%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL118-1 : 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 : n001.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 12:28:10 PM UTC 2026 % Result : Unsatisfiable 9.70s 1.66s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL118-1 : 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 % 0.10/0.37 % Computer : n001.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 15:21:17 UTC 2026 % 0.10/0.37 % CPUTime : % 9.70/1.66 % SZS status Unsatisfiable % 9.70/1.66 % SZS output begin IncompleteProof % 9.70/1.66 cnf(c0, axiom, % 9.70/1.66 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a))))). % 9.70/1.66 cnf(c1, plain, % 9.70/1.66 ~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))), % 9.70/1.66 inference(start, [], [c0])). % 9.70/1.66 % 9.70/1.66 cnf(c2, axiom, % 9.70/1.66 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 9.70/1.66 cnf(a0, assumption, % 9.70/1.66 equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a))) = X0). % 9.70/1.66 cnf(c3, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 9.70/1.66 cnf(c4, plain, % 9.70/1.66 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 9.70/1.66 % 9.70/1.66 cnf(c5, axiom, % 9.70/1.66 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2))). % 9.70/1.66 cnf(a1, assumption, % 9.70/1.66 X1 = X2). % 9.70/1.66 cnf(c6, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X1,X0)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 9.70/1.66 cnf(c7, plain, % 9.70/1.66 ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 9.70/1.66 % 9.70/1.66 cnf(c8, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X4,equivalent(X5,X6)),equivalent(X6,equivalent(X5,X4))))). % 9.70/1.66 cnf(a2, assumption, % 9.70/1.66 X3 = equivalent(equivalent(X4,equivalent(X5,X6)),equivalent(X6,equivalent(X5,X4)))). % 9.70/1.66 cnf(c9, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X3,X2)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 9.70/1.66 cnf(c10, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 9.70/1.66 % 9.70/1.66 cnf(c11, axiom, % 9.70/1.66 is_a_theorem(X7) | ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7))). % 9.70/1.66 cnf(a3, assumption, % 9.70/1.66 equivalent(X3,X2) = X7). % 9.70/1.66 cnf(c12, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a3])], [c9, c11])). % 9.70/1.66 cnf(c13, plain, % 9.70/1.66 ~is_a_theorem(X8) | ~is_a_theorem(equivalent(X8,X7)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a3])], [c9, c11])). % 9.70/1.66 % 9.70/1.66 cnf(c14, axiom, % 9.70/1.66 is_a_theorem(X9) | ~is_a_theorem(X10) | ~is_a_theorem(equivalent(X10,X9))). % 9.70/1.66 cnf(a4, assumption, % 9.70/1.66 X8 = X9). % 9.70/1.66 cnf(c15, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X8,X7)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 9.70/1.66 cnf(c16, plain, % 9.70/1.66 ~is_a_theorem(X10) | ~is_a_theorem(equivalent(X10,X9)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 9.70/1.66 % 9.70/1.66 cnf(c17, axiom, % 9.70/1.66 is_a_theorem(X11) | ~is_a_theorem(X12) | ~is_a_theorem(equivalent(X12,X11))). % 9.70/1.66 cnf(a5, assumption, % 9.70/1.66 X10 = X11). % 9.70/1.66 cnf(c18, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X10,X9)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 9.70/1.66 cnf(c19, plain, % 9.70/1.66 ~is_a_theorem(X12) | ~is_a_theorem(equivalent(X12,X11)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 9.70/1.66 % 9.70/1.66 cnf(c20, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X13,equivalent(X14,X15)),equivalent(X15,equivalent(X14,X13))))). % 9.70/1.66 cnf(a6, assumption, % 9.70/1.66 X12 = equivalent(equivalent(X13,equivalent(X14,X15)),equivalent(X15,equivalent(X14,X13)))). % 9.70/1.66 