%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET083-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 14:20:36 EDT 2024
% Result : Unsatisfiable 2.36s 2.43s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET083-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.00/0.08 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.28 % Computer : n027.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sun Jun 23 14:47:08 EDT 2024
% 0.12/0.28 % CPUTime :
% 0.13/0.49 start to proof:theBenchmark
% 2.36/2.43 %-------------------------------------------
% 2.36/2.43 % File :CSE---1.7
% 2.36/2.43 % Problem :theBenchmark
% 2.36/2.43 % Transform :cnf
% 2.36/2.43 % Format :tptp:raw
% 2.36/2.43 % Command :java -jar mcs_scs.jar %d %s
% 2.36/2.43
% 2.36/2.43 % Result :Theorem 1.880000s
% 2.36/2.43 % Output :CNFRefutation 1.880000s
% 2.36/2.43 %-------------------------------------------
% 2.36/2.43 %--------------------------------------------------------------------------
% 2.36/2.43 % File : SET083-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 2.36/2.43 % Domain : Set Theory
% 2.36/2.43 % Problem : A singleton set depends on its element, part 1
% 2.36/2.43 % Version : [Qua92] axioms.
% 2.36/2.43 % English :
% 2.36/2.43
% 2.36/2.43 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 2.36/2.43 % Source : [Quaife]
% 2.36/2.43 % Names :
% 2.36/2.43
% 2.36/2.43 % Status : Unsatisfiable
% 2.36/2.43 % Rating : 0.15 v8.2.0, 0.14 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.25 v5.4.0, 0.30 v5.3.0, 0.28 v5.2.0, 0.19 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.36 v4.0.0, 0.27 v3.7.0, 0.30 v3.5.0, 0.27 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.15 v3.1.0, 0.18 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.18 v2.4.0, 0.00 v2.1.0
% 2.36/2.43 % Syntax : Number of clauses : 94 ( 32 unt; 8 nHn; 65 RR)
% 2.36/2.43 % Number of literals : 184 ( 41 equ; 85 neg)
% 2.36/2.43 % Maximal clause size : 5 ( 1 avg)
% 2.36/2.43 % Maximal term depth : 6 ( 1 avg)
% 2.36/2.43 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 2.36/2.43 % Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% 2.36/2.43 % Number of variables : 176 ( 25 sgn)
% 2.36/2.43 % SPC : CNF_UNS_RFO_SEQ_NHN
% 2.36/2.43
% 2.36/2.43 % Comments :
% 2.36/2.43 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 2.36/2.43 %--------------------------------------------------------------------------
% 2.36/2.43 %----Include von Neuman-Bernays-Godel set theory axioms
% 2.36/2.43 include('Axioms/SET004-0.ax').
% 2.36/2.43 %--------------------------------------------------------------------------
% 2.36/2.43 cnf(prove_singleton_identified_by_element1_1,negated_conjecture,
% 2.36/2.43 singleton(x) = singleton(y) ).
% 2.36/2.43
% 2.36/2.43 cnf(prove_singleton_identified_by_element1_2,negated_conjecture,
% 2.36/2.43 member(x,universal_class) ).
% 2.36/2.43
% 2.36/2.43 cnf(prove_singleton_identified_by_element1_3,negated_conjecture,
% 2.36/2.43 x != y ).
