%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET093+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 14:20:39 EDT 2024
% Result : Theorem 0.13s 0.55s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SET093+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.03/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sun Jun 23 12:42:08 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.13/0.47 start to proof:theBenchmark
% 0.13/0.54 %-------------------------------------------
% 0.13/0.54 % File :CSE---1.7
% 0.13/0.54 % Problem :theBenchmark
% 0.13/0.54 % Transform :cnf
% 0.13/0.54 % Format :tptp:raw
% 0.13/0.54 % Command :java -jar mcs_scs.jar %d %s
% 0.13/0.54
% 0.13/0.54 % Result :Theorem 0.030000s
% 0.13/0.54 % Output :CNFRefutation 0.030000s
% 0.13/0.54 %-------------------------------------------
% 0.13/0.54 %--------------------------------------------------------------------------
% 0.13/0.54 % File : SET093+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.13/0.54 % Domain : Set Theory
% 0.13/0.54 % Problem : Corollary to every singleton is a set
% 0.13/0.54 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.13/0.54 % English :
% 0.13/0.54
% 0.13/0.54 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.13/0.54 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.13/0.54 % Source : [Qua92]
% 0.13/0.54 % Names :
% 0.13/0.54
% 0.13/0.54 % Status : Theorem
% 0.13/0.54 % Rating : 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.3.0
% 0.13/0.54 % Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% 0.13/0.54 % Number of atoms : 110 ( 24 equ)
% 0.13/0.54 % Maximal formula atoms : 4 ( 2 avg)
% 0.13/0.54 % Number of connectives : 67 ( 5 ~; 5 |; 26 &)
% 0.13/0.54 % ( 19 <=>; 12 =>; 0 <=; 0 <~>)
% 0.13/0.54 % Maximal formula depth : 7 ( 4 avg)
% 0.13/0.54 % Maximal term depth : 4 ( 1 avg)
% 0.13/0.54 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.13/0.54 % Number of functors : 27 ( 27 usr; 5 con; 0-3 aty)
% 0.13/0.54 % Number of variables : 91 ( 86 !; 5 ?)
% 0.13/0.54 % SPC : FOF_THM_RFO_SEQ
% 0.13/0.54
% 0.13/0.54 % Comments :
% 0.13/0.54 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.13/0.54 % : v7.3.0 - Added axioms for member_of
% 0.13/0.54 %--------------------------------------------------------------------------
% 0.13/0.54 %----Include set theory axioms
% 0.13/0.54 include('Axioms/SET005+0.ax').
% 0.13/0.54 %--------------------------------------------------------------------------
% 0.13/0.54 %----Axioms to define member_of, based on SET086+1
% 0.13/0.54 fof(member_singleton_universal,axiom,
% 0.13/0.54 ! [Y] :
% 0.13/0.54 ( member(Y,universal_class)
% 0.13/0.54 => member(member_of(singleton(Y)),universal_class) ) ).
% 0.13/0.54
% 0.13/0.54 fof(member_singleton_singleton,axiom,
% 0.13/0.54 ! [Y] :
% 0.13/0.54 ( member(Y,universal_class)
% 0.13/0.54 => singleton(member_of(singleton(Y))) = singleton(Y) ) ).
% 0.13/0.54
% 0.13/0.54 fof(member_universal_self,axiom,
% 0.13/0.54 ! [X] :
% 0.13/0.54 ( member(member_of(X),universal_class)
% 0.13/0.54 | member_of(X) = X ) ).
% 0.13/0.54
% 0.13/0.54 fof(singleton_self,axiom,
% 0.13/0.54 ! [X] :
% 0.13/0.55 ( singleton(member_of(X)) = X
% 0.13/0.55 | member_of(X) = X ) ).
