%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET094+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 14:20:40 EDT 2024
% Result : Theorem 0.58s 0.69s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET094+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Jun 23 17:13:09 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.58/0.68 %-------------------------------------------
% 0.58/0.68 % File :CSE---1.7
% 0.58/0.68 % Problem :theBenchmark
% 0.58/0.68 % Transform :cnf
% 0.58/0.68 % Format :tptp:raw
% 0.58/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.58/0.68
% 0.58/0.68 % Result :Theorem 0.070000s
% 0.58/0.68 % Output :CNFRefutation 0.070000s
% 0.58/0.68 %-------------------------------------------
% 0.58/0.69 %--------------------------------------------------------------------------
% 0.58/0.69 % File : SET094+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.58/0.69 % Domain : Set Theory
% 0.58/0.69 % Problem : Property 1 of singletons
% 0.58/0.69 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.58/0.69 % English :
% 0.58/0.69
% 0.58/0.69 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.58/0.69 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.58/0.69 % Source : [Qua92]
% 0.58/0.69 % Names :
% 0.58/0.69
% 0.58/0.69 % Status : Theorem
% 0.58/0.69 % Rating : 0.28 v8.2.0, 0.25 v7.5.0, 0.28 v7.4.0, 0.17 v7.3.0
% 0.58/0.69 % Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% 0.58/0.69 % Number of atoms : 111 ( 25 equ)
% 0.58/0.69 % Maximal formula atoms : 4 ( 2 avg)
% 0.58/0.69 % Number of connectives : 68 ( 5 ~; 5 |; 27 &)
% 0.58/0.69 % ( 19 <=>; 12 =>; 0 <=; 0 <~>)
% 0.58/0.69 % Maximal formula depth : 7 ( 4 avg)
% 0.58/0.69 % Maximal term depth : 4 ( 1 avg)
% 0.58/0.69 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.58/0.69 % Number of functors : 27 ( 27 usr; 5 con; 0-3 aty)
% 0.58/0.69 % Number of variables : 92 ( 87 !; 5 ?)
% 0.58/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.58/0.69
% 0.58/0.69 % Comments :
% 0.58/0.69 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.58/0.69 % : v7.3.0 - Added axioms for member_of
% 0.58/0.69 %--------------------------------------------------------------------------
% 0.58/0.69 %----Include set theory axioms
% 0.58/0.69 include('Axioms/SET005+0.ax').
% 0.58/0.69 %--------------------------------------------------------------------------
% 0.58/0.69 %----Axioms to define member_of, based on SET086+1
% 0.58/0.69 fof(member_singleton_universal,axiom,
% 0.58/0.69 ! [Y] :
% 0.58/0.69 ( member(Y,universal_class)
% 0.58/0.69 => member(member_of(singleton(Y)),universal_class) ) ).
% 0.58/0.69
% 0.58/0.69 fof(member_singleton_singleton,axiom,
% 0.58/0.69 ! [Y] :
% 0.58/0.69 ( member(Y,universal_class)
% 0.58/0.69 => singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.58/0.69
% 0.58/0.69 fof(member_universal_self,axiom,
% 0.58/0.69 ! [X] :
% 0.58/0.69 ( member(member_of(X),universal_class)
% 0.58/0.69 | member_of(X) = X ) ).
% 0.58/0.69
% 0.58/0.69 fof(singleton_self,axiom,
% 0.58/0.69 ! [X] :
% 0.58/0.69 ( singleton(member_of(X)) = X
% 0.58/0.69 | member_of(X) = X ) ).
% 0.58/0.69
% 0.58/0.69 %----SS10
% 0.58/0.69 fof(property_of_singletons1_1,conjecture,
% 0.58/0.69 ! [X,Y] :
% 0.58/0.69 ( ( singleton(member_of(X)) = X
% 0.58/0.69 & member(Y,X) )
% 0.58/0.69 => member_of(X) = Y ) ).