% 2.36/2.43
% 2.36/2.43 %--------------------------------------------------------------------------
% 2.36/2.43 %-------------------------------------------
% 2.36/2.43 % Proof found
% 2.36/2.43 % SZS status Theorem for theBenchmark
% 2.36/2.43 % SZS output start Proof
% 2.36/2.43 %ClaNum:121(EqnAxiom:42)
% 2.36/2.43 %VarNum:718(SingletonVarNum:150)
% 2.36/2.44 %MaxLitNum:5
% 2.36/2.44 %MaxfuncDepth:24
% 2.36/2.44 %SharedTerms:36
% 2.36/2.44 %goalClause: 46 48 59
% 2.36/2.44 %singleGoalClaCount:3
% 2.36/2.44 [43]P1(a1)
% 2.36/2.44 [44]P2(a2)
% 2.36/2.44 [45]P5(a1,a17)
% 2.36/2.44 [46]P5(a23,a17)
% 2.36/2.44 [59]~E(a25,a23)
% 2.36/2.44 [48]E(f24(a25,a25),f24(a23,a23))
% 2.36/2.44 [49]P6(a4,f5(a17,a17))
% 2.36/2.44 [50]P6(a18,f5(a17,a17))
% 2.36/2.44 [56]E(f9(f8(f10(f5(a21,a17))),a21),a12)
% 2.36/2.44 [57]E(f9(f5(a17,a17),f9(f5(a17,a17),f7(f6(f7(a4),f8(f10(f5(a4,a17))))))),a21)
% 2.36/2.44 [47]P6(x471,a17)
% 2.36/2.44 [54]P6(f19(x541),f5(f5(a17,a17),a17))
% 2.36/2.44 [55]P6(f10(x551),f5(f5(a17,a17),a17))
% 2.36/2.44 [58]E(f9(f8(x581),f7(f8(f9(f6(f8(f10(f5(a4,a17))),x581),a12)))),f3(x581))
% 2.36/2.44 [51]P5(f24(x511,x512),a17)
% 2.36/2.44 [52]P6(f6(x521,x522),f5(a17,a17))
% 2.36/2.44 [53]E(f9(f5(x531,x532),x533),f9(x533,f5(x531,x532)))
% 2.36/2.44 [60]~P7(x601)+P2(x601)
% 2.36/2.44 [61]~P8(x611)+P2(x611)
% 2.36/2.44 [64]~P1(x641)+P6(a1,x641)
% 2.36/2.44 [65]~P1(x651)+P5(a13,x651)
% 2.36/2.44 [67]P5(f20(x671),x671)+E(x671,a13)
% 2.36/2.44 [68]~P2(x681)+P6(x681,f5(a17,a17))
% 2.36/2.44 [66]E(x661,a13)+E(f9(x661,f20(x661)),a13)
% 2.36/2.44 [76]~P8(x761)+E(f5(f8(f8(x761)),f8(f8(x761))),f8(x761))
% 2.36/2.44 [86]~P7(x861)+P2(f8(f10(f5(x861,a17))))
% 2.36/2.44 [90]~P5(x901,a17)+P5(f8(f9(a4,f5(a17,x901))),a17)
% 2.36/2.44 [92]~P9(x921)+P6(f6(x921,f8(f10(f5(x921,a17)))),a12)
% 2.36/2.44 [93]~P2(x931)+P6(f6(x931,f8(f10(f5(x931,a17)))),a12)
% 2.36/2.44 [94]~P8(x941)+P6(f8(f8(f10(f5(x941,a17)))),f8(f8(x941)))
% 2.36/2.44 [99]P9(x991)+~P6(f6(x991,f8(f10(f5(x991,a17)))),a12)
% 2.36/2.44 [108]~P1(x1081)+P6(f8(f8(f10(f5(f9(a18,f5(x1081,a17)),a17)))),x1081)
% 2.36/2.44 [112]~P5(x1121,a17)+P5(f7(f8(f8(f10(f5(f9(a4,f5(f7(x1121),a17)),a17))))),a17)
% 2.36/2.44 [62]~E(x622,x621)+P6(x621,x622)
% 2.36/2.44 [63]~E(x631,x632)+P6(x631,x632)
% 2.36/2.44 [70]P6(x701,x702)+P5(f14(x701,x702),x701)
% 2.36/2.44 [71]~P5(x711,x712)+~P5(x711,f7(x712))
% 2.36/2.44 [74]~P5(x741,a17)+P5(x741,f24(x742,x741))
% 2.36/2.44 [75]~P5(x751,a17)+P5(x751,f24(x751,x752))
% 2.36/2.44 [80]P6(x801,x802)+~P5(f14(x801,x802),x802)
% 2.36/2.44 [89]~P5(x892,f8(x891))+~E(f9(x891,f5(f24(x892,x892),a17)),a13)
% 2.36/2.44 [98]P5(x981,x982)+~P5(f24(f24(x981,x981),f24(x981,f24(x982,x982))),a4)
% 2.36/2.44 [105]~P5(f24(f24(x1051,x1051),f24(x1051,f24(x1052,x1052))),a18)+E(f7(f9(f7(x1051),f7(f24(x1051,x1051)))),x1052)
% 2.36/2.44 [82]P2(x821)+~P3(x821,x822,x823)
