TSTP Solution File: SET077+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET077+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 : Thu Aug 31 14:28:30 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET077+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 14:34:44 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 % File : SET077+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.19/0.62 % Domain : Set Theory
% 0.19/0.62 % Problem : Every singleton is a set
% 0.19/0.62 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.19/0.62 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.19/0.62 % Source : [Qua92]
% 0.19/0.62 % Names :
% 0.19/0.62
% 0.19/0.62 % Status : Theorem
% 0.19/0.62 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0
% 0.19/0.62 % Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% 0.19/0.62 % Number of atoms : 101 ( 19 equ)
% 0.19/0.62 % Maximal formula atoms : 4 ( 2 avg)
% 0.19/0.62 % Number of connectives : 62 ( 5 ~; 3 |; 26 &)
% 0.19/0.62 % ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% 0.19/0.62 % Maximal formula depth : 7 ( 4 avg)
% 0.19/0.62 % Maximal term depth : 4 ( 1 avg)
% 0.19/0.62 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.19/0.62 % Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% 0.19/0.62 % Number of variables : 87 ( 82 !; 5 ?)
% 0.19/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.62
% 0.19/0.62 % Comments :
% 0.19/0.62 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %----Include set theory axioms
% 0.19/0.62 include('Axioms/SET005+0.ax').
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.63 %----SS1: Every singleton is a set
% 0.19/0.63 fof(singletons_are_sets,conjecture,
% 0.19/0.63 ! [X] : member(singleton(X),universal_class) ).
% 0.19/0.63
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:119(EqnAxiom:37)
% 0.19/0.63 %VarNum:607(SingletonVarNum:169)
% 0.19/0.63 %MaxLitNum:4
% 0.19/0.63 %MaxfuncDepth:13
% 0.19/0.63 %SharedTerms:17
% 0.19/0.63 %goalClause: 49
% 0.19/0.63 %singleGoalClaCount:1
% 0.19/0.63 [38]P1(a1)
% 0.19/0.63 [39]P2(a8)
% 0.19/0.63 [40]P4(a1,a13)
% 0.19/0.63 [42]P5(a2,f3(a13,a13))
% 0.19/0.63 [43]P5(a14,f3(a13,a13))
% 0.19/0.63 [49]~P4(f26(a17,a17),a13)
% 0.19/0.63 [41]P5(x411,a13)
% 0.19/0.63 [48]~P4(x481,a19)
% 0.19/0.63 [46]P5(f15(x461),f3(f3(a13,a13),a13))
% 0.19/0.63 [47]P5(f16(x471),f3(f3(a13,a13),a13))
% 0.19/0.63 [44]P4(f26(x441,x442),a13)
% 0.19/0.63 [45]P5(f4(x451,x452),f3(a13,a13))
% 0.19/0.63 [52]~P1(x521)+P5(a1,x521)
% 0.19/0.63 [53]~P1(x531)+P4(a19,x531)
% 0.19/0.63 [54]E(x541,a19)+P4(f9(x541),a13)
% 0.19/0.63 [55]P4(f9(x551),x551)+E(x551,a19)
% 0.19/0.63 [56]P3(f9(x561),x561)+E(x561,a19)
% 0.19/0.63 [57]~P4(x571,a13)+P4(f24(x571),a13)
% 0.19/0.63 [58]~P4(x581,a13)+P4(f22(x581),a13)
% 0.19/0.63 [59]~P4(x591,a20)+P4(f10(x591),a13)
% 0.19/0.63 [60]~P2(x601)+P5(x601,f3(a13,a13))
% 0.19/0.63 [91]~P4(x911,a20)+E(f26(f26(f10(x911),f10(x911)),f26(f10(x911),f26(f10(x911),f10(x911)))),x911)
% 0.19/0.63 [92]~P2(x921)+P5(f4(x921,f6(f16(f3(x921,a13)))),a20)
% 0.19/0.63 [108]~P1(x1081)+P5(f6(f6(f16(f3(f21(a14,f3(x1081,a13)),a13)))),x1081)
% 0.19/0.63 [51]~E(x511,x512)+P5(x511,x512)