% 0.58/0.69
% 0.58/0.69 %--------------------------------------------------------------------------
% 0.58/0.69 %-------------------------------------------
% 0.58/0.69 % Proof found
% 0.58/0.69 % SZS status Theorem for theBenchmark
% 0.58/0.69 % SZS output start Proof
% 0.58/0.69 %ClaNum:126(EqnAxiom:38)
% 0.58/0.69 %VarNum:625(SingletonVarNum:173)
% 0.58/0.69 %MaxLitNum:4
% 0.58/0.69 %MaxfuncDepth:13
% 0.58/0.69 %SharedTerms:21
% 0.58/0.69 %goalClause: 42 44 51
% 0.58/0.69 %singleGoalClaCount:3
% 0.58/0.69 [39]P1(a1)
% 0.58/0.69 [40]P2(a8)
% 0.58/0.69 [41]P4(a1,a13)
% 0.58/0.69 [42]P4(a14,a15)
% 0.58/0.69 [45]P5(a2,f3(a13,a13))
% 0.58/0.69 [46]P5(a21,f3(a13,a13))
% 0.58/0.69 [51]~E(f16(a15),a14)
% 0.58/0.69 [44]E(f28(f16(a15),f16(a15)),a15)
% 0.58/0.69 [43]P5(x431,a13)
% 0.58/0.69 [52]~P4(x521,a23)
% 0.58/0.69 [49]P5(f22(x491),f3(f3(a13,a13),a13))
% 0.58/0.69 [50]P5(f17(x501),f3(f3(a13,a13),a13))
% 0.58/0.69 [47]P4(f28(x471,x472),a13)
% 0.58/0.69 [48]P5(f4(x481,x482),f3(a13,a13))
% 0.58/0.69 [55]~P1(x551)+P5(a1,x551)
% 0.58/0.69 [56]~P1(x561)+P4(a23,x561)
% 0.58/0.69 [57]E(x571,a23)+P4(f9(x571),a13)
% 0.58/0.69 [58]P4(f9(x581),x581)+E(x581,a23)
% 0.58/0.69 [59]P3(f9(x591),x591)+E(x591,a23)
% 0.58/0.69 [60]E(f16(x601),x601)+P4(f16(x601),a13)
% 0.58/0.69 [62]~P4(x621,a13)+P4(f26(x621),a13)
% 0.58/0.69 [63]~P4(x631,a13)+P4(f24(x631),a13)
% 0.58/0.69 [64]~P4(x641,a19)+P4(f10(x641),a13)
% 0.58/0.69 [65]~P2(x651)+P5(x651,f3(a13,a13))
% 0.58/0.69 [61]E(f16(x611),x611)+E(f28(f16(x611),f16(x611)),x611)
% 0.58/0.69 [92]~P4(x921,a13)+P4(f16(f28(x921,x921)),a13)
% 0.58/0.69 [95]~P4(x951,a13)+E(f28(f16(f28(x951,x951)),f16(f28(x951,x951))),f28(x951,x951))
% 0.58/0.69 [98]~P4(x981,a19)+E(f28(f28(f10(x981),f10(x981)),f28(f10(x981),f28(f10(x981),f10(x981)))),x981)
% 0.58/0.69 [99]~P2(x991)+P5(f4(x991,f6(f17(f3(x991,a13)))),a19)
% 0.58/0.69 [115]~P1(x1151)+P5(f6(f6(f17(f3(f20(a21,f3(x1151,a13)),a13)))),x1151)
% 0.58/0.69 [54]~E(x541,x542)+P5(x541,x542)
% 0.58/0.69 [66]P4(x661,a13)+~P4(x661,f5(x662))
% 0.58/0.69 [67]P4(x671,a13)+~P4(x671,f6(x672))
% 0.58/0.69 [68]P4(x681,a13)+~P4(x681,f24(x682))
% 0.58/0.69 [69]P5(x691,x692)+~P4(x691,f24(x692))
% 0.58/0.69 [71]P5(x711,x712)+P4(f7(x711,x712),x711)
% 0.58/0.69 [72]P3(x721,x722)+P4(f12(x721,x722),x722)
% 0.58/0.69 [73]P3(x731,x732)+P4(f12(x731,x732),x731)
% 0.58/0.69 [74]~P4(x741,x742)+~P4(x741,f5(x742))
% 0.58/0.69 [85]~P4(x851,f26(x852))+P4(x851,f11(x851,x852))
% 0.58/0.69 [86]~P4(x861,f26(x862))+P4(f11(x861,x862),x862)
% 0.58/0.69 [90]P5(x901,x902)+~P4(f7(x901,x902),x902)
% 0.58/0.69 [96]~P4(x962,f6(x961))+~E(f20(x961,f3(f28(x962,x962),a13)),a23)
% 0.58/0.69 [106]P4(x1061,a13)+~P4(f28(f28(x1062,x1062),f28(x1062,f28(x1061,x1061))),a2)