% 2.36/2.44 [83]P8(x831)+~P4(x832,x833,x831)
% 2.36/2.44 [84]P8(x841)+~P4(x842,x841,x843)
% 2.36/2.44 [88]~P4(x881,x882,x883)+P3(x881,x882,x883)
% 2.36/2.44 [78]P5(x781,x782)+~P5(x781,f9(x783,x782))
% 2.36/2.44 [79]P5(x791,x792)+~P5(x791,f9(x792,x793))
% 2.36/2.44 [85]~P3(x852,x851,x853)+E(f8(f8(x851)),f8(x852))
% 2.36/2.44 [95]~P5(x951,f5(x952,x953))+E(f24(f24(f11(x951),f11(x951)),f24(f11(x951),f24(f22(x951),f22(x951)))),x951)
% 2.36/2.44 [97]~P3(x971,x973,x972)+P6(f8(f8(f10(f5(x971,a17)))),f8(f8(x972)))
% 2.36/2.44 [100]P5(x1001,x1002)+~P5(f24(f24(x1003,x1003),f24(x1003,f24(x1001,x1001))),f5(x1004,x1002))
% 2.36/2.44 [101]P5(x1011,x1012)+~P5(f24(f24(x1011,x1011),f24(x1011,f24(x1013,x1013))),f5(x1012,x1014))
% 2.36/2.44 [113]~P5(f24(f24(f24(f24(x1133,x1133),f24(x1133,f24(x1131,x1131))),f24(f24(x1133,x1133),f24(x1133,f24(x1131,x1131)))),f24(f24(f24(x1133,x1133),f24(x1133,f24(x1131,x1131))),f24(x1132,x1132))),f19(x1134))+P5(f24(f24(f24(f24(x1131,x1131),f24(x1131,f24(x1132,x1132))),f24(f24(x1131,x1131),f24(x1131,f24(x1132,x1132)))),f24(f24(f24(x1131,x1131),f24(x1131,f24(x1132,x1132))),f24(x1133,x1133))),x1134)
% 2.36/2.44 [114]~P5(f24(f24(f24(f24(x1142,x1142),f24(x1142,f24(x1141,x1141))),f24(f24(x1142,x1142),f24(x1142,f24(x1141,x1141)))),f24(f24(f24(x1142,x1142),f24(x1142,f24(x1141,x1141))),f24(x1143,x1143))),f10(x1144))+P5(f24(f24(f24(f24(x1141,x1141),f24(x1141,f24(x1142,x1142))),f24(f24(x1141,x1141),f24(x1141,f24(x1142,x1142)))),f24(f24(f24(x1141,x1141),f24(x1141,f24(x1142,x1142))),f24(x1143,x1143))),x1144)
% 2.36/2.44 [118]~P5(f24(f24(x1184,x1184),f24(x1184,f24(x1181,x1181))),f6(x1182,x1183))+P5(x1181,f8(f8(f10(f5(f9(x1182,f5(f8(f8(f10(f5(f9(x1183,f5(f24(x1184,x1184),a17)),a17)))),a17)),a17)))))
% 2.36/2.44 [91]~P2(x911)+P7(x911)+~P2(f8(f10(f5(x911,a17))))
% 2.36/2.44 [102]P2(x1021)+~P6(x1021,f5(a17,a17))+~P6(f6(x1021,f8(f10(f5(x1021,a17)))),a12)
% 2.36/2.44 [110]P1(x1101)+~P5(a13,x1101)+~P6(f8(f8(f10(f5(f9(a18,f5(x1101,a17)),a17)))),x1101)
% 2.36/2.44 [117]~P5(x1171,a17)+E(x1171,a13)+P5(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(a2,f5(f24(x1171,x1171),a17)),a17))))))),x1171)
% 2.36/2.44 [69]~P6(x692,x691)+~P6(x691,x692)+E(x691,x692)
% 2.36/2.44 [72]P5(x721,x722)+P5(x721,f7(x722))+~P5(x721,a17)
% 2.36/2.44 [87]P5(x872,f8(x871))+~P5(x872,a17)+E(f9(x871,f5(f24(x872,x872),a17)),a13)
% 2.36/2.44 [106]~P5(x1061,x1062)+~P5(f24(f24(x1061,x1061),f24(x1061,f24(x1062,x1062))),f5(a17,a17))+P5(f24(f24(x1061,x1061),f24(x1061,f24(x1062,x1062))),a4)
% 2.36/2.44 [107]~P5(f24(f24(x1071,x1071),f24(x1071,f24(x1072,x1072))),f5(a17,a17))+~E(f7(f9(f7(x1071),f7(f24(x1071,x1071)))),x1072)+P5(f24(f24(x1071,x1071),f24(x1071,f24(x1072,x1072))),a18)
% 2.36/2.44 [109]~P2(x1091)+~P5(x1092,a17)+P5(f8(f8(f10(f5(f9(x1091,f5(x1092,a17)),a17)))),a17)
% 2.36/2.44 [73]~P5(x731,x733)+P5(x731,x732)+~P6(x733,x732)
% 2.36/2.44 [77]E(x771,x772)+E(x771,x773)+~P5(x771,f24(x773,x772))
