%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n002.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 12:28:41 PM UTC 2026 % Result : Unsatisfiable 0.02s 0.37s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.03 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.08/0.35 % Computer : n002.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.02/0.35 % CPULimit : 300 % 0.02/0.35 % WCLimit : 300 % 0.02/0.35 % DateTime : Fri Sep 4 19:43:20 UTC 2026 % 0.02/0.36 % CPUTime : % 0.02/0.37 % SZS status Unsatisfiable % 0.02/0.37 % SZS output begin IncompleteProof % 0.02/0.37 cnf(c0, axiom, % 0.02/0.37 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.02/0.37 cnf(c1, plain, % 0.02/0.37 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)), % 0.02/0.37 inference(start, [], [c0])). % 0.02/0.37 % 0.02/0.37 cnf(c2, axiom, % 0.02/0.37 c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) | ~c_lessequals(X4,X2,tc_set(tc_PropLog_Opl(X3))) | ~c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3))). % 0.02/0.37 cnf(a0, assumption, % 0.02/0.37 v_p = X1). % 0.02/0.37 cnf(a1, assumption, % 0.02/0.37 c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a) = c_PropLog_Othms(X4,X3)). % 0.02/0.37 cnf(a2, assumption, % 0.02/0.37 tc_PropLog_Opl(t_a) = tc_PropLog_Opl(X3)). % 0.02/0.37 cnf(c3, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 0.02/0.37 cnf(c4, plain, % 0.02/0.37 c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) | ~c_lessequals(X4,X2,tc_set(tc_PropLog_Opl(X3))), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 0.02/0.37 % 0.02/0.37 cnf(c5, axiom, % 0.02/0.37 c_in(X5,c_PropLog_Othms(X6,X7),tc_PropLog_Opl(X7)) | ~c_in(X5,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X8,c_PropLog_Opl_Ofalse,X7),X6,tc_PropLog_Opl(X7)),X7),tc_PropLog_Opl(X7)) | ~c_in(X5,c_PropLog_Othms(c_insert(X8,X6,tc_PropLog_Opl(X7)),X7),tc_PropLog_Opl(X7))). % 0.02/0.37 cnf(a3, assumption, % 0.02/0.37 X1 = X5). % 0.02/0.37 cnf(a4, assumption, % 0.02/0.37 c_PropLog_Othms(X2,X3) = c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X8,c_PropLog_Opl_Ofalse,X7),X6,tc_PropLog_Opl(X7)),X7)). % 0.02/0.37 cnf(a5, assumption, % 0.02/0.37 tc_PropLog_Opl(X3) = tc_PropLog_Opl(X7)). % 0.02/0.37 cnf(c6, plain, % 0.02/0.37 ~c_lessequals(X4,X2,tc_set(tc_PropLog_Opl(X3))), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 0.02/0.37 cnf(c7, plain, % 0.02/0.37 c_in(X5,c_PropLog_Othms(X6,X7),tc_PropLog_Opl(X7)) | ~c_in(X5,c_PropLog_Othms(c_insert(X8,X6,tc_PropLog_Opl(X7)),X7),tc_PropLog_Opl(X7)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 0.02/0.37 % 0.02/0.37 cnf(c8, axiom, % 0.02/0.37 ~c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.02/0.37 cnf(a6, assumption, % 0.02/0.37 X5 = v_p). % 0.02/0.37 cnf(a7, assumption, % 0.02/0.37 c_PropLog_Othms(X6,X7) = c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a)). % 0.02/0.37 cnf(a8, assumption, % 0.02/0.37 tc_PropLog_Opl(X7) = tc_PropLog_Opl(t_a)). % 0.02/0.37 cnf(c9, plain, % 0.02/0.37 ~c_in(X5,c_PropLog_Othms(c_insert(X8,X6,tc_PropLog_Opl(X7)),X7),tc_PropLog_Opl(X7)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 0.02/0.37 cnf(c10, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 0.02/0.37 % 0.02/0.37 cnf(c11, axiom, % 0.02/0.37 c_in(X9,c_PropLog_Othms(X10,X11),tc_PropLog_Opl(X11)) | ~c_lessequals(X12,X10,tc_set(tc_PropLog_Opl(X11))) | ~c_in(X9,c_PropLog_Othms(X12,X11),tc_PropLog_Opl(X11))). % 0.02/0.37 cnf(a9, assumption, % 0.02/0.37 X5 = X9). % 0.02/0.37 