% 0.58/0.69 [107]P4(x1071,a13)+~P4(f28(f28(x1072,x1072),f28(x1072,f28(x1071,x1071))),a21)
% 0.58/0.69 [108]P4(x1081,a13)+~P4(f28(f28(x1081,x1081),f28(x1081,f28(x1082,x1082))),a21)
% 0.58/0.69 [109]P4(x1091,x1092)+~P4(f28(f28(x1091,x1091),f28(x1091,f28(x1092,x1092))),a2)
% 0.58/0.69 [110]E(f27(x1101,f28(x1101,x1101)),x1102)+~P4(f28(f28(x1101,x1101),f28(x1101,f28(x1102,x1102))),a21)
% 0.58/0.69 [77]~P4(x771,x773)+P4(x771,f27(x772,x773))
% 0.58/0.69 [78]~P4(x781,x782)+P4(x781,f27(x782,x783))
% 0.58/0.69 [87]P4(x871,a13)+~P4(x871,f28(x872,x873))
% 0.58/0.69 [88]P4(x881,x882)+~P4(x881,f20(x883,x882))
% 0.58/0.69 [89]P4(x891,x892)+~P4(x891,f20(x892,x893))
% 0.58/0.69 [100]~P4(x1001,f3(x1002,x1003))+E(f28(f28(f18(x1001),f18(x1001)),f28(f18(x1001),f28(f25(x1001),f25(x1001)))),x1001)
% 0.58/0.69 [111]P4(x1111,a13)+~P4(f28(f28(x1111,x1111),f28(x1111,f28(x1112,x1112))),f4(x1113,x1114))
% 0.58/0.69 [112]P4(x1121,x1122)+~P4(f28(f28(x1123,x1123),f28(x1123,f28(x1121,x1121))),f3(x1124,x1122))
% 0.58/0.69 [113]P4(x1131,x1132)+~P4(f28(f28(x1131,x1131),f28(x1131,f28(x1133,x1133))),f3(x1132,x1134))
% 0.58/0.69 [119]~P4(f28(f28(f28(f28(x1193,x1193),f28(x1193,f28(x1191,x1191))),f28(f28(x1193,x1193),f28(x1193,f28(x1191,x1191)))),f28(f28(f28(x1193,x1193),f28(x1193,f28(x1191,x1191))),f28(x1192,x1192))),f22(x1194))+P4(f28(f28(f28(f28(x1191,x1191),f28(x1191,f28(x1192,x1192))),f28(f28(x1191,x1191),f28(x1191,f28(x1192,x1192)))),f28(f28(f28(x1191,x1191),f28(x1191,f28(x1192,x1192))),f28(x1193,x1193))),x1194)
% 0.58/0.69 [120]~P4(f28(f28(f28(f28(x1202,x1202),f28(x1202,f28(x1201,x1201))),f28(f28(x1202,x1202),f28(x1202,f28(x1201,x1201)))),f28(f28(f28(x1202,x1202),f28(x1202,f28(x1201,x1201))),f28(x1203,x1203))),f17(x1204))+P4(f28(f28(f28(f28(x1201,x1201),f28(x1201,f28(x1202,x1202))),f28(f28(x1201,x1201),f28(x1201,f28(x1202,x1202)))),f28(f28(f28(x1201,x1201),f28(x1201,f28(x1202,x1202))),f28(x1203,x1203))),x1204)
% 0.58/0.69 [121]~P4(f28(f28(f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212))),f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212)))),f28(f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212))),f28(x1213,x1213))),f22(x1214))+P4(f28(f28(f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212))),f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212)))),f28(f28(f28(x1211,x1211),f28(x1211,f28(x1212,x1212))),f28(x1213,x1213))),f3(f3(a13,a13),a13))
% 0.58/0.69 [122]~P4(f28(f28(f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222))),f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222)))),f28(f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222))),f28(x1223,x1223))),f17(x1224))+P4(f28(f28(f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222))),f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222)))),f28(f28(f28(x1221,x1221),f28(x1221,f28(x1222,x1222))),f28(x1223,x1223))),f3(f3(a13,a13),a13))
