%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL429-2 : 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 : n027.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 0.10s 0.38s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0. % 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 : n027.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 : Sat Sep 5 19:11:28 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.38 % SZS status Unsatisfiable % 0.10/0.38 % SZS output begin IncompleteProof % 0.10/0.38 cnf(c0, axiom, % 0.10/0.38 ~c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.10/0.38 cnf(c1, plain, % 0.10/0.38 ~c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)), % 0.10/0.38 inference(start, [], [c0])). % 0.10/0.38 % 0.10/0.38 cnf(c2, axiom, % 0.10/0.38 c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) | ~c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X2),X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)) | ~c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2))). % 0.10/0.38 cnf(a0, assumption, % 0.10/0.38 v_p = X0). % 0.10/0.38 cnf(a1, assumption, % 0.10/0.38 c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a) = c_PropLog_Othms(X1,X2)). % 0.10/0.38 cnf(a2, assumption, % 0.10/0.38 tc_PropLog_Opl(t_a) = tc_PropLog_Opl(X2)). % 0.10/0.38 cnf(c3, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 0.10/0.38 cnf(c4, plain, % 0.10/0.38 ~c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X2),X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)) | ~c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 0.10/0.38 % 0.10/0.38 cnf(c5, axiom, % 0.10/0.38 c_in(X4,c_PropLog_Othms(X5,X6),tc_PropLog_Opl(X6)) | ~c_lessequals(X7,X5,tc_set(tc_PropLog_Opl(X6))) | ~c_in(X4,c_PropLog_Othms(X7,X6),tc_PropLog_Opl(X6))). % 0.10/0.38 cnf(a3, assumption, % 0.10/0.38 X0 = X4). % 0.10/0.38 cnf(a4, assumption, % 0.10/0.38 c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X2),X1,tc_PropLog_Opl(X2)),X2) = c_PropLog_Othms(X5,X6)). % 0.10/0.38 cnf(a5, assumption, % 0.10/0.38 tc_PropLog_Opl(X2) = tc_PropLog_Opl(X6)). % 0.10/0.38 cnf(c6, plain, % 0.10/0.38 ~c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 0.10/0.38 cnf(c7, plain, % 0.10/0.38 ~c_lessequals(X7,X5,tc_set(tc_PropLog_Opl(X6))) | ~c_in(X4,c_PropLog_Othms(X7,X6),tc_PropLog_Opl(X6)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 0.10/0.38 % 0.10/0.38 cnf(c8, axiom, % 0.10/0.38 c_lessequals(c_minus(c_insert(X8,c_minus(X9,c_insert(X10,c_emptyset,X11),tc_set(X11)),X11),X12,tc_set(X11)),c_insert(X8,c_minus(X9,c_insert(X10,X12,X11),tc_set(X11)),X11),tc_set(X11))). % 0.10/0.38 cnf(a6, assumption, % 0.10/0.38 X7 = c_minus(c_insert(X8,c_minus(X9,c_insert(X10,c_emptyset,X11),tc_set(X11)),X11),X12,tc_set(X11))). % 0.10/0.38 cnf(a7, assumption, % 0.10/0.38 X5 = c_insert(X8,c_minus(X9,c_insert(X10,X12,X11),tc_set(X11)),X11)). % 0.10/0.38 cnf(a8, assumption, % 0.10/0.38 tc_set(tc_PropLog_Opl(X6)) = tc_set(X11)). % 0.10/0.38 cnf(c9, plain, % 0.10/0.38 ~c_in(X4,c_PropLog_Othms(X7,X6),tc_PropLog_Opl(X6)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 0.10/0.38 cnf(c10, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 0.10/0.38 % 0.10/0.38 cnf(c11, axiom, % 0.10/0.38 c_in(X13,c_PropLog_Othms(c_minus(X14,X15,tc_set(tc_PropLog_Opl(X16))),X16),tc_PropLog_Opl(X16)) | ~c_lessequals(X17,X14,tc_set(tc_PropLog_Opl(X16))) | ~c_in(X13,c_PropLog_Othms(c_minus(X17,X15,tc_set(tc_PropLog_Opl(X16))),X16),tc_PropLog_Opl(X16))). % 