cnf(a10, assumption, % 0.02/0.37 c_PropLog_Othms(c_insert(X8,X6,tc_PropLog_Opl(X7)),X7) = c_PropLog_Othms(X10,X11)). % 0.02/0.37 cnf(a11, assumption, % 0.02/0.37 tc_PropLog_Opl(X7) = tc_PropLog_Opl(X11)). % 0.02/0.37 cnf(c12, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a9, a10, a11])], [c9, c11])). % 0.02/0.37 cnf(c13, plain, % 0.02/0.37 ~c_lessequals(X12,X10,tc_set(tc_PropLog_Opl(X11))) | ~c_in(X9,c_PropLog_Othms(X12,X11),tc_PropLog_Opl(X11)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a9, a10, a11])], [c9, c11])). % 0.02/0.37 % 0.02/0.37 cnf(c14, axiom, % 0.02/0.37 c_lessequals(c_minus(c_insert(X13,c_minus(X14,c_insert(X15,c_emptyset,X16),tc_set(X16)),X16),X17,tc_set(X16)),c_insert(X13,c_minus(X14,c_insert(X15,X17,X16),tc_set(X16)),X16),tc_set(X16))). % 0.02/0.37 cnf(a12, assumption, % 0.02/0.37 X12 = c_minus(c_insert(X13,c_minus(X14,c_insert(X15,c_emptyset,X16),tc_set(X16)),X16),X17,tc_set(X16))). % 0.02/0.37 cnf(a13, assumption, % 0.02/0.37 X10 = c_insert(X13,c_minus(X14,c_insert(X15,X17,X16),tc_set(X16)),X16)). % 0.02/0.37 cnf(a14, assumption, % 0.02/0.37 tc_set(tc_PropLog_Opl(X11)) = tc_set(X16)). % 0.02/0.37 cnf(c15, plain, % 0.02/0.37 ~c_in(X9,c_PropLog_Othms(X12,X11),tc_PropLog_Opl(X11)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a12, a13, a14])], [c13, c14])). % 0.02/0.37 cnf(c16, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a12, a13, a14])], [c13, c14])). % 0.02/0.37 % 0.02/0.37 cnf(c17, axiom, % 0.02/0.37 c_in(X18,c_PropLog_Othms(c_minus(X19,X20,tc_set(tc_PropLog_Opl(X21))),X21),tc_PropLog_Opl(X21)) | ~c_lessequals(X22,X19,tc_set(tc_PropLog_Opl(X21))) | ~c_in(X18,c_PropLog_Othms(c_minus(X22,X20,tc_set(tc_PropLog_Opl(X21))),X21),tc_PropLog_Opl(X21))). % 0.02/0.37 cnf(a15, assumption, % 0.02/0.37 X9 = X18). % 0.02/0.37 cnf(a16, assumption, % 0.02/0.37 c_PropLog_Othms(X12,X11) = c_PropLog_Othms(c_minus(X19,X20,tc_set(tc_PropLog_Opl(X21))),X21)). % 0.02/0.37 cnf(a17, assumption, % 0.02/0.37 tc_PropLog_Opl(X11) = tc_PropLog_Opl(X21)). % 0.02/0.37 cnf(c18, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a15, a16, a17])], [c15, c17])). % 0.02/0.37 cnf(c19, plain, % 0.02/0.37 ~c_lessequals(X22,X19,tc_set(tc_PropLog_Opl(X21))) | ~c_in(X18,c_PropLog_Othms(c_minus(X22,X20,tc_set(tc_PropLog_Opl(X21))),X21),tc_PropLog_Opl(X21)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a15, a16, a17])], [c15, c17])). % 0.02/0.37 % 0.02/0.37 cnf(c20, axiom, % 0.02/0.37 c_lessequals(c_PropLog_Ohyps(X23,c_insert(X24,X25,X26),X26),c_insert(c_PropLog_Opl_Ovar(X24,X26),c_minus(c_PropLog_Ohyps(X23,X25,X26),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X24,X26),c_PropLog_Opl_Ofalse,X26),c_emptyset,tc_PropLog_Opl(X26)),tc_set(tc_PropLog_Opl(X26))),tc_PropLog_Opl(X26)),tc_set(tc_PropLog_Opl(X26)))). % 0.02/0.37 cnf(a18, assumption, % 0.02/0.37 X22 = c_PropLog_Ohyps(X23,c_insert(X24,X25,X26),X26)). % 0.02/0.37 cnf(a19, assumption, % 0.02/0.37 X19 = c_insert(c_PropLog_Opl_Ovar(X24,X26),c_minus(c_PropLog_Ohyps(X23,X25,X26),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X24,X26),c_PropLog_Opl_Ofalse,X26),c_emptyset,tc_PropLog_Opl(X26)),tc_set(tc_PropLog_Opl(X26))),tc_PropLog_Opl(X26))). % 0.02/0.37 cnf(a20, assumption, % 0.02/0.37 tc_set(tc_PropLog_Opl(X21)) = tc_set(tc_PropLog_Opl(X26))). % 0.02/0.37 cnf(c21, plain, % 0.02/0.37 ~c_in(X18,c_PropLog_Othms(c_minus(X22,X20,tc_set(tc_PropLog_Opl(X21))),X21),tc_PropLog_Opl(X21)), % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a18, a19, a20])], [c19, c20])). % 