% 0.58/0.69 [125]~P4(f28(f28(x1254,x1254),f28(x1254,f28(x1251,x1251))),f4(x1252,x1253))+P4(x1251,f6(f6(f17(f3(f20(x1252,f3(f6(f6(f17(f3(f20(x1253,f3(f28(x1254,x1254),a13)),a13)))),a13)),a13)))))
% 0.58/0.69 [114]P2(x1141)+~P5(x1141,f3(a13,a13))+~P5(f4(x1141,f6(f17(f3(x1141,a13)))),a19)
% 0.58/0.69 [117]P1(x1171)+~P4(a23,x1171)+~P5(f6(f6(f17(f3(f20(a21,f3(x1171,a13)),a13)))),x1171)
% 0.58/0.69 [118]~P4(x1181,a13)+E(x1181,a23)+P4(f26(f6(f6(f17(f3(f20(a8,f3(f28(x1181,x1181),a13)),a13))))),x1181)
% 0.58/0.69 [70]~P5(x702,x701)+~P5(x701,x702)+E(x701,x702)
% 0.58/0.69 [75]P4(x751,x752)+P4(x751,f5(x752))+~P4(x751,a13)
% 0.58/0.69 [79]~P5(x791,x792)+~P4(x791,a13)+P4(x791,f24(x792))
% 0.58/0.69 [94]P4(x942,f6(x941))+~P4(x942,a13)+E(f20(x941,f3(f28(x942,x942),a13)),a23)
% 0.58/0.69 [97]~P4(x972,a13)+P4(x971,a19)+~E(x971,f28(f28(x972,x972),f28(x972,f28(x972,x972))))
% 0.58/0.69 [103]~P4(x1031,x1032)+~P4(x1032,a13)+P4(f28(f28(x1031,x1031),f28(x1031,f28(x1032,x1032))),a2)
% 0.58/0.69 [101]~P4(x1012,a13)+~P4(x1011,a13)+E(f18(f28(f28(x1011,x1011),f28(x1011,f28(x1012,x1012)))),x1011)
% 0.58/0.69 [102]~P4(x1022,a13)+~P4(x1021,a13)+E(f25(f28(f28(x1021,x1021),f28(x1021,f28(x1022,x1022)))),x1022)
% 0.58/0.69 [116]~P2(x1161)+~P4(x1162,a13)+P4(f6(f6(f17(f3(f20(x1161,f3(x1162,a13)),a13)))),a13)
% 0.58/0.69 [76]~P4(x761,x763)+P4(x761,x762)+~P5(x763,x762)
% 0.58/0.69 [84]~P3(x843,x842)+~P4(x841,x842)+~P4(x841,x843)
% 0.58/0.69 [80]~E(x801,x803)+~P4(x801,a13)+P4(x801,f28(x802,x803))
% 0.58/0.69 [81]~E(x811,x812)+~P4(x811,a13)+P4(x811,f28(x812,x813))
% 0.58/0.69 [82]~P4(x821,x823)+~P4(x823,x822)+P4(x821,f26(x822))
% 0.58/0.69 [83]E(x831,x832)+E(x831,x833)+~P4(x831,f28(x833,x832))
% 0.58/0.69 [91]~P4(x911,x913)+~P4(x911,x912)+P4(x911,f20(x912,x913))
% 0.58/0.69 [93]P4(x931,x932)+P4(x931,x933)+~P4(x931,f27(x933,x932))
% 0.58/0.69 [104]~P4(x1042,x1044)+~P4(x1041,x1043)+P4(f28(f28(x1041,x1041),f28(x1041,f28(x1042,x1042))),f3(x1043,x1044))
% 0.58/0.69 [123]~P4(f28(f28(f28(f28(x1232,x1232),f28(x1232,f28(x1233,x1233))),f28(f28(x1232,x1232),f28(x1232,f28(x1233,x1233)))),f28(f28(f28(x1232,x1232),f28(x1232,f28(x1233,x1233))),f28(x1231,x1231))),x1234)+P4(f28(f28(f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232))),f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232)))),f28(f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232))),f28(x1233,x1233))),f22(x1234))+~P4(f28(f28(f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232))),f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232)))),f28(f28(f28(x1231,x1231),f28(x1231,f28(x1232,x1232))),f28(x1233,x1233))),f3(f3(a13,a13),a13))