% 0.19/0.63 [61]P4(x611,a13)+~P4(x611,f5(x612))
% 0.19/0.63 [62]P4(x621,a13)+~P4(x621,f6(x622))
% 0.19/0.63 [63]P4(x631,a13)+~P4(x631,f22(x632))
% 0.19/0.63 [64]P5(x641,x642)+~P4(x641,f22(x642))
% 0.19/0.63 [66]P5(x661,x662)+P4(f7(x661,x662),x661)
% 0.19/0.63 [67]P3(x671,x672)+P4(f12(x671,x672),x672)
% 0.19/0.63 [68]P3(x681,x682)+P4(f12(x681,x682),x681)
% 0.19/0.63 [69]~P4(x691,x692)+~P4(x691,f5(x692))
% 0.19/0.63 [80]~P4(x801,f24(x802))+P4(x801,f11(x801,x802))
% 0.19/0.63 [81]~P4(x811,f24(x812))+P4(f11(x811,x812),x812)
% 0.19/0.63 [85]P5(x851,x852)+~P4(f7(x851,x852),x852)
% 0.19/0.63 [89]~P4(x892,f6(x891))+~E(f21(x891,f3(f26(x892,x892),a13)),a19)
% 0.19/0.63 [99]P4(x991,a13)+~P4(f26(f26(x992,x992),f26(x992,f26(x991,x991))),a2)
% 0.19/0.63 [100]P4(x1001,a13)+~P4(f26(f26(x1002,x1002),f26(x1002,f26(x1001,x1001))),a14)
% 0.19/0.63 [101]P4(x1011,a13)+~P4(f26(f26(x1011,x1011),f26(x1011,f26(x1012,x1012))),a14)
% 0.19/0.63 [102]P4(x1021,x1022)+~P4(f26(f26(x1021,x1021),f26(x1021,f26(x1022,x1022))),a2)
% 0.19/0.63 [103]E(f25(x1031,f26(x1031,x1031)),x1032)+~P4(f26(f26(x1031,x1031),f26(x1031,f26(x1032,x1032))),a14)
% 0.19/0.63 [72]~P4(x721,x723)+P4(x721,f25(x722,x723))
% 0.19/0.63 [73]~P4(x731,x732)+P4(x731,f25(x732,x733))
% 0.19/0.63 [82]P4(x821,a13)+~P4(x821,f26(x822,x823))
% 0.19/0.63 [83]P4(x831,x832)+~P4(x831,f21(x833,x832))
% 0.19/0.63 [84]P4(x841,x842)+~P4(x841,f21(x842,x843))
% 0.19/0.63 [93]~P4(x931,f3(x932,x933))+E(f26(f26(f18(x931),f18(x931)),f26(f18(x931),f26(f23(x931),f23(x931)))),x931)
% 0.19/0.63 [104]P4(x1041,a13)+~P4(f26(f26(x1041,x1041),f26(x1041,f26(x1042,x1042))),f4(x1043,x1044))
% 0.19/0.63 [105]P4(x1051,x1052)+~P4(f26(f26(x1053,x1053),f26(x1053,f26(x1051,x1051))),f3(x1054,x1052))
% 0.19/0.63 [106]P4(x1061,x1062)+~P4(f26(f26(x1061,x1061),f26(x1061,f26(x1063,x1063))),f3(x1062,x1064))
% 0.19/0.63 [112]~P4(f26(f26(f26(f26(x1123,x1123),f26(x1123,f26(x1121,x1121))),f26(f26(x1123,x1123),f26(x1123,f26(x1121,x1121)))),f26(f26(f26(x1123,x1123),f26(x1123,f26(x1121,x1121))),f26(x1122,x1122))),f15(x1124))+P4(f26(f26(f26(f26(x1121,x1121),f26(x1121,f26(x1122,x1122))),f26(f26(x1121,x1121),f26(x1121,f26(x1122,x1122)))),f26(f26(f26(x1121,x1121),f26(x1121,f26(x1122,x1122))),f26(x1123,x1123))),x1124)
% 0.19/0.63 [113]~P4(f26(f26(f26(f26(x1132,x1132),f26(x1132,f26(x1131,x1131))),f26(f26(x1132,x1132),f26(x1132,f26(x1131,x1131)))),f26(f26(f26(x1132,x1132),f26(x1132,f26(x1131,x1131))),f26(x1133,x1133))),f16(x1134))+P4(f26(f26(f26(f26(x1131,x1131),f26(x1131,f26(x1132,x1132))),f26(f26(x1131,x1131),f26(x1131,f26(x1132,x1132)))),f26(f26(f26(x1131,x1131),f26(x1131,f26(x1132,x1132))),f26(x1133,x1133))),x1134)
% 0.19/0.63 [114]~P4(f26(f26(f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142))),f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142)))),f26(f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142))),f26(x1143,x1143))),f15(x1144))+P4(f26(f26(f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142))),f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142)))),f26(f26(f26(x1141,x1141),f26(x1141,f26(x1142,x1142))),f26(x1143,x1143))),f3(f3(a13,a13),a13))
