%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL010-1 : 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 : n029.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 113.01s 14.65s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0. % 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 : n029.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 12:41:10 UTC 2026 % 0.08/0.34 % CPUTime : % 113.01/14.65 % SZS status Unsatisfiable % 113.01/14.65 % SZS output begin IncompleteProof % 113.01/14.65 cnf(c0, axiom, % 113.01/14.65 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c))))). % 113.01/14.65 cnf(c1, plain, % 113.01/14.65 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))), % 113.01/14.65 inference(start, [], [c0])). % 113.01/14.65 % 113.01/14.65 cnf(c2, axiom, % 113.01/14.65 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 113.01/14.65 cnf(a0, assumption, % 113.01/14.65 equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c))) = X0). % 113.01/14.65 cnf(c3, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 113.01/14.65 cnf(c4, plain, % 113.01/14.65 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 113.01/14.65 % 113.01/14.65 cnf(c5, axiom, % 113.01/14.65 is_a_theorem(equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X4,X3))))). % 113.01/14.65 cnf(a1, assumption, % 113.01/14.65 X1 = equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X4,X3)))). % 113.01/14.65 cnf(c6, plain, % 113.01/14.65 ~is_a_theorem(equivalent(X1,X0)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 113.01/14.65 cnf(c7, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 113.01/14.65 % 113.01/14.65 cnf(c8, axiom, % 113.01/14.65 is_a_theorem(X5) | ~is_a_theorem(X6) | ~is_a_theorem(equivalent(X6,X5))). % 113.01/14.65 cnf(a2, assumption, % 113.01/14.65 equivalent(X1,X0) = X5). % 113.01/14.65 cnf(c9, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 113.01/14.65 cnf(c10, plain, % 113.01/14.65 ~is_a_theorem(X6) | ~is_a_theorem(equivalent(X6,X5)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 113.01/14.65 % 113.01/14.65 cnf(c11, axiom, % 113.01/14.65 is_a_theorem(X7) | ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7))). % 113.01/14.65 cnf(a3, assumption, % 113.01/14.65 X6 = X7). % 113.01/14.65 cnf(c12, plain, % 113.01/14.65 ~is_a_theorem(equivalent(X6,X5)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 113.01/14.65 cnf(c13, plain, % 113.01/14.65 ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 113.01/14.65 % 113.01/14.65 cnf(c14, plain, % 113.01/14.65 is_a_theorem(X1)). % 113.01/14.65 cnf(a4, assumption, % 113.01/14.65 X8 = X1). % 113.01/14.65 cnf(c15, plain, % 113.01/14.65 ~is_a_theorem(equivalent(X8,X7)), % 113.01/14.65 inference(predicate_reduction, [assumptions([a4])], [c13, c14])). % 113.01/14.65 % 113.01/14.65 cnf(c16, axiom, % 113.01/14.65 is_a_theorem(equivalent(equivalent(X9,X10),equivalent(equivalent(X9,X11),equivalent(X11,X10))))). % 113.01/14.65 cnf(a5, assumption, % 113.01/14.65 equivalent(X8,X7) = equivalent(equivalent(X9,X10),equivalent(equivalent(X9,X11),equivalent(X11,X10)))). % 113.01/14.65 cnf(c17, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a5])], [c15, c16])). % 113.01/14.65 cnf(c18, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a5])], [c15, c16])). % 113.01/14.65 % 113.01/14.65 cnf(c19, axiom, % 113.01/14.65 is_a_theorem(X12) | ~is_a_theorem(X13) | ~is_a_theorem(equivalent(X13,X12))). % 113.01/14.65 cnf(a6, assumption, % 113.01/14.65 equivalent(X6,X5) = X12). % 113.01/14.65 cnf(c20, plain, % 113.01/14.65 $false, % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a6])], [c12, c19])). % 113.01/14.65 cnf(c21, plain, % 113.01/14.65 ~is_a_theorem(X13) | ~is_a_theorem(equivalent(X13,X12)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a6])], [c12, c19])). % 113.01/14.65 % 113.01/14.65 cnf(c22, axiom, % 113.01/14.65 is_a_theorem(X14) | ~is_a_theorem(X15) | ~is_a_theorem(equivalent(X15,X14))). % 