TSTP Solution File: SET064+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET064+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n012.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 14:28:21 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 : SET064+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:25:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.000000s
% 0.19/0.63 % Output :CNFRefutation 0.000000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 % File : SET064+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.19/0.63 % Domain : Set Theory
% 0.19/0.63 % Problem : Uniqueness of null class
% 0.19/0.63 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.19/0.63 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.19/0.63 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.19/0.63 % Source : [Qua92]
% 0.19/0.63 % Names :
% 0.19/0.63
% 0.19/0.63 % Status : Theorem
% 0.19/0.63 % Rating : 0.19 v7.4.0, 0.23 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.22 v7.0.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.24 v6.1.0, 0.23 v6.0.0, 0.30 v5.5.0, 0.26 v5.4.0
% 0.19/0.63 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.19/0.63 % Number of atoms : 102 ( 20 equ)
% 0.19/0.63 % Maximal formula atoms : 4 ( 2 avg)
% 0.19/0.63 % Number of connectives : 63 ( 5 ~; 4 |; 26 &)
% 0.19/0.63 % ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% 0.19/0.63 % Maximal formula depth : 7 ( 4 avg)
% 0.19/0.63 % Maximal term depth : 4 ( 1 avg)
% 0.19/0.63 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.19/0.63 % Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% 0.19/0.63 % Number of variables : 88 ( 82 !; 6 ?)
% 0.19/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.63
% 0.19/0.63 % Comments :
% 0.19/0.63 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.19/0.63 % Bugfixes : v2.7.0 - Fixed null_class_is_unique to not mention Skolem
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %----Include set theory axioms
% 0.19/0.63 include('Axioms/SET005+0.ax').
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %----SP4: Uniqueness of null class
% 0.19/0.63 fof(null_class_is_unique,conjecture,
% 0.19/0.63 ! [Z] :
% 0.19/0.63 ( Z = null_class
% 0.19/0.63 | ? [Y] : member(Y,Z) ) ).
% 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:120(EqnAxiom:37)
% 0.19/0.63 %VarNum:608(SingletonVarNum:170)
% 0.19/0.63 %MaxLitNum:4
% 0.19/0.63 %MaxfuncDepth:13
% 0.19/0.63 %SharedTerms:16
% 0.19/0.63 %goalClause: 48 50
% 0.19/0.63 %singleGoalClaCount:2
% 0.19/0.64 [38]P1(a1)
% 0.19/0.64 [39]P2(a8)
% 0.19/0.64 [40]P4(a1,a13)
% 0.19/0.64 [48]~E(a17,a19)
% 0.19/0.64 [42]P5(a2,f3(a13,a13))
% 0.19/0.64 [43]P5(a14,f3(a13,a13))
% 0.19/0.64 [41]P5(x411,a13)
% 0.19/0.64 [49]~P4(x491,a19)
% 0.19/0.64 [50]~P4(x501,a17)
% 0.19/0.64 [46]P5(f15(x461),f3(f3(a13,a13),a13))
% 0.19/0.64 [47]P5(f16(x471),f3(f3(a13,a13),a13))
% 0.19/0.64 [44]P4(f26(x441,x442),a13)