% 0.13/0.55
% 0.13/0.55 %----SS9: Corollary to (SS1)
% 0.13/0.55 fof(corollary_2_to_singletons_are_sets,conjecture,
% 0.13/0.55 ! [X] :
% 0.13/0.55 ( singleton(member_of(X)) = X
% 0.13/0.55 => member(X,universal_class) ) ).
% 0.13/0.55
% 0.13/0.55 %--------------------------------------------------------------------------
% 0.13/0.55 %-------------------------------------------
% 0.13/0.55 % Proof found
% 0.13/0.55 % SZS status Theorem for theBenchmark
% 0.13/0.55 % SZS output start Proof
% 0.13/0.55 %ClaNum:125(EqnAxiom:38)
% 0.13/0.55 %VarNum:625(SingletonVarNum:173)
% 0.13/0.55 %MaxLitNum:4
% 0.13/0.55 %MaxfuncDepth:13
% 0.13/0.55 %SharedTerms:19
% 0.13/0.55 %goalClause: 43 50
% 0.13/0.55 %singleGoalClaCount:2
% 0.13/0.55 [39]P1(a1)
% 0.13/0.55 [40]P2(a8)
% 0.13/0.55 [41]P4(a1,a13)
% 0.13/0.55 [50]~P4(a14,a13)
% 0.13/0.55 [44]P5(a2,f3(a13,a13))
% 0.13/0.55 [45]P5(a20,f3(a13,a13))
% 0.13/0.55 [43]E(f27(f15(a14),f15(a14)),a14)
% 0.13/0.55 [42]P5(x421,a13)
% 0.13/0.55 [51]~P4(x511,a22)
% 0.13/0.55 [48]P5(f21(x481),f3(f3(a13,a13),a13))
% 0.13/0.55 [49]P5(f16(x491),f3(f3(a13,a13),a13))
% 0.13/0.55 [46]P4(f27(x461,x462),a13)
% 0.13/0.55 [47]P5(f4(x471,x472),f3(a13,a13))
% 0.13/0.55 [54]~P1(x541)+P5(a1,x541)
% 0.13/0.55 [55]~P1(x551)+P4(a22,x551)
% 0.13/0.55 [56]E(x561,a22)+P4(f9(x561),a13)
% 0.13/0.55 [57]P4(f9(x571),x571)+E(x571,a22)
% 0.13/0.55 [58]P3(f9(x581),x581)+E(x581,a22)
% 0.13/0.55 [59]E(f15(x591),x591)+P4(f15(x591),a13)
% 0.13/0.55 [61]~P4(x611,a13)+P4(f25(x611),a13)
% 0.13/0.55 [62]~P4(x621,a13)+P4(f23(x621),a13)
% 0.13/0.55 [63]~P4(x631,a18)+P4(f10(x631),a13)
% 0.13/0.55 [64]~P2(x641)+P5(x641,f3(a13,a13))
% 0.13/0.55 [60]E(f15(x601),x601)+E(f27(f15(x601),f15(x601)),x601)
% 0.13/0.55 [91]~P4(x911,a13)+P4(f15(f27(x911,x911)),a13)
% 0.13/0.55 [94]~P4(x941,a13)+E(f27(f15(f27(x941,x941)),f15(f27(x941,x941))),f27(x941,x941))
% 0.13/0.55 [97]~P4(x971,a18)+E(f27(f27(f10(x971),f10(x971)),f27(f10(x971),f27(f10(x971),f10(x971)))),x971)
% 0.13/0.55 [98]~P2(x981)+P5(f4(x981,f6(f16(f3(x981,a13)))),a18)
% 0.13/0.55 [114]~P1(x1141)+P5(f6(f6(f16(f3(f19(a20,f3(x1141,a13)),a13)))),x1141)
% 0.13/0.55 [53]~E(x531,x532)+P5(x531,x532)
% 0.13/0.55 [65]P4(x651,a13)+~P4(x651,f5(x652))
% 0.13/0.55 [66]P4(x661,a13)+~P4(x661,f6(x662))
% 0.13/0.55 [67]P4(x671,a13)+~P4(x671,f23(x672))
% 0.13/0.55 [68]P5(x681,x682)+~P4(x681,f23(x682))
% 0.13/0.55 [70]P5(x701,x702)+P4(f7(x701,x702),x701)
% 0.13/0.55 [71]P3(x711,x712)+P4(f12(x711,x712),x712)