0.02/0.37 cnf(c22, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a18, a19, a20])], [c19, c20])). % 0.02/0.37 % 0.02/0.37 cnf(c23, axiom, % 0.02/0.37 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X27,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.02/0.37 cnf(a21, assumption, % 0.02/0.37 X18 = v_p). % 0.02/0.37 cnf(a22, assumption, % 0.02/0.37 c_PropLog_Othms(c_minus(X22,X20,tc_set(tc_PropLog_Opl(X21))),X21) = c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X27,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a)). % 0.02/0.37 cnf(a23, assumption, % 0.02/0.37 tc_PropLog_Opl(X21) = tc_PropLog_Opl(t_a)). % 0.02/0.37 cnf(c24, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a21, a22, a23])], [c21, c23])). % 0.02/0.37 cnf(c25, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a21, a22, a23])], [c21, c23])). % 0.02/0.37 % 0.02/0.37 cnf(c26, axiom, % 0.02/0.37 c_lessequals(c_minus(X28,X29,tc_set(X30)),c_insert(X31,c_minus(X28,c_insert(X31,X29,X30),tc_set(X30)),X30),tc_set(X30))). % 0.02/0.37 cnf(a24, assumption, % 0.02/0.37 X4 = c_minus(X28,X29,tc_set(X30))). % 0.02/0.37 cnf(a25, assumption, % 0.02/0.37 X2 = c_insert(X31,c_minus(X28,c_insert(X31,X29,X30),tc_set(X30)),X30)). % 0.02/0.37 cnf(a26, assumption, % 0.02/0.37 tc_set(tc_PropLog_Opl(X3)) = tc_set(X30)). % 0.02/0.37 cnf(c27, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a24, a25, a26])], [c6, c26])). % 0.02/0.37 cnf(c28, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(strict_predicate_extension, [assumptions([a24, a25, a26])], [c6, c26])). % 0.02/0.37 % 0.02/0.37 cnf(c29, plain, % 0.02/0.37 $false, % 0.02/0.37 inference(constraint_solving, [ % 0.02/0.37 bind(X0, v_t), % 0.02/0.37 bind(X1, v_p), % 0.02/0.37 bind(X2, c_insert(c_PropLog_Opl_Oop_A_N_62(X8,c_PropLog_Opl_Ofalse,X7),X6,tc_PropLog_Opl(X7))), % 0.02/0.37 bind(X3, t_a), % 0.02/0.37 bind(X4, c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a)))), % 0.02/0.37 bind(X5, v_p), % 0.02/0.37 bind(X6, c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a)))), % 0.02/0.37 bind(X7, t_a), % 0.02/0.37 bind(X8, c_PropLog_Opl_Ovar(X24,X26)), % 0.02/0.37 bind(X9, v_p), % 0.02/0.37 bind(X10, c_insert(X8,X6,tc_PropLog_Opl(X7))), % 0.02/0.37 bind(X11, t_a), % 0.02/0.37 bind(X12, c_minus(c_insert(X13,c_minus(X14,c_insert(X15,c_emptyset,X16),tc_set(X16)),X16),X17,tc_set(X16))), % 0.02/0.37 bind(X13, c_PropLog_Opl_Ovar(X24,X26)), % 0.02/0.37 bind(X14, c_PropLog_Ohyps(v_p,v_t,t_a)), % 0.02/0.37 bind(X15, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a)), % 0.02/0.37 bind(X16, tc_PropLog_Opl(t_a)), % 0.02/0.37 bind(X17, v_F), % 0.02/0.37 bind(X18, v_p), % 0.02/0.37 bind(X19, c_insert(X13,c_minus(X14,c_insert(X15,c_emptyset,X16),tc_set(X16)),X16)), % 0.02/0.37 bind(X20, v_F), % 0.02/0.37 bind(X21, t_a), % 0.02/0.37 bind(X22, c_PropLog_Ohyps(X23,c_insert(X24,X25,X26),X26)), % 0.02/0.37 bind(X23, v_p), % 0.02/0.37 bind(X24, v_v), % 0.02/0.37 bind(X25, v_t), % 0.02/0.37 bind(X26, t_a), % 0.02/0.37 bind(X27, c_insert(X24,X25,X26)), % 0.02/0.37 bind(X28, c_PropLog_Ohyps(v_p,X0,t_a)), % 0.02/0.37 bind(X29, v_F), % 0.02/0.37 bind(X30, tc_PropLog_Opl(t_a)), % 0.02/0.37 bind(X31, c_PropLog_Opl_Oop_A_N_62(X8,c_PropLog_Opl_Ofalse,X7)) % 0.02/0.37 ], % 0.02/0.37 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, a25, a26])). % 0.02/0.37 % 0.02/0.37 % SZS output end IncompleteProof %------------------------------------------------------------------------------