% 0.58/0.69 [124]~P4(f28(f28(f28(f28(x1242,x1242),f28(x1242,f28(x1241,x1241))),f28(f28(x1242,x1242),f28(x1242,f28(x1241,x1241)))),f28(f28(f28(x1242,x1242),f28(x1242,f28(x1241,x1241))),f28(x1243,x1243))),x1244)+P4(f28(f28(f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242))),f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242)))),f28(f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242))),f28(x1243,x1243))),f17(x1244))+~P4(f28(f28(f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242))),f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242)))),f28(f28(f28(x1241,x1241),f28(x1241,f28(x1242,x1242))),f28(x1243,x1243))),f3(f3(a13,a13),a13))
% 0.58/0.69 [126]~P4(x1261,a13)+P4(f28(f28(x1261,x1261),f28(x1261,f28(x1262,x1262))),f4(x1263,x1264))+~P4(x1262,f6(f6(f17(f3(f20(x1263,f3(f6(f6(f17(f3(f20(x1264,f3(f28(x1261,x1261),a13)),a13)))),a13)),a13)))))
% 0.58/0.69 [105]~P4(x1052,a13)+~P4(x1051,a13)+~E(f27(x1051,f28(x1051,x1051)),x1052)+P4(f28(f28(x1051,x1051),f28(x1051,f28(x1052,x1052))),a21)
% 0.58/0.69 %EqnAxiom
% 0.58/0.69 [1]E(x11,x11)
% 0.58/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.58/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.58/0.69 [4]~E(x41,x42)+E(f16(x41),f16(x42))
% 0.58/0.69 [5]~E(x51,x52)+E(f6(x51),f6(x52))
% 0.58/0.69 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63))
% 0.58/0.69 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72))
% 0.58/0.69 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.58/0.69 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.58/0.69 [10]~E(x101,x102)+E(f27(x101,x103),f27(x102,x103))
% 0.58/0.69 [11]~E(x111,x112)+E(f27(x113,x111),f27(x113,x112))
% 0.58/0.69 [12]~E(x121,x122)+E(f10(x121),f10(x122))
% 0.58/0.69 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 0.58/0.69 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 0.58/0.70 [15]~E(x151,x152)+E(f17(x151),f17(x152))
% 0.58/0.70 [16]~E(x161,x162)+E(f22(x161),f22(x162))
% 0.58/0.70 [17]~E(x171,x172)+E(f20(x171,x173),f20(x172,x173))
% 0.58/0.70 [18]~E(x181,x182)+E(f20(x183,x181),f20(x183,x182))
% 0.58/0.70 [19]~E(x191,x192)+E(f18(x191),f18(x192))
% 0.58/0.70 [20]~E(x201,x202)+E(f25(x201),f25(x202))
% 0.58/0.70 [21]~E(x211,x212)+E(f26(x211),f26(x212))
% 0.58/0.70 [22]~E(x221,x222)+E(f12(x221,x223),f12(x222,x223))
% 0.58/0.70 [23]~E(x231,x232)+E(f12(x233,x231),f12(x233,x232))
% 0.58/0.70 [24]~E(x241,x242)+E(f11(x241,x243),f11(x242,x243))
% 0.58/0.70 [25]~E(x251,x252)+E(f11(x253,x251),f11(x253,x252))
% 0.58/0.70 [26]~E(x261,x262)+E(f9(x261),f9(x262))
% 0.58/0.70 [27]~E(x271,x272)+E(f5(x271),f5(x272))
% 0.58/0.70 [28]~E(x281,x282)+E(f24(x281),f24(x282))
% 0.58/0.70 [29]~E(x291,x292)+E(f7(x291,x293),f7(x292,x293))
