%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL111-1 : 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 : n005.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 2.58s 0.73s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL111-1 : 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 % 0.11/0.37 % Computer : n005.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Fri Sep 4 18:59:35 UTC 2026 % 0.11/0.37 % CPUTime : % 2.58/0.73 % SZS status Unsatisfiable % 2.58/0.73 % SZS output begin IncompleteProof % 2.58/0.73 cnf(c0, axiom, % 2.58/0.73 ~is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b))))). % 2.58/0.73 cnf(c1, plain, % 2.58/0.73 ~is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b)))), % 2.58/0.73 inference(start, [], [c0])). % 2.58/0.73 % 2.58/0.73 cnf(c2, axiom, % 2.58/0.73 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 2.58/0.73 cnf(a0, assumption, % 2.58/0.73 implies(implies(a,b),implies(implies(c,a),implies(c,b))) = X0). % 2.58/0.73 cnf(c3, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 2.58/0.73 cnf(c4, plain, % 2.58/0.73 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 2.58/0.73 % 2.58/0.73 cnf(c5, axiom, % 2.58/0.73 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2))). % 2.58/0.73 cnf(a1, assumption, % 2.58/0.73 X1 = X2). % 2.58/0.73 cnf(c6, plain, % 2.58/0.73 ~is_a_theorem(implies(X1,X0)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 2.58/0.73 cnf(c7, plain, % 2.58/0.73 ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 2.58/0.73 % 2.58/0.73 cnf(c8, axiom, % 2.58/0.73 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4))). % 2.58/0.73 cnf(a2, assumption, % 2.58/0.73 X3 = X4). % 2.58/0.73 cnf(c9, plain, % 2.58/0.73 ~is_a_theorem(implies(X3,X2)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 2.58/0.73 cnf(c10, plain, % 2.58/0.73 ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 2.58/0.73 % 2.58/0.73 cnf(c11, axiom, % 2.58/0.73 is_a_theorem(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))))). % 2.58/0.73 cnf(a3, assumption, % 2.58/0.73 X5 = implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8)))). % 2.58/0.73 cnf(c12, plain, % 2.58/0.73 ~is_a_theorem(implies(X5,X4)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 2.58/0.73 cnf(c13, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 2.58/0.73 % 2.58/0.73 cnf(c14, axiom, % 2.58/0.73 is_a_theorem(implies(implies(X9,X10),implies(implies(X10,X11),implies(X9,X11))))). % 2.58/0.73 cnf(a4, assumption, % 2.58/0.73 implies(X5,X4) = implies(implies(X9,X10),implies(implies(X10,X11),implies(X9,X11)))). % 2.58/0.73 cnf(c15, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 2.58/0.73 cnf(c16, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 2.58/0.73 % 2.58/0.73 cnf(c17, axiom, % 2.58/0.73 is_a_theorem(X12) | ~is_a_theorem(X13) | ~is_a_theorem(implies(X13,X12))). % 2.58/0.73 cnf(a5, assumption, % 2.58/0.73 implies(X3,X2) = X12). % 2.58/0.73 cnf(c18, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 2.58/0.73 cnf(c19, plain, % 2.58/0.73 ~is_a_theorem(X13) | ~is_a_theorem(implies(X13,X12)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 2.58/0.73 % 2.58/0.73 cnf(c20, axiom, % 2.58/0.73 is_a_theorem(implies(implies(implies(X14,X15),X15),implies(implies(X15,X14),X14)))). % 2.58/0.73 cnf(a6, assumption, % 2.58/0.73 X13 = implies(implies(implies(X14,X15),X15),implies(implies(X15,X14),X14))). % 2.58/0.73 cnf(c21, plain, % 