% 0.13/0.55 [72]P3(x721,x722)+P4(f12(x721,x722),x721)
% 0.13/0.55 [73]~P4(x731,x732)+~P4(x731,f5(x732))
% 0.13/0.55 [84]~P4(x841,f25(x842))+P4(x841,f11(x841,x842))
% 0.13/0.55 [85]~P4(x851,f25(x852))+P4(f11(x851,x852),x852)
% 0.13/0.55 [89]P5(x891,x892)+~P4(f7(x891,x892),x892)
% 0.13/0.55 [95]~P4(x952,f6(x951))+~E(f19(x951,f3(f27(x952,x952),a13)),a22)
% 0.13/0.55 [105]P4(x1051,a13)+~P4(f27(f27(x1052,x1052),f27(x1052,f27(x1051,x1051))),a2)
% 0.13/0.55 [106]P4(x1061,a13)+~P4(f27(f27(x1062,x1062),f27(x1062,f27(x1061,x1061))),a20)
% 0.13/0.55 [107]P4(x1071,a13)+~P4(f27(f27(x1071,x1071),f27(x1071,f27(x1072,x1072))),a20)
% 0.13/0.55 [108]P4(x1081,x1082)+~P4(f27(f27(x1081,x1081),f27(x1081,f27(x1082,x1082))),a2)
% 0.13/0.55 [109]E(f26(x1091,f27(x1091,x1091)),x1092)+~P4(f27(f27(x1091,x1091),f27(x1091,f27(x1092,x1092))),a20)
% 0.13/0.55 [76]~P4(x761,x763)+P4(x761,f26(x762,x763))
% 0.13/0.55 [77]~P4(x771,x772)+P4(x771,f26(x772,x773))
% 0.13/0.55 [86]P4(x861,a13)+~P4(x861,f27(x862,x863))
% 0.13/0.55 [87]P4(x871,x872)+~P4(x871,f19(x873,x872))
% 0.13/0.55 [88]P4(x881,x882)+~P4(x881,f19(x882,x883))
% 0.13/0.55 [99]~P4(x991,f3(x992,x993))+E(f27(f27(f17(x991),f17(x991)),f27(f17(x991),f27(f24(x991),f24(x991)))),x991)
% 0.13/0.55 [110]P4(x1101,a13)+~P4(f27(f27(x1101,x1101),f27(x1101,f27(x1102,x1102))),f4(x1103,x1104))
% 0.13/0.55 [111]P4(x1111,x1112)+~P4(f27(f27(x1113,x1113),f27(x1113,f27(x1111,x1111))),f3(x1114,x1112))
% 0.13/0.55 [112]P4(x1121,x1122)+~P4(f27(f27(x1121,x1121),f27(x1121,f27(x1123,x1123))),f3(x1122,x1124))
% 0.13/0.55 [118]~P4(f27(f27(f27(f27(x1183,x1183),f27(x1183,f27(x1181,x1181))),f27(f27(x1183,x1183),f27(x1183,f27(x1181,x1181)))),f27(f27(f27(x1183,x1183),f27(x1183,f27(x1181,x1181))),f27(x1182,x1182))),f21(x1184))+P4(f27(f27(f27(f27(x1181,x1181),f27(x1181,f27(x1182,x1182))),f27(f27(x1181,x1181),f27(x1181,f27(x1182,x1182)))),f27(f27(f27(x1181,x1181),f27(x1181,f27(x1182,x1182))),f27(x1183,x1183))),x1184)
% 0.13/0.55 [119]~P4(f27(f27(f27(f27(x1192,x1192),f27(x1192,f27(x1191,x1191))),f27(f27(x1192,x1192),f27(x1192,f27(x1191,x1191)))),f27(f27(f27(x1192,x1192),f27(x1192,f27(x1191,x1191))),f27(x1193,x1193))),f16(x1194))+P4(f27(f27(f27(f27(x1191,x1191),f27(x1191,f27(x1192,x1192))),f27(f27(x1191,x1191),f27(x1191,f27(x1192,x1192)))),f27(f27(f27(x1191,x1191),f27(x1191,f27(x1192,x1192))),f27(x1193,x1193))),x1194)
