%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL098-1 : 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 12:28:09 PM UTC 2026 % Result : Unsatisfiable 0.12s 0.37s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL098-1 : 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 % 0.07/0.34 % Computer : n029.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Fri Sep 4 22:23:25 UTC 2026 % 0.07/0.34 % CPUTime : % 0.12/0.37 % SZS status Unsatisfiable % 0.12/0.37 % SZS output begin IncompleteProof % 0.12/0.37 cnf(c0, axiom, % 0.12/0.37 ~is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))). % 0.12/0.37 cnf(c1, plain, % 0.12/0.37 ~is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))), % 0.12/0.37 inference(start, [], [c0])). % 0.12/0.37 % 0.12/0.37 cnf(c2, axiom, % 0.12/0.37 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 0.12/0.37 cnf(a0, assumption, % 0.12/0.37 equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))) = X0). % 0.12/0.37 cnf(c3, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.12/0.37 cnf(c4, plain, % 0.12/0.37 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 0.12/0.37 % 0.12/0.37 cnf(c5, axiom, % 0.12/0.37 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2))). % 0.12/0.37 cnf(a1, assumption, % 0.12/0.37 X1 = X2). % 0.12/0.37 cnf(c6, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X1,X0)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.12/0.37 cnf(c7, plain, % 0.12/0.37 ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 0.12/0.37 % 0.12/0.37 cnf(c8, axiom, % 0.12/0.37 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(equivalent(X5,X4))). % 0.12/0.37 cnf(a2, assumption, % 0.12/0.37 X3 = X4). % 0.12/0.37 cnf(c9, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X3,X2)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.12/0.37 cnf(c10, plain, % 0.12/0.37 ~is_a_theorem(X5) | ~is_a_theorem(equivalent(X5,X4)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 0.12/0.37 % 0.12/0.37 cnf(c11, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X7),equivalent(X6,X8)),X9),equivalent(equivalent(X7,X8),X9)),X10),X10))). % 0.12/0.37 cnf(a3, assumption, % 0.12/0.37 X5 = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X7),equivalent(X6,X8)),X9),equivalent(equivalent(X7,X8),X9)),X10),X10)). % 0.12/0.37 cnf(c12, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X5,X4)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.12/0.37 cnf(c13, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 0.12/0.37 % 0.12/0.37 cnf(c14, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X11,X12),equivalent(X11,X13)),X14),equivalent(equivalent(X12,X13),X14)),X15),X15))). % 0.12/0.37 cnf(a4, assumption, % 0.12/0.37 equivalent(X5,X4) = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X11,X12),equivalent(X11,X13)),X14),equivalent(equivalent(X12,X13),X14)),X15),X15)). % 0.12/0.37 cnf(c15, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.12/0.37 cnf(c16, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 0.12/0.37 % 0.12/0.37 cnf(c17, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X16,X17),equivalent(X16,X18)),X19),equivalent(equivalent(X17,X18),X19)),X20),X20))). % 0.12/0.37 cnf(a5, assumption, % 0.12/0.37 equivalent(X3,X2) = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X16,X17),equivalent(X16,X18)),X19),equivalent(equivalent(X17,X18),X19)),X20),X20)). % 0.12/0.37 cnf(c18, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 0.12/0.37 cnf(c19, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 0.12/0.37 % 0.12/0.37 cnf(c20, axiom, % 0.12/0.37 is_a_theorem(X21) | ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21))). % 0.12/0.37 cnf(a6, assumption, % 0.12/0.37 equivalent(X1,X0) = X21). % 0.12/0.37 cnf(c21, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a6])], [c6, c20])). % 0.12/0.37 cnf(c22, plain, % 0.12/0.37 ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a6])], [c6, c20])). % 0.12/0.37 % 0.12/0.37 cnf(c23, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),X26),equivalent(equivalent(X24,X25),X26)),X27),X27))). % 0.12/0.37 cnf(a7, assumption, % 0.12/0.37 X22 = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),X26),equivalent(equivalent(X24,X25),X26)),X27),X27)). % 0.12/0.37 cnf(c24, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X22,X21)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 0.12/0.37 cnf(c25, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 0.12/0.37 % 0.12/0.37 cnf(c26, axiom, % 0.12/0.37 is_a_theorem(X28) | ~is_a_theorem(X29) | ~is_a_theorem(equivalent(X29,X28))). % 0.12/0.37 cnf(a8, assumption, % 0.12/0.37 equivalent(X22,X21) = X28). % 0.12/0.37 cnf(c27, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a8])], [c24, c26])). % 0.12/0.37 cnf(c28, plain, % 0.12/0.37 ~is_a_theorem(X29) | ~is_a_theorem(equivalent(X29,X28)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a8])], [c24, c26])). % 0.12/0.37 % 0.12/0.37 cnf(c29, axiom, % 0.12/0.37 is_a_theorem(X30) | ~is_a_theorem(X31) | ~is_a_theorem(equivalent(X31,X30))). % 0.12/0.37 cnf(a9, assumption, % 0.12/0.37 X29 = X30). % 