% 0.19/0.64 [45]P5(f4(x451,x452),f3(a13,a13))
% 0.19/0.64 [53]~P1(x531)+P5(a1,x531)
% 0.19/0.64 [54]~P1(x541)+P4(a19,x541)
% 0.19/0.64 [55]E(x551,a19)+P4(f9(x551),a13)
% 0.19/0.64 [56]P4(f9(x561),x561)+E(x561,a19)
% 0.19/0.64 [57]P3(f9(x571),x571)+E(x571,a19)
% 0.19/0.64 [58]~P4(x581,a13)+P4(f24(x581),a13)
% 0.19/0.64 [59]~P4(x591,a13)+P4(f22(x591),a13)
% 0.19/0.64 [60]~P4(x601,a20)+P4(f10(x601),a13)
% 0.19/0.64 [61]~P2(x611)+P5(x611,f3(a13,a13))
% 0.19/0.64 [92]~P4(x921,a20)+E(f26(f26(f10(x921),f10(x921)),f26(f10(x921),f26(f10(x921),f10(x921)))),x921)
% 0.19/0.64 [93]~P2(x931)+P5(f4(x931,f6(f16(f3(x931,a13)))),a20)
% 0.19/0.64 [109]~P1(x1091)+P5(f6(f6(f16(f3(f21(a14,f3(x1091,a13)),a13)))),x1091)
% 0.19/0.64 [52]~E(x521,x522)+P5(x521,x522)
% 0.19/0.64 [62]P4(x621,a13)+~P4(x621,f5(x622))
% 0.19/0.64 [63]P4(x631,a13)+~P4(x631,f6(x632))
% 0.19/0.64 [64]P4(x641,a13)+~P4(x641,f22(x642))
% 0.19/0.64 [65]P5(x651,x652)+~P4(x651,f22(x652))
% 0.19/0.64 [67]P5(x671,x672)+P4(f7(x671,x672),x671)
% 0.19/0.64 [68]P3(x681,x682)+P4(f12(x681,x682),x682)
% 0.19/0.64 [69]P3(x691,x692)+P4(f12(x691,x692),x691)
% 0.19/0.64 [70]~P4(x701,x702)+~P4(x701,f5(x702))
% 0.19/0.64 [81]~P4(x811,f24(x812))+P4(x811,f11(x811,x812))
% 0.19/0.64 [82]~P4(x821,f24(x822))+P4(f11(x821,x822),x822)
% 0.19/0.64 [86]P5(x861,x862)+~P4(f7(x861,x862),x862)
% 0.19/0.64 [90]~P4(x902,f6(x901))+~E(f21(x901,f3(f26(x902,x902),a13)),a19)
% 0.19/0.64 [100]P4(x1001,a13)+~P4(f26(f26(x1002,x1002),f26(x1002,f26(x1001,x1001))),a2)
% 0.19/0.64 [101]P4(x1011,a13)+~P4(f26(f26(x1012,x1012),f26(x1012,f26(x1011,x1011))),a14)
% 0.19/0.64 [102]P4(x1021,a13)+~P4(f26(f26(x1021,x1021),f26(x1021,f26(x1022,x1022))),a14)
% 0.19/0.64 [103]P4(x1031,x1032)+~P4(f26(f26(x1031,x1031),f26(x1031,f26(x1032,x1032))),a2)
% 0.19/0.64 [104]E(f25(x1041,f26(x1041,x1041)),x1042)+~P4(f26(f26(x1041,x1041),f26(x1041,f26(x1042,x1042))),a14)
% 0.19/0.64 [73]~P4(x731,x733)+P4(x731,f25(x732,x733))
% 0.19/0.64 [74]~P4(x741,x742)+P4(x741,f25(x742,x743))
% 0.19/0.64 [83]P4(x831,a13)+~P4(x831,f26(x832,x833))
% 0.19/0.64 [84]P4(x841,x842)+~P4(x841,f21(x843,x842))
% 0.19/0.64 [85]P4(x851,x852)+~P4(x851,f21(x852,x853))
% 0.19/0.64 [94]~P4(x941,f3(x942,x943))+E(f26(f26(f18(x941),f18(x941)),f26(f18(x941),f26(f23(x941),f23(x941)))),x941)
% 0.19/0.64 [105]P4(x1051,a13)+~P4(f26(f26(x1051,x1051),f26(x1051,f26(x1052,x1052))),f4(x1053,x1054))
% 0.19/0.64 [106]P4(x1061,x1062)+~P4(f26(f26(x1063,x1063),f26(x1063,f26(x1061,x1061))),f3(x1064,x1062))
% 0.19/0.64 [107]P4(x1071,x1072)+~P4(f26(f26(x1071,x1071),f26(x1071,f26(x1073,x1073))),f3(x1072,x1074))
% 0.19/0.64 [113]~P4(f26(f26(f26(f26(x1133,x1133),f26(x1133,f26(x1131,x1131))),f26(f26(x1133,x1133),f26(x1133,f26(x1131,x1131)))),f26(f26(f26(x1133,x1133),f26(x1133,f26(x1131,x1131))),f26(x1132,x1132))),f15(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)
