%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL120-1 : 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 : n004.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 12:28:11 PM UTC 2026 % Result : Unsatisfiable 4.21s 1.01s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL120-1 : 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 % 0.10/0.36 % Computer : n004.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 % 0.10/0.37 % DateTime : Fri Sep 4 20:41:44 UTC 2026 % 0.10/0.37 % CPUTime : % 4.21/1.01 % SZS status Unsatisfiable % 4.21/1.01 % SZS output begin IncompleteProof % 4.21/1.01 cnf(c0, axiom, % 4.21/1.01 ~is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c))))). % 4.21/1.01 cnf(c1, plain, % 4.21/1.01 ~is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))), % 4.21/1.01 inference(start, [], [c0])). % 4.21/1.01 % 4.21/1.01 cnf(c2, axiom, % 4.21/1.01 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0))). % 4.21/1.01 cnf(a0, assumption, % 4.21/1.01 equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c))) = X0). % 4.21/1.01 cnf(c3, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 4.21/1.01 cnf(c4, plain, % 4.21/1.01 ~is_a_theorem(X1) | ~is_a_theorem(equivalent(X1,X0)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 4.21/1.01 % 4.21/1.01 cnf(c5, axiom, % 4.21/1.01 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2))). % 4.21/1.01 cnf(a1, assumption, % 4.21/1.01 X1 = X2). % 4.21/1.01 cnf(c6, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X1,X0)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 4.21/1.01 cnf(c7, plain, % 4.21/1.01 ~is_a_theorem(X3) | ~is_a_theorem(equivalent(X3,X2)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 4.21/1.01 % 4.21/1.01 cnf(c8, axiom, % 4.21/1.01 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(equivalent(X5,X4))). % 4.21/1.01 cnf(a2, assumption, % 4.21/1.01 X3 = X4). % 4.21/1.01 cnf(c9, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X3,X2)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 4.21/1.01 cnf(c10, plain, % 4.21/1.01 ~is_a_theorem(X5) | ~is_a_theorem(equivalent(X5,X4)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 4.21/1.01 % 4.21/1.01 cnf(c11, axiom, % 4.21/1.01 is_a_theorem(X6) | ~is_a_theorem(X7) | ~is_a_theorem(equivalent(X7,X6))). % 4.21/1.01 cnf(a3, assumption, % 4.21/1.01 X5 = X6). % 4.21/1.01 cnf(c12, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X5,X4)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 4.21/1.01 cnf(c13, plain, % 4.21/1.01 ~is_a_theorem(X7) | ~is_a_theorem(equivalent(X7,X6)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 4.21/1.01 % 4.21/1.01 cnf(c14, axiom, % 4.21/1.01 is_a_theorem(X8) | ~is_a_theorem(X9) | ~is_a_theorem(equivalent(X9,X8))). % 4.21/1.01 cnf(a4, assumption, % 4.21/1.01 X7 = X8). % 4.21/1.01 cnf(c15, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X7,X6)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 4.21/1.01 cnf(c16, plain, % 4.21/1.01 ~is_a_theorem(X9) | ~is_a_theorem(equivalent(X9,X8)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a4])], [c13, c14])). % 4.21/1.01 % 4.21/1.01 cnf(c17, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X10,X11),equivalent(X10,X12)),equivalent(X12,X11)))). % 4.21/1.01 cnf(a5, assumption, % 4.21/1.01 X9 = equivalent(equivalent(equivalent(X10,X11),equivalent(X10,X12)),equivalent(X12,X11))). % 4.21/1.01 