% 0.13/0.55 [120]~P4(f27(f27(f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202))),f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202)))),f27(f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202))),f27(x1203,x1203))),f21(x1204))+P4(f27(f27(f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202))),f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202)))),f27(f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202))),f27(x1203,x1203))),f3(f3(a13,a13),a13))
% 0.13/0.55 [121]~P4(f27(f27(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212)))),f27(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f27(x1213,x1213))),f16(x1214))+P4(f27(f27(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212)))),f27(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f27(x1213,x1213))),f3(f3(a13,a13),a13))
% 0.13/0.55 [124]~P4(f27(f27(x1244,x1244),f27(x1244,f27(x1241,x1241))),f4(x1242,x1243))+P4(x1241,f6(f6(f16(f3(f19(x1242,f3(f6(f6(f16(f3(f19(x1243,f3(f27(x1244,x1244),a13)),a13)))),a13)),a13)))))
% 0.13/0.55 [113]P2(x1131)+~P5(x1131,f3(a13,a13))+~P5(f4(x1131,f6(f16(f3(x1131,a13)))),a18)
% 0.13/0.55 [116]P1(x1161)+~P4(a22,x1161)+~P5(f6(f6(f16(f3(f19(a20,f3(x1161,a13)),a13)))),x1161)
% 0.13/0.55 [117]~P4(x1171,a13)+E(x1171,a22)+P4(f25(f6(f6(f16(f3(f19(a8,f3(f27(x1171,x1171),a13)),a13))))),x1171)
% 0.13/0.55 [69]~P5(x692,x691)+~P5(x691,x692)+E(x691,x692)
% 0.13/0.55 [74]P4(x741,x742)+P4(x741,f5(x742))+~P4(x741,a13)
% 0.13/0.55 [78]~P5(x781,x782)+~P4(x781,a13)+P4(x781,f23(x782))
% 0.13/0.55 [93]P4(x932,f6(x931))+~P4(x932,a13)+E(f19(x931,f3(f27(x932,x932),a13)),a22)
% 0.13/0.55 [96]~P4(x962,a13)+P4(x961,a18)+~E(x961,f27(f27(x962,x962),f27(x962,f27(x962,x962))))
% 0.13/0.55 [102]~P4(x1021,x1022)+~P4(x1022,a13)+P4(f27(f27(x1021,x1021),f27(x1021,f27(x1022,x1022))),a2)
% 0.13/0.55 [100]~P4(x1002,a13)+~P4(x1001,a13)+E(f17(f27(f27(x1001,x1001),f27(x1001,f27(x1002,x1002)))),x1001)
% 0.13/0.55 [101]~P4(x1012,a13)+~P4(x1011,a13)+E(f24(f27(f27(x1011,x1011),f27(x1011,f27(x1012,x1012)))),x1012)
% 0.13/0.55 [115]~P2(x1151)+~P4(x1152,a13)+P4(f6(f6(f16(f3(f19(x1151,f3(x1152,a13)),a13)))),a13)
% 0.13/0.55 [75]~P4(x751,x753)+P4(x751,x752)+~P5(x753,x752)
% 0.13/0.55 [83]~P3(x833,x832)+~P4(x831,x832)+~P4(x831,x833)
% 0.13/0.55 [79]~E(x791,x793)+~P4(x791,a13)+P4(x791,f27(x792,x793))
% 0.13/0.55 [80]~E(x801,x802)+~P4(x801,a13)+P4(x801,f27(x802,x803))
% 0.13/0.55 [81]~P4(x811,x813)+~P4(x813,x812)+P4(x811,f25(x812))
% 0.13/0.55 [82]E(x821,x822)+E(x821,x823)+~P4(x821,f27(x823,x822))
% 0.13/0.55 [90]~P4(x901,x903)+~P4(x901,x902)+P4(x901,f19(x902,x903))
% 0.13/0.55 [92]P4(x921,x922)+P4(x921,x923)+~P4(x921,f26(x923,x922))