% 0.19/0.64 [114]~P4(f26(f26(f26(f26(x1142,x1142),f26(x1142,f26(x1141,x1141))),f26(f26(x1142,x1142),f26(x1142,f26(x1141,x1141)))),f26(f26(f26(x1142,x1142),f26(x1142,f26(x1141,x1141))),f26(x1143,x1143))),f16(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))),x1144)
% 0.19/0.64 [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))),f15(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))
% 0.19/0.64 [116]~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))),f16(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))
% 0.19/0.64 [119]~P4(f26(f26(x1194,x1194),f26(x1194,f26(x1191,x1191))),f4(x1192,x1193))+P4(x1191,f6(f6(f16(f3(f21(x1192,f3(f6(f6(f16(f3(f21(x1193,f3(f26(x1194,x1194),a13)),a13)))),a13)),a13)))))
% 0.19/0.64 [108]P2(x1081)+~P5(x1081,f3(a13,a13))+~P5(f4(x1081,f6(f16(f3(x1081,a13)))),a20)
% 0.19/0.64 [111]P1(x1111)+~P4(a19,x1111)+~P5(f6(f6(f16(f3(f21(a14,f3(x1111,a13)),a13)))),x1111)
% 0.19/0.64 [112]~P4(x1121,a13)+E(x1121,a19)+P4(f24(f6(f6(f16(f3(f21(a8,f3(f26(x1121,x1121),a13)),a13))))),x1121)
% 0.19/0.64 [66]~P5(x662,x661)+~P5(x661,x662)+E(x661,x662)
% 0.19/0.64 [71]P4(x711,x712)+P4(x711,f5(x712))+~P4(x711,a13)
% 0.19/0.64 [75]~P5(x751,x752)+~P4(x751,a13)+P4(x751,f22(x752))
% 0.19/0.64 [89]P4(x892,f6(x891))+~P4(x892,a13)+E(f21(x891,f3(f26(x892,x892),a13)),a19)
% 0.19/0.64 [91]~P4(x912,a13)+P4(x911,a20)+~E(x911,f26(f26(x912,x912),f26(x912,f26(x912,x912))))
% 0.19/0.64 [97]~P4(x971,x972)+~P4(x972,a13)+P4(f26(f26(x971,x971),f26(x971,f26(x972,x972))),a2)
% 0.19/0.64 [95]~P4(x952,a13)+~P4(x951,a13)+E(f18(f26(f26(x951,x951),f26(x951,f26(x952,x952)))),x951)
% 0.19/0.64 [96]~P4(x962,a13)+~P4(x961,a13)+E(f23(f26(f26(x961,x961),f26(x961,f26(x962,x962)))),x962)
% 0.19/0.64 [110]~P2(x1101)+~P4(x1102,a13)+P4(f6(f6(f16(f3(f21(x1101,f3(x1102,a13)),a13)))),a13)
% 0.19/0.64 [72]~P4(x721,x723)+P4(x721,x722)+~P5(x723,x722)
% 0.19/0.64 [80]~P3(x803,x802)+~P4(x801,x802)+~P4(x801,x803)
% 0.19/0.64 [76]~E(x761,x763)+~P4(x761,a13)+P4(x761,f26(x762,x763))
% 0.19/0.64 [77]~E(x771,x772)+~P4(x771,a13)+P4(x771,f26(x772,x773))
% 0.19/0.64 [78]~P4(x781,x783)+~P4(x783,x782)+P4(x781,f24(x782))
% 0.19/0.64 [79]E(x791,x792)+E(x791,x793)+~P4(x791,f26(x793,x792))
% 0.19/0.64 [87]~P4(x871,x873)+~P4(x871,x872)+P4(x871,f21(x872,x873))
% 0.19/0.64 [88]P4(x881,x882)+P4(x881,x883)+~P4(x881,f25(x883,x882))
% 0.19/0.64 [98]~P4(x982,x984)+~P4(x981,x983)+P4(f26(f26(x981,x981),f26(x981,f26(x982,x982))),f3(x983,x984))
% 0.19/0.64 [117]~P4(f26(f26(f26(f26(x1172,x1172),f26(x1172,f26(x1173,x1173))),f26(f26(x1172,x1172),f26(x1172,f26(x1173,x1173)))),f26(f26(f26(x1172,x1172),f26(x1172,f26(x1173,x1173))),f26(x1171,x1171))),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))),f15(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))