cnf(c21, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X12,X11)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 9.70/1.66 cnf(c22, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 9.70/1.66 % 9.70/1.66 cnf(c23, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X16,equivalent(X17,X18)),equivalent(X18,equivalent(X17,X16))))). % 9.70/1.66 cnf(a7, assumption, % 9.70/1.66 equivalent(X12,X11) = equivalent(equivalent(X16,equivalent(X17,X18)),equivalent(X18,equivalent(X17,X16)))). % 9.70/1.66 cnf(c24, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 9.70/1.66 cnf(c25, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 9.70/1.66 % 9.70/1.66 cnf(c26, axiom, % 9.70/1.66 is_a_theorem(X19) | ~is_a_theorem(X20) | ~is_a_theorem(equivalent(X20,X19))). % 9.70/1.66 cnf(a8, assumption, % 9.70/1.66 equivalent(X10,X9) = X19). % 9.70/1.66 cnf(c27, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a8])], [c18, c26])). % 9.70/1.66 cnf(c28, plain, % 9.70/1.66 ~is_a_theorem(X20) | ~is_a_theorem(equivalent(X20,X19)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a8])], [c18, c26])). % 9.70/1.66 % 9.70/1.66 cnf(c29, axiom, % 9.70/1.66 is_a_theorem(X21) | ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21))). % 9.70/1.66 cnf(a9, assumption, % 9.70/1.66 X20 = X21). % 9.70/1.66 cnf(c30, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X20,X19)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 9.70/1.66 cnf(c31, plain, % 9.70/1.66 ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 9.70/1.66 % 9.70/1.66 cnf(c32, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X23,equivalent(X24,X25)),equivalent(X25,equivalent(X24,X23))))). % 9.70/1.66 cnf(a10, assumption, % 9.70/1.66 X22 = equivalent(equivalent(X23,equivalent(X24,X25)),equivalent(X25,equivalent(X24,X23)))). % 9.70/1.66 cnf(c33, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X22,X21)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 9.70/1.66 cnf(c34, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 9.70/1.66 % 9.70/1.66 cnf(c35, axiom, % 9.70/1.66 is_a_theorem(X26) | ~is_a_theorem(X27) | ~is_a_theorem(equivalent(X27,X26))). % 9.70/1.66 cnf(a11, assumption, % 9.70/1.66 equivalent(X22,X21) = X26). % 9.70/1.66 cnf(c36, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 9.70/1.66 cnf(c37, plain, % 9.70/1.66 ~is_a_theorem(X27) | ~is_a_theorem(equivalent(X27,X26)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 9.70/1.66 % 9.70/1.66 cnf(c38, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X28,equivalent(X29,X30)),equivalent(X30,equivalent(X29,X28))))). % 9.70/1.66 cnf(a12, assumption, % 9.70/1.66 X27 = equivalent(equivalent(X28,equivalent(X29,X30)),equivalent(X30,equivalent(X29,X28)))). % 9.70/1.66 cnf(c39, plain, % 9.70/1.66 ~is_a_theorem(equivalent(X27,X26)), % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a12])], [c37, c38])). % 9.70/1.66 cnf(c40, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a12])], [c37, c38])). % 9.70/1.66 % 9.70/1.66 cnf(c41, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X31,equivalent(X32,X33)),equivalent(X33,equivalent(X32,X31))))). % 9.70/1.66 cnf(a13, assumption, % 9.70/1.66 equivalent(X27,X26) = equivalent(equivalent(X31,equivalent(X32,X33)),equivalent(X33,equivalent(X32,X31)))). % 9.70/1.66 cnf(c42, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a13])], [c39, c41])). % 9.70/1.66 cnf(c43, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a13])], [c39, c41])). % 9.70/1.66 % 9.70/1.66 cnf(c44, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X34,equivalent(X35,X36)),equivalent(X36,equivalent(X35,X34))))). % 9.70/1.66 cnf(a14, assumption, % 9.70/1.66 equivalent(X20,X19) = equivalent(equivalent(X34,equivalent(X35,X36)),equivalent(X36,equivalent(X35,X34)))). % 