% 0.13/0.55 [103]~P4(x1032,x1034)+~P4(x1031,x1033)+P4(f27(f27(x1031,x1031),f27(x1031,f27(x1032,x1032))),f3(x1033,x1034))
% 0.13/0.55 [122]~P4(f27(f27(f27(f27(x1222,x1222),f27(x1222,f27(x1223,x1223))),f27(f27(x1222,x1222),f27(x1222,f27(x1223,x1223)))),f27(f27(f27(x1222,x1222),f27(x1222,f27(x1223,x1223))),f27(x1221,x1221))),x1224)+P4(f27(f27(f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222))),f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222)))),f27(f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222))),f27(x1223,x1223))),f21(x1224))+~P4(f27(f27(f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222))),f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222)))),f27(f27(f27(x1221,x1221),f27(x1221,f27(x1222,x1222))),f27(x1223,x1223))),f3(f3(a13,a13),a13))
% 0.13/0.55 [123]~P4(f27(f27(f27(f27(x1232,x1232),f27(x1232,f27(x1231,x1231))),f27(f27(x1232,x1232),f27(x1232,f27(x1231,x1231)))),f27(f27(f27(x1232,x1232),f27(x1232,f27(x1231,x1231))),f27(x1233,x1233))),x1234)+P4(f27(f27(f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232))),f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232)))),f27(f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232))),f27(x1233,x1233))),f16(x1234))+~P4(f27(f27(f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232))),f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232)))),f27(f27(f27(x1231,x1231),f27(x1231,f27(x1232,x1232))),f27(x1233,x1233))),f3(f3(a13,a13),a13))
% 0.13/0.55 [125]~P4(x1251,a13)+P4(f27(f27(x1251,x1251),f27(x1251,f27(x1252,x1252))),f4(x1253,x1254))+~P4(x1252,f6(f6(f16(f3(f19(x1253,f3(f6(f6(f16(f3(f19(x1254,f3(f27(x1251,x1251),a13)),a13)))),a13)),a13)))))
% 0.13/0.55 [104]~P4(x1042,a13)+~P4(x1041,a13)+~E(f26(x1041,f27(x1041,x1041)),x1042)+P4(f27(f27(x1041,x1041),f27(x1041,f27(x1042,x1042))),a20)
% 0.13/0.55 %EqnAxiom
% 0.13/0.55 [1]E(x11,x11)
% 0.13/0.55 [2]E(x22,x21)+~E(x21,x22)
% 0.13/0.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.13/0.55 [4]~E(x41,x42)+E(f15(x41),f15(x42))
% 0.13/0.55 [5]~E(x51,x52)+E(f6(x51),f6(x52))
% 0.13/0.55 [6]~E(x61,x62)+E(f27(x61,x63),f27(x62,x63))
% 0.13/0.55 [7]~E(x71,x72)+E(f27(x73,x71),f27(x73,x72))
% 0.13/0.55 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.13/0.55 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.13/0.55 [10]~E(x101,x102)+E(f26(x101,x103),f26(x102,x103))
% 0.13/0.55 [11]~E(x111,x112)+E(f26(x113,x111),f26(x113,x112))
% 0.13/0.55 [12]~E(x121,x122)+E(f25(x121),f25(x122))