% 0.58/0.70 [30]~E(x301,x302)+E(f7(x303,x301),f7(x303,x302))
% 0.58/0.70 [31]~P1(x311)+P1(x312)+~E(x311,x312)
% 0.58/0.70 [32]~P2(x321)+P2(x322)+~E(x321,x322)
% 0.58/0.70 [33]P4(x332,x333)+~E(x331,x332)+~P4(x331,x333)
% 0.58/0.70 [34]P4(x343,x342)+~E(x341,x342)+~P4(x343,x341)
% 0.58/0.70 [35]P5(x352,x353)+~E(x351,x352)+~P5(x351,x353)
% 0.58/0.70 [36]P5(x363,x362)+~E(x361,x362)+~P5(x363,x361)
% 0.58/0.70 [37]P3(x372,x373)+~E(x371,x372)+~P3(x371,x373)
% 0.58/0.70 [38]P3(x383,x382)+~E(x381,x382)+~P3(x383,x381)
% 0.58/0.70
% 0.58/0.70 %-------------------------------------------
% 0.58/0.70 cnf(127,plain,
% 0.58/0.70 (P5(x1271,x1271)),
% 0.58/0.70 inference(equality_inference,[],[54])).
% 0.58/0.70 cnf(128,plain,
% 0.58/0.70 (~P4(x1281,a13)+P4(x1281,f28(x1282,x1281))),
% 0.58/0.70 inference(equality_inference,[],[80])).
% 0.58/0.70 cnf(129,plain,
% 0.58/0.70 (~P4(x1291,a13)+P4(x1291,f28(x1291,x1292))),
% 0.58/0.70 inference(equality_inference,[],[81])).
% 0.58/0.70 cnf(136,plain,
% 0.58/0.70 (E(a15,f28(f16(a15),f16(a15)))),
% 0.58/0.70 inference(scs_inference,[],[44,41,128,129,2])).
% 0.58/0.70 cnf(138,plain,
% 0.58/0.70 (~P4(x1381,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(141,plain,
% 0.58/0.70 (~P4(x1411,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(144,plain,
% 0.58/0.70 (~P4(x1441,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(147,plain,
% 0.58/0.70 (~P4(x1471,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(149,plain,
% 0.58/0.70 (~P4(x1491,f26(a23))),
% 0.58/0.70 inference(scs_inference,[],[44,52,138,141,144,147,41,128,129,2,56,71,72,73,86])).
% 0.58/0.70 cnf(150,plain,
% 0.58/0.70 (~P4(x1501,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(152,plain,
% 0.58/0.70 (~P4(f28(f28(f28(f28(x1521,x1521),f28(x1521,f28(x1522,x1522))),f28(f28(x1521,x1521),f28(x1521,f28(x1522,x1522)))),f28(f28(f28(x1521,x1521),f28(x1521,f28(x1522,x1522))),f28(x1523,x1523))),f22(a23))),
% 0.58/0.70 inference(scs_inference,[],[44,52,138,141,144,147,150,41,128,129,2,56,71,72,73,86,119])).
% 0.58/0.70 cnf(153,plain,
% 0.58/0.70 (~P4(x1531,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(156,plain,
% 0.58/0.70 (~P4(x1561,a23)),
% 0.58/0.70 inference(rename_variables,[],[52])).
% 0.58/0.70 cnf(158,plain,
% 0.58/0.70 (P4(a14,a13)),
% 0.58/0.70 inference(scs_inference,[],[42,44,43,52,138,141,144,147,150,153,41,128,129,2,56,71,72,73,86,119,120,76])).
% 0.58/0.70 cnf(162,plain,
% 0.58/0.70 (P4(f28(x1621,x1622),a13)),
% 0.58/0.70 inference(rename_variables,[],[47])).
% 0.58/0.70 cnf(164,plain,
% 0.58/0.70 (P4(f28(f16(a15),f16(a15)),f28(a15,x1641))),
% 0.58/0.70 inference(scs_inference,[],[42,44,43,52,138,141,144,147,150,153,41,47,162,128,129,2,56,71,72,73,86,119,120,76,80,81])).
