77/9.81 bind(X8, sK83), % 73.77/9.81 bind(X9, sK83) % 73.77/9.81 ], % 73.77/9.81 [a0, a1, a2, a3, a4, a5])). % 73.77/9.81 % 73.77/9.81 % SZS output end IncompleteProof %------------------------------------------------------------------------------