113.01/14.65 cnf(a7, assumption, % 113.01/14.65 X13 = X14). % 113.01/14.65 cnf(c23, plain, % 113.01/14.65 ~is_a_theorem(equivalent(X13,X12)), % 113.01/14.65 inference(strict_predicate_extension, [assumptions([a7])], [c21, c22])). % 113.01/14.65 cnf(c24, plain, % 113.01/14.65 ~is_a_theorem(X15) | ~is_a_theorem(equivalent(X15,X14)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a7])], [c21, c22])). % 113.01/14.66 % 113.01/14.66 cnf(c25, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X16,X17),equivalent(equivalent(X16,X18),equivalent(X18,X17))))). % 113.01/14.66 cnf(a8, assumption, % 113.01/14.66 X15 = equivalent(equivalent(X16,X17),equivalent(equivalent(X16,X18),equivalent(X18,X17)))). % 113.01/14.66 cnf(c26, plain, % 113.01/14.66 ~is_a_theorem(equivalent(X15,X14)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 113.01/14.66 cnf(c27, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a8])], [c24, c25])). % 113.01/14.66 % 113.01/14.66 cnf(c28, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X19,X20),equivalent(equivalent(X19,X21),equivalent(X21,X20))))). % 113.01/14.66 cnf(a9, assumption, % 113.01/14.66 equivalent(X15,X14) = equivalent(equivalent(X19,X20),equivalent(equivalent(X19,X21),equivalent(X21,X20)))). % 113.01/14.66 cnf(c29, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a9])], [c26, c28])). % 113.01/14.66 cnf(c30, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a9])], [c26, c28])). % 113.01/14.66 % 113.01/14.66 cnf(c31, axiom, % 113.01/14.66 is_a_theorem(X22) | ~is_a_theorem(X23) | ~is_a_theorem(equivalent(X23,X22))). % 113.01/14.66 cnf(a10, assumption, % 113.01/14.66 equivalent(X13,X12) = X22). % 113.01/14.66 cnf(c32, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a10])], [c23, c31])). % 113.01/14.66 cnf(c33, plain, % 113.01/14.66 ~is_a_theorem(X23) | ~is_a_theorem(equivalent(X23,X22)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a10])], [c23, c31])). % 113.01/14.66 % 113.01/14.66 cnf(c34, axiom, % 113.01/14.66 is_a_theorem(X24) | ~is_a_theorem(X25) | ~is_a_theorem(equivalent(X25,X24))). % 113.01/14.66 cnf(a11, assumption, % 113.01/14.66 X23 = X24). % 113.01/14.66 cnf(c35, plain, % 113.01/14.66 ~is_a_theorem(equivalent(X23,X22)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a11])], [c33, c34])). % 113.01/14.66 cnf(c36, plain, % 113.01/14.66 ~is_a_theorem(X25) | ~is_a_theorem(equivalent(X25,X24)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a11])], [c33, c34])). % 113.01/14.66 % 113.01/14.66 cnf(c37, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X26,X27),equivalent(equivalent(X26,X28),equivalent(X28,X27))))). % 113.01/14.66 cnf(a12, assumption, % 113.01/14.66 X25 = equivalent(equivalent(X26,X27),equivalent(equivalent(X26,X28),equivalent(X28,X27)))). % 113.01/14.66 cnf(c38, plain, % 113.01/14.66 ~is_a_theorem(equivalent(X25,X24)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a12])], [c36, c37])). % 113.01/14.66 cnf(c39, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a12])], [c36, c37])). % 113.01/14.66 % 113.01/14.66 cnf(c40, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X29,X30),equivalent(equivalent(X29,X31),equivalent(X31,X30))))). % 113.01/14.66 cnf(a13, assumption, % 113.01/14.66 equivalent(X25,X24) = equivalent(equivalent(X29,X30),equivalent(equivalent(X29,X31),equivalent(X31,X30)))). % 113.01/14.66 cnf(c41, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a13])], [c38, c40])). % 113.01/14.66 cnf(c42, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a13])], [c38, c40])). % 113.01/14.66 % 113.01/14.66 cnf(c43, axiom, % 113.01/14.66 is_a_theorem(X32) | ~is_a_theorem(X33) | ~is_a_theorem(equivalent(X33,X32))). % 113.01/14.66 cnf(a14, assumption, % 113.01/14.66 equivalent(X23,X22) = X32). % 113.01/14.66 cnf(c44, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a14])], [c35, c43])). % 113.01/14.66 cnf(c45, plain, % 113.01/14.66 ~is_a_theorem(X33) | ~is_a_theorem(equivalent(X33,X32)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a14])], [c35, c43])). % 113.01/14.66 % 113.01/14.66 cnf(c46, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X34,X35),equivalent(equivalent(X34,X36),equivalent(X36,X35))))). % 113.01/14.66 cnf(a15, assumption, % 113.01/14.66 X33 = equivalent(equivalent(X34,X35),equivalent(equivalent(X34,X36),equivalent(X36,X35)))). % 113.01/14.66 cnf(c47, plain, % 113.01/14.66 ~is_a_theorem(equivalent(X33,X32)), % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a15])], [c45, c46])). % 113.01/14.66 cnf(c48, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a15])], [c45, c46])). % 113.01/14.66 % 113.01/14.66 cnf(c49, axiom, % 113.01/14.66 is_a_theorem(equivalent(equivalent(X37,X38),equivalent(equivalent(X37,X39),equivalent(X39,X38))))). % 113.01/14.66 cnf(a16, assumption, % 113.01/14.66 equivalent(X33,X32) = equivalent(equivalent(X37,X38),equivalent(equivalent(X37,X39),equivalent(X39,X38)))). % 113.01/14.66 cnf(c50, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a16])], [c47, c49])). % 113.01/14.66 cnf(c51, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(strict_predicate_extension, [assumptions([a16])], [c47, c49])). % 113.01/14.66 % 113.01/14.66 cnf(c52, plain, % 113.01/14.66 $false, % 113.01/14.66 inference(constraint_solving, [ % 113.01/14.66 bind(X0, equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))), % 113.01/14.66 bind(X1, equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X4,X3)))), % 113.01/14.66 bind(X2, c), % 113.01/14.66 bind(X3, b), % 113.01/14.66 bind(X4, X4), % 113.01/14.66 bind(X5, equivalent(X1,X0)), % 113.01/14.66 bind(X6, equivalent(equivalent(X9,X11),equivalent(X11,X10))), % 113.01/14.66 bind(X7, equivalent(equivalent(X9,X11),equivalent(X11,X10))), % 113.01/14.66 bind(X8, equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X4,X3)))), % 113.01/14.66 bind(X9, equivalent(X2,X3)), % 113.01/14.66 bind(X10, equivalent(equivalent(X2,X4),equivalent(X4,X3))), % 113.01/14.66 bind(X11, equivalent(X18,X17)), % 113.01/14.66 bind(X12, equivalent(X6,X5)), % 113.01/14.66 bind(X13, equivalent(equivalent(X19,X21),equivalent(X21,X20))), % 113.01/14.66 bind(X14, equivalent(equivalent(X19,X21),equivalent(X21,X20))), % 113.01/14.66 bind(X15, equivalent(equivalent(X16,X17),equivalent(equivalent(X16,X18),equivalent(X18,X17)))), % 113.01/14.66 bind(X16, a), % 113.01/14.66 bind(X17, b), % 113.01/14.66 bind(X18, c), % 113.01/14.66 bind(X19, equivalent(X16,X17)), % 113.01/14.66 bind(X20, equivalent(equivalent(X16,X18),equivalent(X18,X17))), % 113.01/14.66 bind(X21, equivalent(X26,X28)), % 113.01/14.66 bind(X22, equivalent(X13,X12)), % 113.01/14.66 bind(X23, equivalent(equivalent(X29,X31),equivalent(X31,X30))), % 113.01/14.66 bind(X24, equivalent(equivalent(X29,X31),equivalent(X31,X30))), % 113.01/14.66 bind(X25, equivalent(equivalent(X26,X27),equivalent(equivalent(X26,X28),equivalent(X28,X27)))), % 113.01/14.66 bind(X26, equivalent(X2,X3)), % 113.01/14.66 bind(X27, equivalent(X18,X17)), % 113.01/14.66 bind(X28, equivalent(X16,X18)), % 113.01/14.66 bind(X29, equivalent(X26,X27)), % 113.01/14.66 bind(X30, equivalent(equivalent(X26,X28),equivalent(X28,X27))), % 113.01/14.66 bind(X31, equivalent(X19,X21)), % 113.01/14.66 bind(X32, equivalent(X23,X22)), % 113.01/14.66 bind(X33, equivalent(equivalent(X34,X35),equivalent(equivalent(X34,X36),equivalent(X36,X35)))), % 113.01/14.66 bind(X34, equivalent(X26,X27)), % 113.01/14.66 bind(X35, equivalent(X19,X21)), % 113.01/14.66 bind(X36, equivalent(X11,X10)), % 113.01/14.66 bind(X37, equivalent(X34,X35)), % 113.01/14.66 bind(X38, equivalent(equivalent(X34,X36),equivalent(X36,X35))), % 113.01/14.66 bind(X39, equivalent(X31,X30)) % 113.01/14.66 ], % 113.01/14.66 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16])). % 113.01/14.66 % 113.01/14.66 % SZS output end IncompleteProof %------------------------------------------------------------------------------