% 0.58/0.70 cnf(165,plain,
% 0.58/0.70 (P4(f28(x1651,x1652),a13)),
% 0.58/0.70 inference(rename_variables,[],[47])).
% 0.58/0.70 cnf(167,plain,
% 0.58/0.70 (P4(a15,a13)),
% 0.58/0.70 inference(scs_inference,[],[42,44,43,52,138,141,144,147,150,153,41,47,162,165,128,129,2,56,71,72,73,86,119,120,76,80,81,33])).
% 0.58/0.70 cnf(172,plain,
% 0.58/0.70 (P5(x1721,x1721)),
% 0.58/0.70 inference(rename_variables,[],[127])).
% 0.58/0.70 cnf(174,plain,
% 0.58/0.70 (P5(a15,f28(f16(a15),f16(a15)))),
% 0.58/0.70 inference(scs_inference,[],[42,44,127,172,43,52,138,141,144,147,150,153,156,41,47,162,165,128,129,2,56,71,72,73,86,119,120,76,80,81,33,34,79,35])).
% 0.58/0.70 cnf(194,plain,
% 0.58/0.70 (~P4(x1941,f26(f26(a23)))),
% 0.58/0.70 inference(scs_inference,[],[149,86])).
% 0.58/0.70 cnf(195,plain,
% 0.58/0.70 (~P4(x1951,f26(a23))),
% 0.58/0.70 inference(rename_variables,[],[149])).
% 0.58/0.70 cnf(197,plain,
% 0.58/0.70 (~P4(f28(f28(f28(f28(x1971,x1971),f28(x1971,f28(x1972,x1972))),f28(f28(x1971,x1971),f28(x1971,f28(x1972,x1972)))),f28(f28(f28(x1971,x1971),f28(x1971,f28(x1972,x1972))),f28(x1973,x1973))),f17(f22(a23)))),
% 0.58/0.70 inference(scs_inference,[],[152,149,86,120])).
% 0.58/0.70 cnf(200,plain,
% 0.58/0.70 (~P4(x2001,f26(a23))),
% 0.58/0.70 inference(rename_variables,[],[149])).
% 0.58/0.70 cnf(205,plain,
% 0.58/0.70 (~P4(x2051,f26(a23))),
% 0.58/0.70 inference(rename_variables,[],[149])).
% 0.58/0.70 cnf(212,plain,
% 0.58/0.70 (~P4(x2121,f26(a23))),
% 0.58/0.70 inference(rename_variables,[],[149])).
% 0.58/0.70 cnf(215,plain,
% 0.58/0.70 (~P4(x2151,f26(a23))),
% 0.58/0.70 inference(rename_variables,[],[149])).
% 0.58/0.70 cnf(229,plain,
% 0.58/0.70 (E(a14,f16(a15))),
% 0.58/0.70 inference(scs_inference,[],[42,44,164,136,158,167,127,152,149,195,200,205,212,215,174,86,120,71,129,72,119,128,73,56,76,81,80,79,34,33,83])).
% 0.58/0.70 cnf(242,plain,
% 0.58/0.70 (~P4(x2421,f26(f26(a23)))),
% 0.58/0.70 inference(rename_variables,[],[194])).
% 0.58/0.70 cnf(245,plain,
% 0.58/0.70 (~P4(x2451,f26(f26(a23)))),
% 0.58/0.70 inference(rename_variables,[],[194])).
% 0.58/0.70 cnf(248,plain,
% 0.58/0.70 (~P4(x2481,f26(f26(a23)))),
% 0.58/0.70 inference(rename_variables,[],[194])).
% 0.58/0.70 cnf(251,plain,
% 0.58/0.70 (~P4(x2511,f26(f26(a23)))),
% 0.58/0.70 inference(rename_variables,[],[194])).
% 0.58/0.70 cnf(262,plain,
% 0.58/0.70 ($false),
% 0.58/0.70 inference(scs_inference,[],[51,167,47,197,194,242,245,248,251,229,120,71,86,73,72,129,119,128,56,2]),
% 0.58/0.70 ['proof']).
% 0.58/0.70 % SZS output end Proof
% 0.58/0.70 % Total time :0.070000s
%------------------------------------------------------------------------------