% 2.36/2.44 [81]~P5(x811,x813)+~P5(x811,x812)+P5(x811,f9(x812,x813))
% 2.36/2.44 [96]~P5(x962,x964)+~P5(x961,x963)+P5(f24(f24(x961,x961),f24(x961,f24(x962,x962))),f5(x963,x964))
% 2.36/2.44 [115]~P5(f24(f24(f24(f24(x1152,x1152),f24(x1152,f24(x1153,x1153))),f24(f24(x1152,x1152),f24(x1152,f24(x1153,x1153)))),f24(f24(f24(x1152,x1152),f24(x1152,f24(x1153,x1153))),f24(x1151,x1151))),x1154)+P5(f24(f24(f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152))),f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152)))),f24(f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152))),f24(x1153,x1153))),f19(x1154))+~P5(f24(f24(f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152))),f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152)))),f24(f24(f24(x1151,x1151),f24(x1151,f24(x1152,x1152))),f24(x1153,x1153))),f5(f5(a17,a17),a17))
% 2.36/2.44 [116]~P5(f24(f24(f24(f24(x1162,x1162),f24(x1162,f24(x1161,x1161))),f24(f24(x1162,x1162),f24(x1162,f24(x1161,x1161)))),f24(f24(f24(x1162,x1162),f24(x1162,f24(x1161,x1161))),f24(x1163,x1163))),x1164)+P5(f24(f24(f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162))),f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162)))),f24(f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162))),f24(x1163,x1163))),f10(x1164))+~P5(f24(f24(f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162))),f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162)))),f24(f24(f24(x1161,x1161),f24(x1161,f24(x1162,x1162))),f24(x1163,x1163))),f5(f5(a17,a17),a17))
% 2.36/2.44 [119]P5(f24(f24(x1191,x1191),f24(x1191,f24(x1192,x1192))),f6(x1193,x1194))+~P5(f24(f24(x1191,x1191),f24(x1191,f24(x1192,x1192))),f5(a17,a17))+~P5(x1192,f8(f8(f10(f5(f9(x1193,f5(f8(f8(f10(f5(f9(x1194,f5(f24(x1191,x1191),a17)),a17)))),a17)),a17)))))
% 2.36/2.44 [120]~P4(x1202,x1205,x1201)+~P5(f24(f24(x1203,x1203),f24(x1203,f24(x1204,x1204))),f8(x1205))+E(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1201,f5(f24(f24(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17)))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1204,x1204),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1204,x1204),a17)),a17)))))))))),f24(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17)))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1203,x1203),a17)),a17))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1204,x1204),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(x1204,x1204),a17)),a17))))))))))),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1202,f5(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1205,f5(f24(f24(f24(x1203,x1203),f24(x1203,f24(x1204,x1204))),f24(f24(x1203,x1203),f24(x1203,f24(x1204,x1204)))),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1205,f5(f24(f24(f24(x1203,x1203),f24(x1203,f24(x1204,x1204))),f24(f24(x1203,x1203),f24(x1203,f24(x1204,x1204)))),a17)),a17)))))))),a17)),a17))))))))
