%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL126-1 : 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 : n010.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 12:28:11 PM UTC 2026 % Result : Unsatisfiable 0.09s 0.38s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL126-1 : 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 % 0.09/0.36 % Computer : n010.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 10:58:53 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.38 % SZS status Unsatisfiable % 0.09/0.38 % SZS output begin IncompleteProof % 0.09/0.38 cnf(c0, axiom, % 0.09/0.38 ~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))). % 0.09/0.38 cnf(c1, plain, % 0.09/0.38 ~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))), % 0.09/0.38 inference(start, [], [c0])). % 0.09/0.38 % 0.09/0.38 cnf(c2, axiom, % 0.09/0.38 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 0.09/0.38 cnf(a0, assumption, % 0.09/0.38 equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)) = X0). % 0.09/0.38 cnf(c3, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.09/0.38 cnf(c4, plain, % 0.09/0.38 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.09/0.38 % 0.09/0.38 cnf(c5, axiom, % 0.09/0.38 is_a_theorem(equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3))))). % 0.09/0.38 cnf(a1, assumption, % 0.09/0.38 X1 = equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)))). % 0.09/0.38 cnf(c6, plain, % 0.09/0.38 ~is_a_theorem(equivalent(X1,X0)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.09/0.38 cnf(c7, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.09/0.38 % 0.09/0.38 cnf(c8, axiom, % 0.09/0.38 is_a_theorem(X5) | ~is_a_theorem(X6) | ~is_a_theorem(equivalent(X6,X5))). % 0.09/0.38 cnf(a2, assumption, % 0.09/0.38 equivalent(X1,X0) = X5). % 0.09/0.38 cnf(c9, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 0.09/0.38 cnf(c10, plain, % 0.09/0.38 ~is_a_theorem(X6) | ~is_a_theorem(equivalent(X6,X5)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 0.09/0.38 % 0.09/0.38 cnf(c11, axiom, % 0.09/0.38 is_a_theorem(equivalent(equivalent(X7,X8),equivalent(equivalent(X7,X9),equivalent(X8,X9))))). % 0.09/0.38 cnf(a3, assumption, % 0.09/0.38 X6 = equivalent(equivalent(X7,X8),equivalent(equivalent(X7,X9),equivalent(X8,X9)))). % 0.09/0.38 cnf(c12, plain, % 0.09/0.38 ~is_a_theorem(equivalent(X6,X5)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.09/0.38 cnf(c13, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.09/0.38 % 0.09/0.38 cnf(c14, axiom, % 0.09/0.38 is_a_theorem(X10) | ~is_a_theorem(X11) | ~is_a_theorem(equivalent(X11,X10))). % 0.09/0.38 cnf(a4, assumption, % 0.09/0.38 equivalent(X6,X5) = X10). % 0.09/0.38 cnf(c15, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.09/0.38 cnf(c16, plain, % 0.09/0.38 ~is_a_theorem(X11) | ~is_a_theorem(equivalent(X11,X10)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.09/0.38 % 0.09/0.38 cnf(c17, axiom, % 0.09/0.38 is_a_theorem(equivalent(X12,equivalent(equivalent(X12,equivalent(X13,X14)),equivalent(X14,X13))))). % 0.09/0.38 cnf(a5, assumption, % 0.09/0.38 X11 = equivalent(X12,equivalent(equivalent(X12,equivalent(X13,X14)),equivalent(X14,X13)))). % 0.09/0.38 cnf(c18, plain, % 0.09/0.38 ~is_a_theorem(equivalent(X11,X10)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 0.09/0.38 cnf(c19, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 0.09/0.38 % 0.09/0.38 cnf(c20, axiom, % 0.09/0.38 is_a_theorem(X15) | ~is_a_theorem(X16) | ~is_a_theorem(equivalent(X16,X15))). % 0.09/0.38 cnf(a6, assumption, % 0.09/0.38 equivalent(X11,X10) = X15). % 0.09/0.38 cnf(c21, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a6])], [c18, c20])). % 0.09/0.38 cnf(c22, plain, % 0.09/0.38 ~is_a_theorem(X16) | ~is_a_theorem(equivalent(X16,X15)), % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a6])], [c18, c20])). % 0.09/0.38 % 0.09/0.38 cnf(c23, plain, % 0.09/0.38 is_a_theorem(X1)). % 0.09/0.38 cnf(a7, assumption, % 0.09/0.38 X16 = X1). % 0.09/0.38 cnf(c24, plain, % 0.09/0.38 ~is_a_theorem(equivalent(X16,X15)), % 0.09/0.38 inference(predicate_reduction, [assumptions([a7])], [c22, c23])). % 0.09/0.38 % 0.09/0.38 cnf(c25, axiom, % 0.09/0.38 is_a_theorem(equivalent(X17,equivalent(equivalent(X17,equivalent(X18,X19)),equivalent(X19,X18))))). % 0.09/0.38 cnf(a8, assumption, % 0.09/0.38 equivalent(X16,X15) = equivalent(X17,equivalent(equivalent(X17,equivalent(X18,X19)),equivalent(X19,X18)))). % 0.09/0.38 cnf(c26, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 0.09/0.38 cnf(c27, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 0.09/0.38 % 0.09/0.38 cnf(c28, plain, % 0.09/0.38 $false, % 0.09/0.38 inference(constraint_solving, [ % 0.09/0.38 bind(X0, equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))), % 0.09/0.38 bind(X1, equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)))), % 0.09/0.38 bind(X2, X2), % 0.09/0.38 bind(X3, X3), % 0.09/0.38 bind(X4, X4), % 0.09/0.38 bind(X5, equivalent(X1,X0)), % 0.09/0.38 bind(X6, equivalent(equivalent(X7,X8),equivalent(equivalent(X7,X9),equivalent(X8,X9)))), % 0.09/0.38 bind(X7, a), % 0.09/0.38 bind(X8, c), % 0.09/0.38 bind(X9, b), % 0.09/0.38 bind(X10, equivalent(X6,X5)), % 0.09/0.38 bind(X11, equivalent(X12,equivalent(equivalent(X12,equivalent(X13,X14)),equivalent(X14,X13)))), % 0.09/0.38 bind(X12, equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)))), % 0.09/0.38 bind(X13, equivalent(equivalent(X7,X9),equivalent(X8,X9))), % 0.09/0.38 bind(X14, equivalent(X7,X8)), % 0.09/0.38 bind(X15, equivalent(X11,X10)), % 0.09/0.38 bind(X16, equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)))), % 0.09/0.38 bind(X17, equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X4)),equivalent(X4,X3)))), % 0.09/0.38 bind(X18, equivalent(X12,equivalent(X13,X14))), % 0.09/0.38 bind(X19, equivalent(X14,X13)) % 0.09/0.38 ], % 0.09/0.38 [a0, a1, a2, a3, a4, a5, a6, a7, a8])). % 0.09/0.38 % 0.09/0.38 % SZS output end IncompleteProof %------------------------------------------------------------------------------