% 0.13/0.55 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 0.13/0.55 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 0.13/0.55 [15]~E(x151,x152)+E(f16(x151),f16(x152))
% 0.13/0.55 [16]~E(x161,x162)+E(f21(x161),f21(x162))
% 0.13/0.55 [17]~E(x171,x172)+E(f19(x171,x173),f19(x172,x173))
% 0.13/0.55 [18]~E(x181,x182)+E(f19(x183,x181),f19(x183,x182))
% 0.13/0.55 [19]~E(x191,x192)+E(f17(x191),f17(x192))
% 0.13/0.55 [20]~E(x201,x202)+E(f7(x201,x203),f7(x202,x203))
% 0.13/0.55 [21]~E(x211,x212)+E(f7(x213,x211),f7(x213,x212))
% 0.13/0.55 [22]~E(x221,x222)+E(f24(x221),f24(x222))
% 0.13/0.55 [23]~E(x231,x232)+E(f23(x231),f23(x232))
% 0.13/0.55 [24]~E(x241,x242)+E(f9(x241),f9(x242))
% 0.13/0.55 [25]~E(x251,x252)+E(f5(x251),f5(x252))
% 0.13/0.55 [26]~E(x261,x262)+E(f12(x261,x263),f12(x262,x263))
% 0.13/0.55 [27]~E(x271,x272)+E(f12(x273,x271),f12(x273,x272))
% 0.13/0.55 [28]~E(x281,x282)+E(f10(x281),f10(x282))
% 0.13/0.55 [29]~E(x291,x292)+E(f11(x291,x293),f11(x292,x293))
% 0.13/0.55 [30]~E(x301,x302)+E(f11(x303,x301),f11(x303,x302))
% 0.13/0.55 [31]~P1(x311)+P1(x312)+~E(x311,x312)
% 0.13/0.55 [32]~P2(x321)+P2(x322)+~E(x321,x322)
% 0.13/0.55 [33]P4(x332,x333)+~E(x331,x332)+~P4(x331,x333)
% 0.13/0.55 [34]P4(x343,x342)+~E(x341,x342)+~P4(x343,x341)
% 0.13/0.55 [35]P5(x352,x353)+~E(x351,x352)+~P5(x351,x353)
% 0.13/0.55 [36]P5(x363,x362)+~E(x361,x362)+~P5(x363,x361)
% 0.13/0.55 [37]P3(x372,x373)+~E(x371,x372)+~P3(x371,x373)
% 0.13/0.55 [38]P3(x383,x382)+~E(x381,x382)+~P3(x383,x381)
% 0.13/0.55
% 0.13/0.55 %-------------------------------------------
% 0.13/0.55 cnf(126,plain,
% 0.13/0.55 (P5(x1261,x1261)),
% 0.13/0.55 inference(equality_inference,[],[53])).
% 0.13/0.55 cnf(127,plain,
% 0.13/0.55 (~P4(x1271,a13)+P4(x1271,f27(x1272,x1271))),
% 0.13/0.55 inference(equality_inference,[],[79])).
% 0.13/0.55 cnf(128,plain,
% 0.13/0.55 (~P4(x1281,a13)+P4(x1281,f27(x1281,x1282))),
% 0.13/0.55 inference(equality_inference,[],[80])).
% 0.13/0.55 cnf(137,plain,
% 0.13/0.55 (~P4(x1371,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(146,plain,
% 0.13/0.55 (~P4(x1461,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(149,plain,
% 0.13/0.55 (~P4(x1491,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(152,plain,
% 0.13/0.55 (~P4(x1521,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(154,plain,
% 0.13/0.55 (~P4(x1541,f25(a22))),
% 0.13/0.55 inference(scs_inference,[],[43,50,51,137,146,149,152,41,127,128,2,55,65,66,67,70,71,72,85])).