% 2.36/2.44 [104]~P2(x1041)+P8(x1041)+~E(f5(f8(f8(x1041)),f8(f8(x1041))),f8(x1041))+~P6(f8(f8(f10(f5(x1041,a17)))),f8(f8(x1041)))
% 2.36/2.44 [103]~P2(x1031)+P3(x1031,x1032,x1033)+~E(f8(f8(x1032)),f8(x1031))+~P6(f8(f8(f10(f5(x1031,a17)))),f8(f8(x1033)))
% 2.36/2.44 [111]~P8(x1113)+~P8(x1112)+~P3(x1111,x1112,x1113)+P4(x1111,x1112,x1113)+P5(f24(f24(f15(x1111,x1112,x1113),f15(x1111,x1112,x1113)),f24(f15(x1111,x1112,x1113),f24(f16(x1111,x1112,x1113),f16(x1111,x1112,x1113)))),f8(x1112))
% 2.36/2.44 [121]~P8(x1213)+~P8(x1212)+~P3(x1211,x1212,x1213)+P4(x1211,x1212,x1213)+~E(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1213,f5(f24(f24(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17)))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)),a17)),a17)))))))))),f24(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17)))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),a17)),a17))))))),f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)),a17)),a17))))))))))),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1211,f5(f24(f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1212,f5(f24(f24(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),f24(f15(x1211,x1212,x1213),f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)))),f24(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),f24(f15(x1211,x1212,x1213),f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213))))),a17)),a17))))))),f8(f9(a4,f5(a17,f8(f8(f10(f5(f9(x1212,f5(f24(f24(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),f24(f15(x1211,x1212,x1213),f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213)))),f24(f24(f15(x1211,x1212,x1213),f15(x1211,x1212,x1213)),f24(f15(x1211,x1212,x1213),f24(f16(x1211,x1212,x1213),f16(x1211,x1212,x1213))))),a17)),a17)))))))),a17)),a17))))))))
% 2.36/2.44 %EqnAxiom
% 2.36/2.44 [1]E(x11,x11)
% 2.36/2.44 [2]E(x22,x21)+~E(x21,x22)
% 2.36/2.44 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.36/2.44 [4]~E(x41,x42)+E(f24(x41,x43),f24(x42,x43))
% 2.36/2.44 [5]~E(x51,x52)+E(f24(x53,x51),f24(x53,x52))
% 2.36/2.44 [6]~E(x61,x62)+E(f8(x61),f8(x62))
% 2.36/2.44 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73))
% 2.36/2.44 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82))
% 2.36/2.44 [9]~E(x91,x92)+E(f10(x91),f10(x92))
% 2.36/2.44 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103))
% 2.36/2.44 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112))
% 2.36/2.44 [12]~E(x121,x122)+E(f6(x121,x123),f6(x122,x123))
% 2.36/2.44 [13]~E(x131,x132)+E(f6(x133,x131),f6(x133,x132))
% 2.36/2.44 [14]~E(x141,x142)+E(f16(x141,x143,x144),f16(x142,x143,x144))
% 2.36/2.44 [15]~E(x151,x152)+E(f16(x153,x151,x154),f16(x153,x152,x154))
% 2.36/2.44 [16]~E(x161,x162)+E(f16(x163,x164,x161),f16(x163,x164,x162))
% 2.36/2.44 [17]~E(x171,x172)+E(f7(x171),f7(x172))
