%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL064-2 : 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 : n006.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 12:28:06 PM UTC 2026 % Result : Unsatisfiable 74.92s 9.86s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL064-2 : 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 % 0.10/0.36 % Computer : n006.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 22:26:31 UTC 2026 % 0.14/0.36 % CPUTime : % 74.92/9.86 % SZS status Unsatisfiable % 74.92/9.86 % SZS output begin IncompleteProof % 74.92/9.86 cnf(c0, axiom, % 74.92/9.86 ~is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c))))). % 74.92/9.86 cnf(c1, plain, % 74.92/9.86 ~is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))), % 74.92/9.86 inference(start, [], [c0])). % 74.92/9.86 % 74.92/9.86 cnf(c2, axiom, % 74.92/9.86 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 74.92/9.86 cnf(a0, assumption, % 74.92/9.86 implies(implies(a,b),implies(implies(b,c),implies(a,c))) = X0). % 74.92/9.86 cnf(c3, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 74.92/9.86 cnf(c4, plain, % 74.92/9.86 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 74.92/9.86 % 74.92/9.86 cnf(c5, axiom, % 74.92/9.86 is_a_theorem(implies(X2,implies(X3,X2)))). % 74.92/9.86 cnf(a1, assumption, % 74.92/9.86 X1 = implies(X2,implies(X3,X2))). % 74.92/9.86 cnf(c6, plain, % 74.92/9.86 ~is_a_theorem(implies(X1,X0)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 74.92/9.86 cnf(c7, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 74.92/9.86 % 74.92/9.86 cnf(c8, axiom, % 74.92/9.86 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4))). % 74.92/9.86 cnf(a2, assumption, % 74.92/9.86 implies(X1,X0) = X4). % 74.92/9.86 cnf(c9, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 74.92/9.86 cnf(c10, plain, % 74.92/9.86 ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a2])], [c6, c8])). % 74.92/9.86 % 74.92/9.86 cnf(c11, axiom, % 74.92/9.86 is_a_theorem(X6) | ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6))). % 74.92/9.86 cnf(a3, assumption, % 74.92/9.86 X5 = X6). % 74.92/9.86 cnf(c12, plain, % 74.92/9.86 ~is_a_theorem(implies(X5,X4)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 74.92/9.86 cnf(c13, plain, % 74.92/9.86 ~is_a_theorem(X7) | ~is_a_theorem(implies(X7,X6)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 74.92/9.86 % 74.92/9.86 cnf(c14, axiom, % 74.92/9.86 is_a_theorem(X8) | ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8))). % 74.92/9.86 cnf(a4, assumption, % 74.92/9.86 X7 = X8). % 74.92/9.86 cnf(c15, plain, % 74.92/9.86 ~is_a_theorem(implies(X7,X6)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 74.92/9.86 cnf(c16, plain, % 74.92/9.86 ~is_a_theorem(X9) | ~is_a_theorem(implies(X9,X8)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 74.92/9.86 % 74.92/9.86 cnf(c17, axiom, % 74.92/9.86 is_a_theorem(X10) | ~is_a_theorem(X11) | ~is_a_theorem(implies(X11,X10))). % 74.92/9.86 cnf(a5, assumption, % 74.92/9.86 X9 = X10). % 74.92/9.86 cnf(c18, plain, % 74.92/9.86 ~is_a_theorem(implies(X9,X8)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 74.92/9.86 cnf(c19, plain, % 74.92/9.86 ~is_a_theorem(X11) | ~is_a_theorem(implies(X11,X10)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 74.92/9.86 % 74.92/9.86 cnf(c20, axiom, % 74.92/9.86 is_a_theorem(implies(X12,implies(X13,X12)))). % 74.92/9.86 cnf(a6, assumption, % 74.92/9.86 X11 = implies(X12,implies(X13,X12))). % 74.92/9.86 cnf(c21, plain, % 74.92/9.86 ~is_a_theorem(implies(X11,X10)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 74.92/9.86 cnf(c22, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 74.92/9.86 % 74.92/9.86 cnf(c23, axiom, % 74.92/9.86 is_a_theorem(X14) | ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14))). % 74.92/9.86 cnf(a7, assumption, % 74.92/9.86 implies(X11,X10) = X14). % 74.92/9.86 cnf(c24, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 74.92/9.86 cnf(c25, plain, % 74.92/9.86 ~is_a_theorem(X15) | ~is_a_theorem(implies(X15,X14)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 74.92/9.86 % 74.92/9.86 cnf(c26, axiom, % 74.92/9.86 is_a_theorem(X16) | ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16))). % 74.92/9.86 cnf(a8, assumption, % 74.92/9.86 X15 = X16). % 74.92/9.86 cnf(c27, plain, % 74.92/9.86 ~is_a_theorem(implies(X15,X14)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 74.92/9.86 cnf(c28, plain, % 74.92/9.86 ~is_a_theorem(X17) | ~is_a_theorem(implies(X17,X16)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 74.92/9.86 % 74.92/9.86 cnf(c29, axiom, % 74.92/9.86 