%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL008-1 : 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 : n005.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 12:28:02 PM UTC 2026 % Result : Unsatisfiable 0.12s 0.36s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL008-1 : 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 % 0.10/0.35 % Computer : n005.cluster.edu % 0.10/0.35 % Model : x86_64 x86_64 % 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.35 % Memory : 8046.5625MB % 0.10/0.35 % OS : Linux 6.8.0-71-generic % 0.10/0.35 % CPULimit : 300 % 0.10/0.35 % WCLimit : 300 % 0.10/0.35 % DateTime : Fri Sep 4 22:42:35 UTC 2026 % 0.10/0.35 % CPUTime : % 0.12/0.36 % SZS status Unsatisfiable % 0.12/0.36 % SZS output begin IncompleteProof % 0.12/0.36 cnf(c0, axiom, % 0.12/0.36 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a)))). % 0.12/0.36 cnf(c1, plain, % 0.12/0.36 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))), % 0.12/0.36 inference(start, [], [c0])). % 0.12/0.36 % 0.12/0.36 cnf(c2, axiom, % 0.12/0.36 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 0.12/0.36 cnf(a0, assumption, % 0.12/0.36 equivalent(equivalent(a,b),equivalent(b,a)) = X0). % 0.12/0.36 cnf(c3, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.12/0.36 cnf(c4, plain, % 0.12/0.36 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.12/0.36 % 0.12/0.36 cnf(c5, axiom, % 0.12/0.36 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2))). % 0.12/0.36 cnf(a1, assumption, % 0.12/0.36 X1 = X2). % 0.12/0.36 cnf(c6, plain, % 0.12/0.36 ~is_a_theorem(equivalent(X1,X0)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.12/0.36 cnf(c7, plain, % 0.12/0.36 ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.12/0.36 % 0.12/0.36 cnf(c8, axiom, % 0.12/0.36 is_a_theorem(equivalent(equivalent(X4,X5),equivalent(equivalent(X6,X5),equivalent(X4,X6))))). % 0.12/0.36 cnf(a2, assumption, % 0.12/0.36 X3 = equivalent(equivalent(X4,X5),equivalent(equivalent(X6,X5),equivalent(X4,X6)))). % 0.12/0.36 cnf(c9, plain, % 0.12/0.36 ~is_a_theorem(equivalent(X3,X2)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.12/0.36 cnf(c10, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.12/0.36 % 0.12/0.36 cnf(c11, axiom, % 0.12/0.36 is_a_theorem(X7) | ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7))). % 0.12/0.36 cnf(a3, assumption, % 0.12/0.36 equivalent(X3,X2) = X7). % 0.12/0.36 cnf(c12, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a3])], [c9, c11])). % 0.12/0.36 cnf(c13, plain, % 0.12/0.36 ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a3])], [c9, c11])). % 0.12/0.36 % 0.12/0.36 cnf(c14, plain, % 0.12/0.36 is_a_theorem(X3)). % 0.12/0.36 cnf(a4, assumption, % 0.12/0.36 X8 = X3). % 0.12/0.36 cnf(c15, plain, % 0.12/0.36 ~is_a_theorem(equivalent(X8,X7)), % 0.12/0.36 inference(predicate_reduction, [assumptions([a4])], [c13, c14])). % 0.12/0.36 % 0.12/0.36 cnf(c16, axiom, % 0.12/0.36 is_a_theorem(X9) | ~is_a_theorem(X10) | ~is_a_theorem(equivalent(X10,X9))). % 0.12/0.36 cnf(a5, assumption, % 0.12/0.36 equivalent(X8,X7) = X9). % 0.12/0.36 cnf(c17, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a5])], [c15, c16])). % 0.12/0.36 cnf(c18, plain, % 0.12/0.36 ~is_a_theorem(X10) | ~is_a_theorem(equivalent(X10,X9)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a5])], [c15, c16])). % 0.12/0.36 % 0.12/0.36 cnf(c19, axiom, % 0.12/0.36 is_a_theorem(X11) | ~is_a_theorem(X12) | ~is_a_theorem(equivalent(X12,X11))). % 0.12/0.36 cnf(a6, assumption, % 0.12/0.36 X10 = X11). % 0.12/0.36 