cnf(c18, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X9,X8)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 4.21/1.01 cnf(c19, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a5])], [c16, c17])). % 4.21/1.01 % 4.21/1.01 cnf(c20, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X13,X14),equivalent(X13,X15)),equivalent(X15,X14)))). % 4.21/1.01 cnf(a6, assumption, % 4.21/1.01 equivalent(X9,X8) = equivalent(equivalent(equivalent(X13,X14),equivalent(X13,X15)),equivalent(X15,X14))). % 4.21/1.01 cnf(c21, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a6])], [c18, c20])). % 4.21/1.01 cnf(c22, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a6])], [c18, c20])). % 4.21/1.01 % 4.21/1.01 cnf(c23, axiom, % 4.21/1.01 is_a_theorem(X16) | ~is_a_theorem(X17) | ~is_a_theorem(equivalent(X17,X16))). % 4.21/1.01 cnf(a7, assumption, % 4.21/1.01 equivalent(X7,X6) = X16). % 4.21/1.01 cnf(c24, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a7])], [c15, c23])). % 4.21/1.01 cnf(c25, plain, % 4.21/1.01 ~is_a_theorem(X17) | ~is_a_theorem(equivalent(X17,X16)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a7])], [c15, c23])). % 4.21/1.01 % 4.21/1.01 cnf(c26, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X18,X19),equivalent(X18,X20)),equivalent(X20,X19)))). % 4.21/1.01 cnf(a8, assumption, % 4.21/1.01 X17 = equivalent(equivalent(equivalent(X18,X19),equivalent(X18,X20)),equivalent(X20,X19))). % 4.21/1.01 cnf(c27, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X17,X16)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 4.21/1.01 cnf(c28, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 4.21/1.01 % 4.21/1.01 cnf(c29, axiom, % 4.21/1.01 is_a_theorem(X21) | ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21))). % 4.21/1.01 cnf(a9, assumption, % 4.21/1.01 equivalent(X17,X16) = X21). % 4.21/1.01 cnf(c30, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a9])], [c27, c29])). % 4.21/1.01 cnf(c31, plain, % 4.21/1.01 ~is_a_theorem(X22) | ~is_a_theorem(equivalent(X22,X21)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a9])], [c27, c29])). % 4.21/1.01 % 4.21/1.01 cnf(c32, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),equivalent(X25,X24)))). % 4.21/1.01 cnf(a10, assumption, % 4.21/1.01 X22 = equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),equivalent(X25,X24))). % 4.21/1.01 cnf(c33, plain, % 4.21/1.01 ~is_a_theorem(equivalent(X22,X21)), % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 4.21/1.01 cnf(c34, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a10])], [c31, c32])). % 4.21/1.01 % 4.21/1.01 cnf(c35, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X26,X27),equivalent(X26,X28)),equivalent(X28,X27)))). % 4.21/1.01 cnf(a11, assumption, % 4.21/1.01 equivalent(X22,X21) = equivalent(equivalent(equivalent(X26,X27),equivalent(X26,X28)),equivalent(X28,X27))). % 4.21/1.01 cnf(c36, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 4.21/1.01 cnf(c37, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a11])], [c33, c35])). % 4.21/1.01 % 4.21/1.01 cnf(c38, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X29,X30),equivalent(X29,X31)),equivalent(X31,X30)))). % 4.21/1.01 cnf(a12, assumption, % 4.21/1.01 equivalent(X5,X4) = equivalent(equivalent(equivalent(X29,X30),equivalent(X29,X31)),equivalent(X31,X30))). % 4.21/1.01 cnf(c39, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a12])], [c12, c38])). % 4.21/1.01 