0.10/0.38 cnf(a9, assumption, % 0.10/0.38 X4 = X13). % 0.10/0.38 cnf(a10, assumption, % 0.10/0.38 c_PropLog_Othms(X7,X6) = c_PropLog_Othms(c_minus(X14,X15,tc_set(tc_PropLog_Opl(X16))),X16)). % 0.10/0.38 cnf(a11, assumption, % 0.10/0.38 tc_PropLog_Opl(X6) = tc_PropLog_Opl(X16)). % 0.10/0.38 cnf(c12, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a9, a10, a11])], [c9, c11])). % 0.10/0.38 cnf(c13, plain, % 0.10/0.38 ~c_lessequals(X17,X14,tc_set(tc_PropLog_Opl(X16))) | ~c_in(X13,c_PropLog_Othms(c_minus(X17,X15,tc_set(tc_PropLog_Opl(X16))),X16),tc_PropLog_Opl(X16)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a9, a10, a11])], [c9, c11])). % 0.10/0.38 % 0.10/0.38 cnf(c14, axiom, % 0.10/0.38 c_lessequals(c_PropLog_Ohyps(X18,c_minus(X19,c_insert(X20,c_emptyset,X21),tc_set(X21)),X21),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X20,X21),c_PropLog_Opl_Ofalse,X21),c_minus(c_PropLog_Ohyps(X18,X19,X21),c_insert(c_PropLog_Opl_Ovar(X20,X21),c_emptyset,tc_PropLog_Opl(X21)),tc_set(tc_PropLog_Opl(X21))),tc_PropLog_Opl(X21)),tc_set(tc_PropLog_Opl(X21)))). % 0.10/0.38 cnf(a12, assumption, % 0.10/0.38 X17 = c_PropLog_Ohyps(X18,c_minus(X19,c_insert(X20,c_emptyset,X21),tc_set(X21)),X21)). % 0.10/0.38 cnf(a13, assumption, % 0.10/0.38 X14 = c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X20,X21),c_PropLog_Opl_Ofalse,X21),c_minus(c_PropLog_Ohyps(X18,X19,X21),c_insert(c_PropLog_Opl_Ovar(X20,X21),c_emptyset,tc_PropLog_Opl(X21)),tc_set(tc_PropLog_Opl(X21))),tc_PropLog_Opl(X21))). % 0.10/0.38 cnf(a14, assumption, % 0.10/0.38 tc_set(tc_PropLog_Opl(X16)) = tc_set(tc_PropLog_Opl(X21))). % 0.10/0.38 cnf(c15, plain, % 0.10/0.38 ~c_in(X13,c_PropLog_Othms(c_minus(X17,X15,tc_set(tc_PropLog_Opl(X16))),X16),tc_PropLog_Opl(X16)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a12, a13, a14])], [c13, c14])). % 0.10/0.38 cnf(c16, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a12, a13, a14])], [c13, c14])). % 0.10/0.38 % 0.10/0.38 cnf(c17, axiom, % 0.10/0.38 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X22,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.10/0.38 cnf(a15, assumption, % 0.10/0.38 X13 = v_p). % 0.10/0.38 cnf(a16, assumption, % 0.10/0.38 c_PropLog_Othms(c_minus(X17,X15,tc_set(tc_PropLog_Opl(X16))),X16) = c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X22,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a)). % 0.10/0.38 cnf(a17, assumption, % 0.10/0.38 tc_PropLog_Opl(X16) = tc_PropLog_Opl(t_a)). % 0.10/0.38 cnf(c18, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a15, a16, a17])], [c15, c17])). % 0.10/0.38 cnf(c19, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a15, a16, a17])], [c15, c17])). % 0.10/0.38 % 0.10/0.38 cnf(c20, axiom, % 0.10/0.38 c_in(X23,c_PropLog_Othms(X24,X25),tc_PropLog_Opl(X25)) | ~c_lessequals(X26,X24,tc_set(tc_PropLog_Opl(X25))) | ~c_in(X23,c_PropLog_Othms(X26,X25),tc_PropLog_Opl(X25))). % 0.10/0.38 cnf(a18, assumption, % 0.10/0.38 X0 = X23). % 0.10/0.38 cnf(a19, assumption, % 0.10/0.38 c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2) = c_PropLog_Othms(X24,X25)). % 0.10/0.38 cnf(a20, assumption, % 0.10/0.38 tc_PropLog_Opl(X2) = tc_PropLog_Opl(X25)). % 0.10/0.38 cnf(c21, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a18, a19, a20])], [c6, c20])). % 0.10/0.38 cnf(c22, plain, % 0.10/0.38 ~c_lessequals(X26,X24,tc_set(tc_PropLog_Opl(X25))) | ~c_in(X23,c_PropLog_Othms(X26,X25),tc_PropLog_Opl(X25)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a18, a19, a20])], [c6, c20])). % 