is_a_theorem(implies(implies(X18,implies(X19,X20)),implies(implies(X18,X19),implies(X18,X20))))). % 74.92/9.86 cnf(a9, assumption, % 74.92/9.86 X17 = implies(implies(X18,implies(X19,X20)),implies(implies(X18,X19),implies(X18,X20)))). % 74.92/9.86 cnf(c30, plain, % 74.92/9.86 ~is_a_theorem(implies(X17,X16)), % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 74.92/9.86 cnf(c31, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 74.92/9.86 % 74.92/9.86 cnf(c32, axiom, % 74.92/9.86 is_a_theorem(implies(X21,implies(X22,X21)))). % 74.92/9.86 cnf(a10, assumption, % 74.92/9.86 implies(X17,X16) = implies(X21,implies(X22,X21))). % 74.92/9.86 cnf(c33, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 74.92/9.86 cnf(c34, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 74.92/9.86 % 74.92/9.86 cnf(c35, axiom, % 74.92/9.86 is_a_theorem(implies(implies(X23,implies(X24,X25)),implies(implies(X23,X24),implies(X23,X25))))). % 74.92/9.86 cnf(a11, assumption, % 74.92/9.86 implies(X15,X14) = implies(implies(X23,implies(X24,X25)),implies(implies(X23,X24),implies(X23,X25)))). % 74.92/9.86 cnf(c36, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 74.92/9.86 cnf(c37, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 74.92/9.86 % 74.92/9.86 cnf(c38, axiom, % 74.92/9.86 is_a_theorem(implies(implies(X26,implies(X27,X28)),implies(implies(X26,X27),implies(X26,X28))))). % 74.92/9.86 cnf(a12, assumption, % 74.92/9.86 implies(X9,X8) = implies(implies(X26,implies(X27,X28)),implies(implies(X26,X27),implies(X26,X28)))). % 74.92/9.86 cnf(c39, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a12])], [c18, c38])). % 74.92/9.86 cnf(c40, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a12])], [c18, c38])). % 74.92/9.86 % 74.92/9.86 cnf(c41, axiom, % 74.92/9.86 is_a_theorem(implies(X29,implies(X30,X29)))). % 74.92/9.86 cnf(a13, assumption, % 74.92/9.86 implies(X7,X6) = implies(X29,implies(X30,X29))). % 74.92/9.86 cnf(c42, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a13])], [c15, c41])). % 74.92/9.86 cnf(c43, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a13])], [c15, c41])). % 74.92/9.86 % 74.92/9.86 cnf(c44, axiom, % 74.92/9.86 is_a_theorem(implies(implies(X31,implies(X32,X33)),implies(implies(X31,X32),implies(X31,X33))))). % 74.92/9.86 cnf(a14, assumption, % 74.92/9.86 implies(X5,X4) = implies(implies(X31,implies(X32,X33)),implies(implies(X31,X32),implies(X31,X33)))). % 74.92/9.86 cnf(c45, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a14])], [c12, c44])). % 74.92/9.86 cnf(c46, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(strict_predicate_extension, [assumptions([a14])], [c12, c44])). % 74.92/9.86 % 74.92/9.86 cnf(c47, plain, % 74.92/9.86 $false, % 74.92/9.86 inference(constraint_solving, [ % 74.92/9.86 bind(X0, implies(implies(a,b),implies(implies(b,c),implies(a,c)))), % 74.92/9.86 bind(X1, implies(X2,implies(X3,X2))), % 74.92/9.86 bind(X2, implies(X18,X19)), % 74.92/9.86 bind(X3, implies(X19,X20)), % 74.92/9.86 bind(X4, implies(X1,X0)), % 74.92/9.86 bind(X5, implies(X30,X29)), % 74.92/9.86 bind(X6, implies(X30,X29)), % 74.92/9.86 bind(X7, implies(implies(X26,X27),implies(X26,X28))), % 74.92/9.86 bind(X8, implies(implies(X26,X27),implies(X26,X28))), % 74.92/9.86 bind(X9, implies(X23,X25)), % 74.92/9.86 bind(X10, implies(X23,X25)), % 74.92/9.86 bind(X11, implies(X12,implies(X13,X12))), % 74.92/9.86 bind(X12, implies(X19,X20)), % 74.92/9.86 bind(X13, a), % 74.92/9.86 bind(X14, implies(X11,X10)), % 74.92/9.86 bind(X15, implies(X22,X21)), % 74.92/9.86 bind(X16, implies(X22,X21)), % 74.92/9.86 bind(X17, implies(implies(X18,implies(X19,X20)),implies(implies(X18,X19),implies(X18,X20)))), % 74.92/9.86 bind(X18, a), % 74.92/9.86 bind(X19, b), % 74.92/9.86 bind(X20, c), % 74.92/9.86 bind(X21, implies(implies(X18,implies(X19,X20)),implies(implies(X18,X19),implies(X18,X20)))), % 74.92/9.86 bind(X22, implies(X19,X20)), % 74.92/9.86 bind(X23, implies(X19,X20)), % 74.92/9.86 bind(X24, implies(X18,implies(X19,X20))), % 74.92/9.86 bind(X25, implies(implies(X18,X19),implies(X18,X20))), % 74.92/9.86 bind(X26, implies(X19,X20)), % 74.92/9.86 bind(X27, implies(X18,X19)), % 74.92/9.86 bind(X28, implies(X18,X20)), % 74.92/9.86 bind(X29, implies(implies(X26,X27),implies(X26,X28))), % 74.92/9.86 bind(X30, implies(X18,X19)), % 74.92/9.86 bind(X31, implies(X18,X19)), % 74.92/9.86 bind(X32, implies(X26,X27)), % 74.92/9.86 bind(X33, implies(X26,X28)) % 74.92/9.86 ], % 74.92/9.86 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 74.92/9.86 % 74.92/9.86 % SZS output end IncompleteProof %------------------------------------------------------------------------------