% 0.19/0.63 [115]~P4(f26(f26(f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152))),f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152)))),f26(f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152))),f26(x1153,x1153))),f16(x1154))+P4(f26(f26(f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152))),f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152)))),f26(f26(f26(x1151,x1151),f26(x1151,f26(x1152,x1152))),f26(x1153,x1153))),f3(f3(a13,a13),a13))
% 0.19/0.63 [118]~P4(f26(f26(x1184,x1184),f26(x1184,f26(x1181,x1181))),f4(x1182,x1183))+P4(x1181,f6(f6(f16(f3(f21(x1182,f3(f6(f6(f16(f3(f21(x1183,f3(f26(x1184,x1184),a13)),a13)))),a13)),a13)))))
% 0.19/0.63 [107]P2(x1071)+~P5(x1071,f3(a13,a13))+~P5(f4(x1071,f6(f16(f3(x1071,a13)))),a20)
% 0.19/0.63 [110]P1(x1101)+~P4(a19,x1101)+~P5(f6(f6(f16(f3(f21(a14,f3(x1101,a13)),a13)))),x1101)
% 0.19/0.63 [111]~P4(x1111,a13)+E(x1111,a19)+P4(f24(f6(f6(f16(f3(f21(a8,f3(f26(x1111,x1111),a13)),a13))))),x1111)
% 0.19/0.63 [65]~P5(x652,x651)+~P5(x651,x652)+E(x651,x652)
% 0.19/0.63 [70]P4(x701,x702)+P4(x701,f5(x702))+~P4(x701,a13)
% 0.19/0.63 [74]~P5(x741,x742)+~P4(x741,a13)+P4(x741,f22(x742))
% 0.19/0.63 [88]P4(x882,f6(x881))+~P4(x882,a13)+E(f21(x881,f3(f26(x882,x882),a13)),a19)
% 0.19/0.63 [90]~P4(x902,a13)+P4(x901,a20)+~E(x901,f26(f26(x902,x902),f26(x902,f26(x902,x902))))
% 0.19/0.63 [96]~P4(x961,x962)+~P4(x962,a13)+P4(f26(f26(x961,x961),f26(x961,f26(x962,x962))),a2)
% 0.19/0.63 [94]~P4(x942,a13)+~P4(x941,a13)+E(f18(f26(f26(x941,x941),f26(x941,f26(x942,x942)))),x941)
% 0.19/0.63 [95]~P4(x952,a13)+~P4(x951,a13)+E(f23(f26(f26(x951,x951),f26(x951,f26(x952,x952)))),x952)
% 0.19/0.63 [109]~P2(x1091)+~P4(x1092,a13)+P4(f6(f6(f16(f3(f21(x1091,f3(x1092,a13)),a13)))),a13)
% 0.19/0.63 [71]~P4(x711,x713)+P4(x711,x712)+~P5(x713,x712)
% 0.19/0.63 [79]~P3(x793,x792)+~P4(x791,x792)+~P4(x791,x793)
% 0.19/0.63 [75]~E(x751,x753)+~P4(x751,a13)+P4(x751,f26(x752,x753))
% 0.19/0.63 [76]~E(x761,x762)+~P4(x761,a13)+P4(x761,f26(x762,x763))
% 0.19/0.63 [77]~P4(x771,x773)+~P4(x773,x772)+P4(x771,f24(x772))
% 0.19/0.63 [78]E(x781,x782)+E(x781,x783)+~P4(x781,f26(x783,x782))
% 0.19/0.63 [86]~P4(x861,x863)+~P4(x861,x862)+P4(x861,f21(x862,x863))
% 0.19/0.63 [87]P4(x871,x872)+P4(x871,x873)+~P4(x871,f25(x873,x872))
% 0.19/0.63 [97]~P4(x972,x974)+~P4(x971,x973)+P4(f26(f26(x971,x971),f26(x971,f26(x972,x972))),f3(x973,x974))
% 0.19/0.63 [116]~P4(f26(f26(f26(f26(x1162,x1162),f26(x1162,f26(x1163,x1163))),f26(f26(x1162,x1162),f26(x1162,f26(x1163,x1163)))),f26(f26(f26(x1162,x1162),f26(x1162,f26(x1163,x1163))),f26(x1161,x1161))),x1164)+P4(f26(f26(f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162))),f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162)))),f26(f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162))),f26(x1163,x1163))),f15(x1164))+~P4(f26(f26(f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162))),f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162)))),f26(f26(f26(x1161,x1161),f26(x1161,f26(x1162,x1162))),f26(x1163,x1163))),f3(f3(a13,a13),a13))