% 0.13/0.55 cnf(155,plain,
% 0.13/0.55 (~P4(x1551,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(157,plain,
% 0.13/0.55 (~P4(a14,f27(x1571,x1572))),
% 0.13/0.55 inference(scs_inference,[],[43,50,51,137,146,149,152,41,127,128,2,55,65,66,67,70,71,72,85,86])).
% 0.13/0.55 cnf(160,plain,
% 0.13/0.55 (~P4(x1601,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(163,plain,
% 0.13/0.55 (~P4(x1631,a22)),
% 0.13/0.55 inference(rename_variables,[],[51])).
% 0.13/0.55 cnf(165,plain,
% 0.13/0.55 (~P4(f27(f27(x1651,x1651),f27(x1651,f27(a14,a14))),f4(x1652,x1653))),
% 0.13/0.55 inference(scs_inference,[],[43,50,51,137,146,149,152,155,160,41,127,128,2,55,65,66,67,70,71,72,85,86,118,119,124])).
% 0.13/0.55 cnf(168,plain,
% 0.13/0.55 (P4(f27(x1681,x1682),a13)),
% 0.13/0.55 inference(rename_variables,[],[46])).
% 0.13/0.55 cnf(170,plain,
% 0.13/0.55 (P4(f27(f15(a14),f15(a14)),f27(a14,x1701))),
% 0.13/0.55 inference(scs_inference,[],[43,50,51,137,146,149,152,155,160,41,46,168,127,128,2,55,65,66,67,70,71,72,85,86,118,119,124,79,80])).
% 0.13/0.55 cnf(177,plain,
% 0.13/0.55 (P5(x1771,x1771)),
% 0.13/0.55 inference(rename_variables,[],[126])).
% 0.13/0.55 cnf(179,plain,
% 0.13/0.55 (P5(x1791,x1791)),
% 0.13/0.55 inference(rename_variables,[],[126])).
% 0.13/0.55 cnf(185,plain,
% 0.13/0.55 (P4(f9(a13),a13)),
% 0.13/0.55 inference(scs_inference,[],[43,50,126,177,179,51,137,146,149,152,155,160,163,41,46,168,127,128,2,55,65,66,67,70,71,72,85,86,118,119,124,79,80,33,34,35,36,75,78,57])).
% 0.13/0.55 cnf(204,plain,
% 0.13/0.55 (~P4(f27(f27(x2041,x2041),f27(x2041,f27(a14,a14))),f4(x2042,x2043))),
% 0.13/0.55 inference(rename_variables,[],[165])).
% 0.13/0.55 cnf(207,plain,
% 0.13/0.55 (~P4(x2071,f25(a22))),
% 0.13/0.55 inference(rename_variables,[],[154])).
% 0.13/0.55 cnf(213,plain,
% 0.13/0.55 (~P4(x2131,f25(a22))),
% 0.13/0.55 inference(rename_variables,[],[154])).
% 0.13/0.55 cnf(216,plain,
% 0.13/0.55 (~P4(x2161,f25(a22))),
% 0.13/0.55 inference(rename_variables,[],[154])).
% 0.13/0.55 cnf(219,plain,
% 0.13/0.55 (~P4(x2191,f25(a22))),
% 0.13/0.55 inference(rename_variables,[],[154])).
% 0.13/0.55 cnf(222,plain,
% 0.13/0.55 (~P4(x2221,f25(a22))),
% 0.13/0.55 inference(rename_variables,[],[154])).
% 0.13/0.55 cnf(231,plain,
% 0.13/0.55 ($false),
% 0.13/0.55 inference(scs_inference,[],[43,170,126,165,204,154,207,213,216,219,222,157,185,127,119,70,118,71,55,72,85,128,78,34,33]),
% 0.13/0.55 ['proof']).
% 0.13/0.55 % SZS output end Proof
% 0.13/0.55 % Total time :0.030000s
%------------------------------------------------------------------------------