% 0.19/0.64 [118]~P4(f26(f26(f26(f26(x1182,x1182),f26(x1182,f26(x1181,x1181))),f26(f26(x1182,x1182),f26(x1182,f26(x1181,x1181)))),f26(f26(f26(x1182,x1182),f26(x1182,f26(x1181,x1181))),f26(x1183,x1183))),x1184)+P4(f26(f26(f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182))),f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182)))),f26(f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182))),f26(x1183,x1183))),f16(x1184))+~P4(f26(f26(f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182))),f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182)))),f26(f26(f26(x1181,x1181),f26(x1181,f26(x1182,x1182))),f26(x1183,x1183))),f3(f3(a13,a13),a13))
% 0.19/0.64 [120]~P4(x1201,a13)+P4(f26(f26(x1201,x1201),f26(x1201,f26(x1202,x1202))),f4(x1203,x1204))+~P4(x1202,f6(f6(f16(f3(f21(x1203,f3(f6(f6(f16(f3(f21(x1204,f3(f26(x1201,x1201),a13)),a13)))),a13)),a13)))))
% 0.19/0.64 [99]~P4(x992,a13)+~P4(x991,a13)+~E(f25(x991,f26(x991,x991)),x992)+P4(f26(f26(x991,x991),f26(x991,f26(x992,x992))),a14)
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.19/0.64 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.19/0.64 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.19/0.64 [7]~E(x71,x72)+E(f26(x71,x73),f26(x72,x73))
% 0.19/0.64 [8]~E(x81,x82)+E(f26(x83,x81),f26(x83,x82))
% 0.19/0.64 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.19/0.64 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.19/0.64 [11]~E(x111,x112)+E(f16(x111),f16(x112))
% 0.19/0.64 [12]~E(x121,x122)+E(f15(x121),f15(x122))
% 0.19/0.64 [13]~E(x131,x132)+E(f23(x131),f23(x132))
% 0.19/0.64 [14]~E(x141,x142)+E(f21(x141,x143),f21(x142,x143))
% 0.19/0.64 [15]~E(x151,x152)+E(f21(x153,x151),f21(x153,x152))
% 0.19/0.64 [16]~E(x161,x162)+E(f18(x161),f18(x162))
% 0.19/0.64 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.19/0.64 [18]~E(x181,x182)+E(f25(x181,x183),f25(x182,x183))
% 0.19/0.64 [19]~E(x191,x192)+E(f25(x193,x191),f25(x193,x192))
% 0.19/0.64 [20]~E(x201,x202)+E(f9(x201),f9(x202))
% 0.19/0.64 [21]~E(x211,x212)+E(f7(x211,x213),f7(x212,x213))
% 0.19/0.64 [22]~E(x221,x222)+E(f7(x223,x221),f7(x223,x222))
% 0.19/0.64 [23]~E(x231,x232)+E(f11(x231,x233),f11(x232,x233))
% 0.19/0.64 [24]~E(x241,x242)+E(f11(x243,x241),f11(x243,x242))
% 0.19/0.64 [25]~E(x251,x252)+E(f24(x251),f24(x252))
% 0.19/0.64 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 0.19/0.64 [27]~E(x271,x272)+E(f5(x271),f5(x272))
% 0.19/0.64 [28]~E(x281,x282)+E(f12(x281,x283),f12(x282,x283))
% 0.19/0.64 [29]~E(x291,x292)+E(f12(x293,x291),f12(x293,x292))
% 0.19/0.64 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.19/0.64 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.19/0.64 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.19/0.64 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.19/0.64 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.19/0.64 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.19/0.64 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363)
% 0.19/0.64 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(121,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[50,48,56]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------