% 2.36/2.44 [18]~E(x181,x182)+E(f14(x181,x183),f14(x182,x183))
% 2.36/2.44 [19]~E(x191,x192)+E(f14(x193,x191),f14(x193,x192))
% 2.36/2.44 [20]~E(x201,x202)+E(f15(x201,x203,x204),f15(x202,x203,x204))
% 2.36/2.44 [21]~E(x211,x212)+E(f15(x213,x211,x214),f15(x213,x212,x214))
% 2.36/2.44 [22]~E(x221,x222)+E(f15(x223,x224,x221),f15(x223,x224,x222))
% 2.36/2.44 [23]~E(x231,x232)+E(f20(x231),f20(x232))
% 2.36/2.44 [24]~E(x241,x242)+E(f19(x241),f19(x242))
% 2.36/2.44 [25]~E(x251,x252)+E(f11(x251),f11(x252))
% 2.36/2.44 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 2.36/2.44 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 2.36/2.44 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 2.36/2.44 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 2.36/2.44 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 2.36/2.44 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 2.36/2.44 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 2.36/2.44 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 2.36/2.44 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 2.36/2.44 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 2.36/2.44 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 2.36/2.44 [37]~P7(x371)+P7(x372)+~E(x371,x372)
% 2.36/2.44 [38]~P8(x381)+P8(x382)+~E(x381,x382)
% 2.36/2.44 [39]P4(x392,x393,x394)+~E(x391,x392)+~P4(x391,x393,x394)
% 2.36/2.44 [40]P4(x403,x402,x404)+~E(x401,x402)+~P4(x403,x401,x404)
% 2.36/2.44 [41]P4(x413,x414,x412)+~E(x411,x412)+~P4(x413,x414,x411)
% 2.36/2.44 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 2.36/2.44
% 2.36/2.44 %-------------------------------------------
% 2.36/2.44 cnf(122,plain,
% 2.36/2.44 (P6(x1221,x1221)),
% 2.36/2.44 inference(equality_inference,[],[62])).
% 2.36/2.44 cnf(127,plain,
% 2.36/2.44 (P6(f24(a23,a23),f24(a25,a25))),
% 2.36/2.44 inference(scs_inference,[],[48,122,2,35])).
% 2.36/2.44 cnf(128,plain,
% 2.36/2.44 (P6(x1281,x1281)),
% 2.36/2.44 inference(rename_variables,[],[122])).
% 2.36/2.44 cnf(129,plain,
% 2.36/2.44 (P6(f24(a25,a25),f24(a23,a23))),
% 2.36/2.44 inference(scs_inference,[],[48,122,128,2,35,36])).
% 2.36/2.44 cnf(136,plain,
% 2.36/2.44 (E(f9(f9(f5(a17,a17),f7(f6(f7(a4),f8(f10(f5(a4,a17)))))),f5(a17,a17)),a21)),
% 2.36/2.44 inference(scs_inference,[],[53,57,2,3])).
% 2.36/2.44 cnf(164,plain,
% 2.36/2.44 (~P5(x1641,f24(a23,a23))+P5(x1641,f24(a25,a25))),
% 2.36/2.44 inference(scs_inference,[],[48,127,136,47,57,54,2,69,37,36,38,73])).
% 2.36/2.44 cnf(1131,plain,
% 2.36/2.44 (P5(a23,f24(a25,a25))),
% 2.36/2.44 inference(scs_inference,[],[46,74,164])).
% 2.36/2.44 cnf(1137,plain,
% 2.36/2.44 ($false),
% 2.36/2.44 inference(scs_inference,[],[46,59,129,1131,77,73,30,2]),
% 2.36/2.44 ['proof']).
% 2.36/2.44 % SZS output end Proof
% 2.36/2.44 % Total time :1.880000s
%------------------------------------------------------------------------------