0.10/0.38 % 0.10/0.38 cnf(c23, axiom, % 0.10/0.38 c_lessequals(c_minus(X27,X28,tc_set(X29)),c_insert(X30,c_minus(X27,c_insert(X30,X28,X29),tc_set(X29)),X29),tc_set(X29))). % 0.10/0.38 cnf(a21, assumption, % 0.10/0.38 X26 = c_minus(X27,X28,tc_set(X29))). % 0.10/0.38 cnf(a22, assumption, % 0.10/0.38 X24 = c_insert(X30,c_minus(X27,c_insert(X30,X28,X29),tc_set(X29)),X29)). % 0.10/0.38 cnf(a23, assumption, % 0.10/0.38 tc_set(tc_PropLog_Opl(X25)) = tc_set(X29)). % 0.10/0.38 cnf(c24, plain, % 0.10/0.38 ~c_in(X23,c_PropLog_Othms(X26,X25),tc_PropLog_Opl(X25)), % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a21, a22, a23])], [c22, c23])). % 0.10/0.38 cnf(c25, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a21, a22, a23])], [c22, c23])). % 0.10/0.38 % 0.10/0.38 cnf(c26, axiom, % 0.10/0.38 c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X31,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))). % 0.10/0.38 cnf(a24, assumption, % 0.10/0.38 X23 = v_p). % 0.10/0.38 cnf(a25, assumption, % 0.10/0.38 c_PropLog_Othms(X26,X25) = c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X31,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a)). % 0.10/0.38 cnf(a26, assumption, % 0.10/0.38 tc_PropLog_Opl(X25) = tc_PropLog_Opl(t_a)). % 0.10/0.38 cnf(c27, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a24, a25, a26])], [c24, c26])). % 0.10/0.38 cnf(c28, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(strict_predicate_extension, [assumptions([a24, a25, a26])], [c24, c26])). % 0.10/0.38 % 0.10/0.38 cnf(c29, plain, % 0.10/0.38 $false, % 0.10/0.38 inference(constraint_solving, [ % 0.10/0.38 bind(X0, v_p), % 0.10/0.38 bind(X1, c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a)))), % 0.10/0.38 bind(X2, t_a), % 0.10/0.38 bind(X3, c_PropLog_Opl_Ovar(X20,X21)), % 0.10/0.38 bind(X4, v_p), % 0.10/0.38 bind(X5, c_insert(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X2),X1,tc_PropLog_Opl(X2))), % 0.10/0.38 bind(X6, t_a), % 0.10/0.38 bind(X7, c_minus(c_insert(X8,c_minus(X9,c_insert(X10,c_emptyset,X11),tc_set(X11)),X11),X12,tc_set(X11))), % 0.10/0.38 bind(X8, c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X2)), % 0.10/0.38 bind(X9, c_PropLog_Ohyps(v_p,v_t,t_a)), % 0.10/0.38 bind(X10, c_PropLog_Opl_Ovar(v_v,t_a)), % 0.10/0.38 bind(X11, tc_PropLog_Opl(t_a)), % 0.10/0.38 bind(X12, v_F), % 0.10/0.38 bind(X13, v_p), % 0.10/0.38 bind(X14, c_insert(X8,c_minus(X9,c_insert(X10,c_emptyset,X11),tc_set(X11)),X11)), % 0.10/0.38 bind(X15, v_F), % 0.10/0.38 bind(X16, t_a), % 0.10/0.38 bind(X17, c_PropLog_Ohyps(X18,c_minus(X19,c_insert(X20,c_emptyset,X21),tc_set(X21)),X21)), % 0.10/0.38 bind(X18, v_p), % 0.10/0.38 bind(X19, v_t), % 0.10/0.38 bind(X20, v_v), % 0.10/0.38 bind(X21, t_a), % 0.10/0.38 bind(X22, c_minus(X19,c_insert(X20,c_emptyset,X21),tc_set(X21))), % 0.10/0.38 bind(X23, v_p), % 0.10/0.38 bind(X24, c_insert(X3,X1,tc_PropLog_Opl(X2))), % 0.10/0.38 bind(X25, t_a), % 0.10/0.38 bind(X26, c_minus(X27,X28,tc_set(X29))), % 0.10/0.38 bind(X27, c_PropLog_Ohyps(v_p,v_t,t_a)), % 0.10/0.38 bind(X28, v_F), % 0.10/0.38 bind(X29, tc_PropLog_Opl(t_a)), % 0.10/0.38 bind(X30, c_PropLog_Opl_Ovar(X20,X21)), % 0.10/0.38 bind(X31, v_t) % 0.10/0.38 ], % 0.10/0.38 [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])). % 0.10/0.38 % 0.10/0.38 % SZS output end IncompleteProof %------------------------------------------------------------------------------