0.12/0.37 cnf(c30, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X29,X28)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 0.12/0.37 cnf(c31, plain, % 0.12/0.37 ~is_a_theorem(X31) | ~is_a_theorem(equivalent(X31,X30)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 0.12/0.37 % 0.12/0.37 cnf(c32, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X32,X33),equivalent(X32,X34)),X35),equivalent(equivalent(X33,X34),X35)),X36),X36))). % 0.12/0.37 cnf(a10, assumption, % 0.12/0.37 X31 = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X32,X33),equivalent(X32,X34)),X35),equivalent(equivalent(X33,X34),X35)),X36),X36)). % 0.12/0.37 cnf(c33, plain, % 0.12/0.37 ~is_a_theorem(equivalent(X31,X30)), % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 0.12/0.37 cnf(c34, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 0.12/0.37 % 0.12/0.37 cnf(c35, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X37,X38),equivalent(X37,X39)),X40),equivalent(equivalent(X38,X39),X40)),X41),X41))). % 0.12/0.37 cnf(a11, assumption, % 0.12/0.37 equivalent(X31,X30) = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X37,X38),equivalent(X37,X39)),X40),equivalent(equivalent(X38,X39),X40)),X41),X41)). % 0.12/0.37 cnf(c36, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 0.12/0.37 cnf(c37, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 0.12/0.37 % 0.12/0.37 cnf(c38, axiom, % 0.12/0.37 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X42,X43),equivalent(X42,X44)),X45),equivalent(equivalent(X43,X44),X45)),X46),X46))). % 0.12/0.37 cnf(a12, assumption, % 0.12/0.37 equivalent(X29,X28) = equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X42,X43),equivalent(X42,X44)),X45),equivalent(equivalent(X43,X44),X45)),X46),X46)). % 0.12/0.37 cnf(c39, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a12])], [c30, c38])). % 0.12/0.37 cnf(c40, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(strict_predicate_extension, [assumptions([a12])], [c30, c38])). % 0.12/0.37 % 0.12/0.37 cnf(c41, plain, % 0.12/0.37 $false, % 0.12/0.37 inference(constraint_solving, [ % 0.12/0.37 bind(X0, equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))), % 0.12/0.37 bind(X1, equivalent(equivalent(X7,X8),X9)), % 0.12/0.37 bind(X2, equivalent(equivalent(X7,X8),X9)), % 0.12/0.37 bind(X3, equivalent(equivalent(X12,X13),X14)), % 0.12/0.37 bind(X4, equivalent(equivalent(X12,X13),X14)), % 0.12/0.37 bind(X5, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X7),equivalent(X6,X8)),X9),equivalent(equivalent(X7,X8),X9)),X10),X10)), % 0.12/0.37 bind(X6, equivalent(equivalent(X16,X17),equivalent(X16,X18))), % 0.12/0.37 bind(X7, equivalent(X42,X43)), % 0.12/0.37 bind(X8, equivalent(X42,X44)), % 0.12/0.37 bind(X9, equivalent(X11,X13)), % 0.12/0.37 bind(X10, equivalent(equivalent(X12,X13),X14)), % 0.12/0.37 bind(X11, equivalent(X6,X7)), % 0.12/0.37 bind(X12, equivalent(X6,X8)), % 0.12/0.37 bind(X13, equivalent(equivalent(X17,X18),X19)), % 0.12/0.37 bind(X14, equivalent(equivalent(X7,X8),X9)), % 0.12/0.37 bind(X15, equivalent(equivalent(X12,X13),X14)), % 0.12/0.37 bind(X16, equivalent(X23,X24)), % 0.12/0.37 bind(X17, equivalent(X23,X25)), % 0.12/0.37 bind(X18, c), % 0.12/0.37 bind(X19, equivalent(X42,X44)), % 0.12/0.37 bind(X20, equivalent(equivalent(X7,X8),X9)), % 0.12/0.37 bind(X21, equivalent(X1,X0)), % 0.12/0.37 bind(X22, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),X26),equivalent(equivalent(X24,X25),X26)),X27),X27)), % 0.12/0.37 bind(X23, a), % 0.12/0.37 bind(X24, b), % 0.12/0.37 bind(X25, falsehood), % 0.12/0.37 bind(X26, equivalent(X16,X18)), % 0.12/0.37 bind(X27, equivalent(equivalent(X17,X18),X19)), % 0.12/0.37 bind(X28, equivalent(X22,X21)), % 0.12/0.37 bind(X29, equivalent(equivalent(X38,X39),X40)), % 0.12/0.37 bind(X30, equivalent(equivalent(X38,X39),X40)), % 0.12/0.37 bind(X31, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X32,X33),equivalent(X32,X34)),X35),equivalent(equivalent(X33,X34),X35)),X36),X36)), % 0.12/0.37 bind(X32, equivalent(equivalent(X42,X43),equivalent(X42,X44))), % 0.12/0.37 bind(X33, equivalent(equivalent(equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),X26),equivalent(equivalent(X24,X25),X26)),X27)), % 0.12/0.37 bind(X34, equivalent(equivalent(X17,X18),X19)), % 0.12/0.37 bind(X35, equivalent(X37,X39)), % 0.12/0.37 bind(X36, equivalent(equivalent(X38,X39),X40)), % 0.12/0.37 bind(X37, equivalent(X32,X33)), % 0.12/0.37 bind(X38, equivalent(X32,X34)), % 0.12/0.37 bind(X39, equivalent(equivalent(X43,X44),X45)), % 0.12/0.37 bind(X40, equivalent(equivalent(X33,X34),X35)), % 0.12/0.37 bind(X41, equivalent(equivalent(X38,X39),X40)), % 0.12/0.37 bind(X42, equivalent(X24,X25)), % 0.12/0.37 bind(X43, equivalent(X16,X18)), % 0.12/0.37 bind(X44, e), % 0.12/0.37 bind(X45, equivalent(equivalent(X17,X18),X19)), % 0.12/0.37 bind(X46, equivalent(equivalent(X33,X34),X35)) % 0.12/0.37 ], % 0.12/0.37 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12])). % 0.12/0.37 % 0.12/0.37 % SZS output end IncompleteProof %------------------------------------------------------------------------------