cnf(c40, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a12])], [c12, c38])). % 4.21/1.01 % 4.21/1.01 cnf(c41, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X32,X33),equivalent(X32,X34)),equivalent(X34,X33)))). % 4.21/1.01 cnf(a13, assumption, % 4.21/1.01 equivalent(X3,X2) = equivalent(equivalent(equivalent(X32,X33),equivalent(X32,X34)),equivalent(X34,X33))). % 4.21/1.01 cnf(c42, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a13])], [c9, c41])). % 4.21/1.01 cnf(c43, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a13])], [c9, c41])). % 4.21/1.01 % 4.21/1.01 cnf(c44, axiom, % 4.21/1.01 is_a_theorem(equivalent(equivalent(equivalent(X35,X36),equivalent(X35,X37)),equivalent(X37,X36)))). % 4.21/1.01 cnf(a14, assumption, % 4.21/1.01 equivalent(X1,X0) = equivalent(equivalent(equivalent(X35,X36),equivalent(X35,X37)),equivalent(X37,X36))). % 4.21/1.01 cnf(c45, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a14])], [c6, c44])). % 4.21/1.01 cnf(c46, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(strict_predicate_extension, [assumptions([a14])], [c6, c44])). % 4.21/1.01 % 4.21/1.01 cnf(c47, plain, % 4.21/1.01 $false, % 4.21/1.01 inference(constraint_solving, [ % 4.21/1.01 bind(X0, equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))), % 4.21/1.01 bind(X1, equivalent(X34,X33)), % 4.21/1.01 bind(X2, equivalent(X34,X33)), % 4.21/1.01 bind(X3, equivalent(X31,X30)), % 4.21/1.01 bind(X4, equivalent(X31,X30)), % 4.21/1.01 bind(X5, equivalent(X23,X24)), % 4.21/1.01 bind(X6, equivalent(X23,X24)), % 4.21/1.01 bind(X7, equivalent(X15,X14)), % 4.21/1.01 bind(X8, equivalent(X15,X14)), % 4.21/1.01 bind(X9, equivalent(equivalent(equivalent(X10,X11),equivalent(X10,X12)),equivalent(X12,X11))), % 4.21/1.01 bind(X10, c), % 4.21/1.01 bind(X11, equivalent(equivalent(X18,X19),equivalent(X18,X20))), % 4.21/1.01 bind(X12, equivalent(X10,X11)), % 4.21/1.01 bind(X13, equivalent(X10,X11)), % 4.21/1.01 bind(X14, equivalent(X10,X12)), % 4.21/1.01 bind(X15, equivalent(equivalent(X18,X19),equivalent(X18,X20))), % 4.21/1.01 bind(X16, equivalent(X7,X6)), % 4.21/1.01 bind(X17, equivalent(equivalent(equivalent(X18,X19),equivalent(X18,X20)),equivalent(X20,X19))), % 4.21/1.01 bind(X18, b), % 4.21/1.01 bind(X19, equivalent(X35,X37)), % 4.21/1.01 bind(X20, c), % 4.21/1.01 bind(X21, equivalent(X17,X16)), % 4.21/1.01 bind(X22, equivalent(equivalent(equivalent(X23,X24),equivalent(X23,X25)),equivalent(X25,X24))), % 4.21/1.01 bind(X23, equivalent(X15,X14)), % 4.21/1.01 bind(X24, equivalent(equivalent(equivalent(X18,X19),equivalent(X18,X20)),equivalent(X20,X19))), % 4.21/1.01 bind(X25, equivalent(X23,X24)), % 4.21/1.01 bind(X26, equivalent(X23,X24)), % 4.21/1.01 bind(X27, equivalent(X23,X25)), % 4.21/1.01 bind(X28, equivalent(equivalent(equivalent(X18,X19),equivalent(X18,X20)),equivalent(X20,X19))), % 4.21/1.01 bind(X29, equivalent(equivalent(X18,X19),equivalent(X18,X20))), % 4.21/1.01 bind(X30, equivalent(X10,X12)), % 4.21/1.01 bind(X31, equivalent(X20,X19)), % 4.21/1.01 bind(X32, c), % 4.21/1.01 bind(X33, equivalent(X35,X37)), % 4.21/1.01 bind(X34, equivalent(X10,X11)), % 4.21/1.01 bind(X35, c), % 4.21/1.01 bind(X36, equivalent(equivalent(X18,X19),equivalent(X18,X20))), % 4.21/1.01 bind(X37, a) % 4.21/1.01 ], % 4.21/1.01 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 4.21/1.02 % 4.21/1.02 % SZS output end IncompleteProof %------------------------------------------------------------------------------