cnf(c20, plain, % 0.12/0.36 ~is_a_theorem(equivalent(X10,X9)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a6])], [c18, c19])). % 0.12/0.36 cnf(c21, plain, % 0.12/0.36 ~is_a_theorem(X12) | ~is_a_theorem(equivalent(X12,X11)), % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a6])], [c18, c19])). % 0.12/0.36 % 0.12/0.36 cnf(c22, plain, % 0.12/0.36 is_a_theorem(X3)). % 0.12/0.36 cnf(a7, assumption, % 0.12/0.36 X12 = X3). % 0.12/0.36 cnf(c23, plain, % 0.12/0.36 ~is_a_theorem(equivalent(X12,X11)), % 0.12/0.36 inference(predicate_reduction, [assumptions([a7])], [c21, c22])). % 0.12/0.36 % 0.12/0.36 cnf(c24, axiom, % 0.12/0.36 is_a_theorem(equivalent(equivalent(X13,X14),equivalent(equivalent(X15,X14),equivalent(X13,X15))))). % 0.12/0.36 cnf(a8, assumption, % 0.12/0.36 equivalent(X12,X11) = equivalent(equivalent(X13,X14),equivalent(equivalent(X15,X14),equivalent(X13,X15)))). % 0.12/0.36 cnf(c25, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a8])], [c23, c24])). % 0.12/0.36 cnf(c26, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a8])], [c23, c24])). % 0.12/0.36 % 0.12/0.36 cnf(c27, axiom, % 0.12/0.36 is_a_theorem(equivalent(equivalent(X16,X17),equivalent(equivalent(X18,X17),equivalent(X16,X18))))). % 0.12/0.36 cnf(a9, assumption, % 0.12/0.36 equivalent(X10,X9) = equivalent(equivalent(X16,X17),equivalent(equivalent(X18,X17),equivalent(X16,X18)))). % 0.12/0.36 cnf(c28, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a9])], [c20, c27])). % 0.12/0.36 cnf(c29, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a9])], [c20, c27])). % 0.12/0.36 % 0.12/0.36 cnf(c30, axiom, % 0.12/0.36 is_a_theorem(equivalent(equivalent(X19,X20),equivalent(equivalent(X21,X20),equivalent(X19,X21))))). % 0.12/0.36 cnf(a10, assumption, % 0.12/0.36 equivalent(X1,X0) = equivalent(equivalent(X19,X20),equivalent(equivalent(X21,X20),equivalent(X19,X21)))). % 0.12/0.36 cnf(c31, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a10])], [c6, c30])). % 0.12/0.36 cnf(c32, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(strict_predicate_extension, [assumptions([a10])], [c6, c30])). % 0.12/0.36 % 0.12/0.36 cnf(c33, plain, % 0.12/0.36 $false, % 0.12/0.36 inference(constraint_solving, [ % 0.12/0.36 bind(X0, equivalent(equivalent(a,b),equivalent(b,a))), % 0.12/0.36 bind(X1, equivalent(X4,X5)), % 0.12/0.36 bind(X2, equivalent(X4,X5)), % 0.12/0.36 bind(X3, equivalent(equivalent(X4,X5),equivalent(equivalent(X6,X5),equivalent(X4,X6)))), % 0.12/0.36 bind(X4, b), % 0.12/0.36 bind(X5, b), % 0.12/0.36 bind(X6, b), % 0.12/0.36 bind(X7, equivalent(X3,X2)), % 0.12/0.36 bind(X8, equivalent(equivalent(X4,X5),equivalent(equivalent(X6,X5),equivalent(X4,X6)))), % 0.12/0.36 bind(X9, equivalent(X8,X7)), % 0.12/0.36 bind(X10, equivalent(equivalent(X15,X14),equivalent(X13,X15))), % 0.12/0.36 bind(X11, equivalent(equivalent(X15,X14),equivalent(X13,X15))), % 0.12/0.36 bind(X12, equivalent(equivalent(X4,X5),equivalent(equivalent(X6,X5),equivalent(X4,X6)))), % 0.12/0.36 bind(X13, equivalent(X4,X5)), % 0.12/0.36 bind(X14, equivalent(equivalent(X6,X5),equivalent(X4,X6))), % 0.12/0.36 bind(X15, equivalent(X4,X6)), % 0.12/0.36 bind(X16, equivalent(X15,X14)), % 0.12/0.36 bind(X17, equivalent(X13,X15)), % 0.12/0.36 bind(X18, equivalent(X4,X5)), % 0.12/0.36 bind(X19, b), % 0.12/0.36 bind(X20, b), % 0.12/0.36 bind(X21, a) % 0.12/0.36 ], % 0.12/0.36 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10])). % 0.12/0.36 % 0.12/0.36 % SZS output end IncompleteProof %------------------------------------------------------------------------------