9.70/1.66 cnf(c45, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a14])], [c30, c44])). % 9.70/1.66 cnf(c46, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a14])], [c30, c44])). % 9.70/1.66 % 9.70/1.66 cnf(c47, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X37,equivalent(X38,X39)),equivalent(X39,equivalent(X38,X37))))). % 9.70/1.66 cnf(a15, assumption, % 9.70/1.66 equivalent(X8,X7) = equivalent(equivalent(X37,equivalent(X38,X39)),equivalent(X39,equivalent(X38,X37)))). % 9.70/1.66 cnf(c48, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a15])], [c15, c47])). % 9.70/1.66 cnf(c49, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a15])], [c15, c47])). % 9.70/1.66 % 9.70/1.66 cnf(c50, axiom, % 9.70/1.66 is_a_theorem(equivalent(equivalent(X40,equivalent(X41,X42)),equivalent(X42,equivalent(X41,X40))))). % 9.70/1.66 cnf(a16, assumption, % 9.70/1.66 equivalent(X1,X0) = equivalent(equivalent(X40,equivalent(X41,X42)),equivalent(X42,equivalent(X41,X40)))). % 9.70/1.66 cnf(c51, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a16])], [c6, c50])). % 9.70/1.66 cnf(c52, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(strict_predicate_extension, [assumptions([a16])], [c6, c50])). % 9.70/1.66 % 9.70/1.66 cnf(c53, plain, % 9.70/1.66 $false, % 9.70/1.66 inference(constraint_solving, [ % 9.70/1.66 bind(X0, equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(c,a)))), % 9.70/1.66 bind(X1, equivalent(X38,X37)), % 9.70/1.66 bind(X2, equivalent(X38,X37)), % 9.70/1.66 bind(X3, equivalent(equivalent(X4,equivalent(X5,X6)),equivalent(X6,equivalent(X5,X4)))), % 9.70/1.66 bind(X4, a), % 9.70/1.66 bind(X5, c), % 9.70/1.66 bind(X6, b), % 9.70/1.66 bind(X7, equivalent(X3,X2)), % 9.70/1.66 bind(X8, equivalent(X35,X34)), % 9.70/1.66 bind(X9, equivalent(X35,X34)), % 9.70/1.66 bind(X10, equivalent(X18,equivalent(X17,X16))), % 9.70/1.66 bind(X11, equivalent(X18,equivalent(X17,X16))), % 9.70/1.66 bind(X12, equivalent(equivalent(X13,equivalent(X14,X15)),equivalent(X15,equivalent(X14,X13)))), % 9.70/1.66 bind(X13, equivalent(X24,X25)), % 9.70/1.66 bind(X14, b), % 9.70/1.66 bind(X15, equivalent(X5,X4)), % 9.70/1.66 bind(X16, equivalent(X13,equivalent(X14,X15))), % 9.70/1.66 bind(X17, equivalent(X5,X4)), % 9.70/1.66 bind(X18, equivalent(X14,X13)), % 9.70/1.66 bind(X19, equivalent(X10,X9)), % 9.70/1.66 bind(X20, equivalent(X32,X31)), % 9.70/1.66 bind(X21, equivalent(X32,X31)), % 9.70/1.66 bind(X22, equivalent(equivalent(X23,equivalent(X24,X25)),equivalent(X25,equivalent(X24,X23)))), % 9.70/1.66 bind(X23, b), % 9.70/1.66 bind(X24, a), % 9.70/1.66 bind(X25, equivalent(X5,X6)), % 9.70/1.66 bind(X26, equivalent(X22,X21)), % 9.70/1.66 bind(X27, equivalent(equivalent(X28,equivalent(X29,X30)),equivalent(X30,equivalent(X29,X28)))), % 9.70/1.66 bind(X28, equivalent(X25,equivalent(X24,X23))), % 9.70/1.66 bind(X29, equivalent(X23,equivalent(X24,X25))), % 9.70/1.66 bind(X30, equivalent(X17,X16)), % 9.70/1.66 bind(X31, equivalent(X28,equivalent(X29,X30))), % 9.70/1.66 bind(X32, equivalent(X17,X16)), % 9.70/1.66 bind(X33, equivalent(X29,X28)), % 9.70/1.66 bind(X34, equivalent(X17,X16)), % 9.70/1.66 bind(X35, equivalent(X25,equivalent(X24,X23))), % 9.70/1.66 bind(X36, equivalent(X29,X30)), % 9.70/1.66 bind(X37, equivalent(X25,equivalent(X24,X23))), % 9.70/1.66 bind(X38, equivalent(X5,X4)), % 9.70/1.66 bind(X39, equivalent(X13,equivalent(X14,X15))), % 9.70/1.66 bind(X40, equivalent(X5,X4)), % 9.70/1.66 bind(X41, equivalent(X5,X6)), % 9.70/1.66 bind(X42, equivalent(X24,X23)) % 9.70/1.66 ], % 9.70/1.66 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16])). % 9.70/1.66 % 9.70/1.66 % SZS output end IncompleteProof %------------------------------------------------------------------------------