2.58/0.73 ~is_a_theorem(implies(X13,X12)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 2.58/0.73 cnf(c22, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a6])], [c19, c20])). % 2.58/0.73 % 2.58/0.73 cnf(c23, axiom, % 2.58/0.73 is_a_theorem(implies(implies(X16,X17),implies(implies(X17,X18),implies(X16,X18))))). % 2.58/0.73 cnf(a7, assumption, % 2.58/0.73 implies(X13,X12) = implies(implies(X16,X17),implies(implies(X17,X18),implies(X16,X18)))). % 2.58/0.73 cnf(c24, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 2.58/0.73 cnf(c25, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a7])], [c21, c23])). % 2.58/0.73 % 2.58/0.73 cnf(c26, axiom, % 2.58/0.73 is_a_theorem(X19) | ~is_a_theorem(X20) | ~is_a_theorem(implies(X20,X19))). % 2.58/0.73 cnf(a8, assumption, % 2.58/0.73 implies(X1,X0) = X19). % 2.58/0.73 cnf(c27, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a8])], [c6, c26])). % 2.58/0.73 cnf(c28, plain, % 2.58/0.73 ~is_a_theorem(X20) | ~is_a_theorem(implies(X20,X19)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a8])], [c6, c26])). % 2.58/0.73 % 2.58/0.73 cnf(c29, axiom, % 2.58/0.73 is_a_theorem(implies(X21,implies(X22,X21)))). % 2.58/0.73 cnf(a9, assumption, % 2.58/0.73 X20 = implies(X21,implies(X22,X21))). % 2.58/0.73 cnf(c30, plain, % 2.58/0.73 ~is_a_theorem(implies(X20,X19)), % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 2.58/0.73 cnf(c31, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 2.58/0.73 % 2.58/0.73 cnf(c32, axiom, % 2.58/0.73 is_a_theorem(implies(implies(X23,X24),implies(implies(X24,X25),implies(X23,X25))))). % 2.58/0.73 cnf(a10, assumption, % 2.58/0.73 implies(X20,X19) = implies(implies(X23,X24),implies(implies(X24,X25),implies(X23,X25)))). % 2.58/0.73 cnf(c33, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 2.58/0.73 cnf(c34, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 2.58/0.73 % 2.58/0.73 cnf(c35, plain, % 2.58/0.73 $false, % 2.58/0.73 inference(constraint_solving, [ % 2.58/0.73 bind(X0, implies(implies(a,b),implies(implies(c,a),implies(c,b)))), % 2.58/0.73 bind(X1, implies(X16,X18)), % 2.58/0.73 bind(X2, implies(X16,X18)), % 2.58/0.73 bind(X3, implies(implies(X10,X11),implies(X9,X11))), % 2.58/0.73 bind(X4, implies(implies(X10,X11),implies(X9,X11))), % 2.58/0.73 bind(X5, implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8)))), % 2.58/0.73 bind(X6, c), % 2.58/0.73 bind(X7, a), % 2.58/0.73 bind(X8, b), % 2.58/0.73 bind(X9, implies(X6,X7)), % 2.58/0.73 bind(X10, implies(implies(X7,X8),implies(X6,X8))), % 2.58/0.73 bind(X11, implies(X6,X8)), % 2.58/0.73 bind(X12, implies(X3,X2)), % 2.58/0.73 bind(X13, implies(implies(implies(X14,X15),X15),implies(implies(X15,X14),X14))), % 2.58/0.73 bind(X14, implies(X6,X8)), % 2.58/0.73 bind(X15, implies(X7,X8)), % 2.58/0.73 bind(X16, implies(implies(X14,X15),X15)), % 2.58/0.73 bind(X17, implies(implies(X15,X14),X14)), % 2.58/0.73 bind(X18, implies(X9,X11)), % 2.58/0.73 bind(X19, implies(X1,X0)), % 2.58/0.73 bind(X20, implies(X21,implies(X22,X21))), % 2.58/0.73 bind(X21, implies(X7,X8)), % 2.58/0.73 bind(X22, implies(X14,X15)), % 2.58/0.73 bind(X23, implies(X7,X8)), % 2.58/0.73 bind(X24, implies(X22,X21)), % 2.58/0.73 bind(X25, implies(X9,X11)) % 2.58/0.73 ], % 2.58/0.73 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10])). % 2.58/0.73 % 2.58/0.73 % SZS output end IncompleteProof %------------------------------------------------------------------------------