% 0.19/0.63 [117]~P4(f26(f26(f26(f26(x1172,x1172),f26(x1172,f26(x1171,x1171))),f26(f26(x1172,x1172),f26(x1172,f26(x1171,x1171)))),f26(f26(f26(x1172,x1172),f26(x1172,f26(x1171,x1171))),f26(x1173,x1173))),x1174)+P4(f26(f26(f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172))),f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172)))),f26(f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172))),f26(x1173,x1173))),f16(x1174))+~P4(f26(f26(f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172))),f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172)))),f26(f26(f26(x1171,x1171),f26(x1171,f26(x1172,x1172))),f26(x1173,x1173))),f3(f3(a13,a13),a13))
% 0.19/0.63 [119]~P4(x1191,a13)+P4(f26(f26(x1191,x1191),f26(x1191,f26(x1192,x1192))),f4(x1193,x1194))+~P4(x1192,f6(f6(f16(f3(f21(x1193,f3(f6(f6(f16(f3(f21(x1194,f3(f26(x1191,x1191),a13)),a13)))),a13)),a13)))))
% 0.19/0.63 [98]~P4(x982,a13)+~P4(x981,a13)+~E(f25(x981,f26(x981,x981)),x982)+P4(f26(f26(x981,x981),f26(x981,f26(x982,x982))),a14)
% 0.19/0.63 %EqnAxiom
% 0.19/0.63 [1]E(x11,x11)
% 0.19/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.63 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.19/0.63 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.19/0.63 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.19/0.63 [7]~E(x71,x72)+E(f26(x71,x73),f26(x72,x73))
% 0.19/0.63 [8]~E(x81,x82)+E(f26(x83,x81),f26(x83,x82))
% 0.19/0.63 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.19/0.63 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.19/0.63 [11]~E(x111,x112)+E(f16(x111),f16(x112))
% 0.19/0.63 [12]~E(x121,x122)+E(f15(x121),f15(x122))
% 0.19/0.63 [13]~E(x131,x132)+E(f18(x131),f18(x132))
% 0.19/0.63 [14]~E(x141,x142)+E(f21(x141,x143),f21(x142,x143))
% 0.19/0.63 [15]~E(x151,x152)+E(f21(x153,x151),f21(x153,x152))
% 0.19/0.63 [16]~E(x161,x162)+E(f25(x161,x163),f25(x162,x163))
% 0.19/0.63 [17]~E(x171,x172)+E(f25(x173,x171),f25(x173,x172))
% 0.19/0.63 [18]~E(x181,x182)+E(f10(x181),f10(x182))
% 0.19/0.63 [19]~E(x191,x192)+E(f24(x191),f24(x192))
% 0.19/0.63 [20]~E(x201,x202)+E(f11(x201,x203),f11(x202,x203))
% 0.19/0.63 [21]~E(x211,x212)+E(f11(x213,x211),f11(x213,x212))
% 0.19/0.63 [22]~E(x221,x222)+E(f9(x221),f9(x222))
% 0.19/0.63 [23]~E(x231,x232)+E(f7(x231,x233),f7(x232,x233))
% 0.19/0.63 [24]~E(x241,x242)+E(f7(x243,x241),f7(x243,x242))
% 0.19/0.63 [25]~E(x251,x252)+E(f5(x251),f5(x252))
% 0.19/0.63 [26]~E(x261,x262)+E(f23(x261),f23(x262))
% 0.19/0.63 [27]~E(x271,x272)+E(f22(x271),f22(x272))
% 0.19/0.63 [28]~E(x281,x282)+E(f12(x281,x283),f12(x282,x283))
% 0.19/0.63 [29]~E(x291,x292)+E(f12(x293,x291),f12(x293,x292))
% 0.19/0.63 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.19/0.63 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.19/0.63 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.19/0.63 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.19/0.63 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.19/0.63 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.19/0.63 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363)
% 0.19/0.63 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371)
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(120,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[49,44]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------