TSTP Solution File: SET095+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET095+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 : 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 14:28:39 EDT 2023
% Result : Theorem 0.76s 0.83s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET095+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
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 12:22:59 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.76/0.83 %-------------------------------------------
% 0.76/0.83 % File :CSE---1.6
% 0.76/0.83 % Problem :theBenchmark
% 0.76/0.83 % Transform :cnf
% 0.76/0.83 % Format :tptp:raw
% 0.76/0.83 % Command :java -jar mcs_scs.jar %d %s
% 0.76/0.83
% 0.76/0.83 % Result :Theorem 0.210000s
% 0.76/0.83 % Output :CNFRefutation 0.210000s
% 0.76/0.83 %-------------------------------------------
% 0.76/0.83 %--------------------------------------------------------------------------
% 0.76/0.83 % File : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.76/0.83 % Domain : Set Theory
% 0.76/0.83 % Problem : Property 2 of singletons
% 0.76/0.83 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.76/0.83 % English :
% 0.76/0.83
% 0.76/0.83 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.76/0.83 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.76/0.83 % Source : [Qua92]
% 0.76/0.83 % Names :
% 0.76/0.83
% 0.76/0.83 % Status : Theorem
% 0.76/0.83 % Rating : 0.31 v7.5.0, 0.34 v7.4.0, 0.23 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.26 v7.0.0, 0.27 v6.4.0, 0.31 v6.3.0, 0.33 v6.2.0, 0.32 v6.1.0, 0.43 v6.0.0, 0.39 v5.5.0, 0.52 v5.4.0
% 0.76/0.83 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.76/0.83 % Number of atoms : 102 ( 19 equ)
% 0.76/0.83 % Maximal formula atoms : 4 ( 2 avg)
% 0.76/0.83 % Number of connectives : 63 ( 5 ~; 3 |; 26 &)
% 0.76/0.83 % ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% 0.76/0.83 % Maximal formula depth : 7 ( 4 avg)
% 0.76/0.83 % Maximal term depth : 4 ( 1 avg)
% 0.76/0.83 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.76/0.83 % Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% 0.76/0.83 % Number of variables : 88 ( 83 !; 5 ?)
% 0.76/0.83 % SPC : FOF_THM_RFO_SEQ
% 0.76/0.83
% 0.76/0.83 % Comments :
% 0.76/0.83 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.76/0.83 %--------------------------------------------------------------------------
% 0.76/0.83 %----Include set theory axioms
% 0.76/0.83 include('Axioms/SET005+0.ax').
% 0.76/0.83 %--------------------------------------------------------------------------
% 0.76/0.83 %----SS11
% 0.76/0.83 fof(property_of_singletons2,conjecture,
% 0.76/0.83 ! [X,Y] :
% 0.76/0.83 ( member(X,Y)
% 0.76/0.83 => subclass(singleton(X),Y) ) ).
% 0.76/0.83
% 0.76/0.83 %--------------------------------------------------------------------------
% 0.76/0.83 %-------------------------------------------
% 0.76/0.83 % Proof found
% 0.76/0.83 % SZS status Theorem for theBenchmark
% 0.76/0.83 % SZS output start Proof
% 0.76/0.84 %ClaNum:120(EqnAxiom:37)
% 0.76/0.84 %VarNum:607(SingletonVarNum:169)
% 0.76/0.84 %MaxLitNum:4
% 0.76/0.84 %MaxfuncDepth:13
% 0.76/0.84 %SharedTerms:19
% 0.76/0.84 %goalClause: 41 50
% 0.76/0.84 %singleGoalClaCount:2
% 0.76/0.84 [38]P1(a1)
% 0.76/0.84 [39]P2(a8)
% 0.76/0.84 [40]P4(a1,a13)
% 0.76/0.84 [41]P4(a14,a15)
% 0.76/0.84 [43]P5(a2,f3(a13,a13))
% 0.76/0.84 [44]P5(a16,f3(a13,a13))
% 0.76/0.84 [50]~P5(f27(a14,a14),a15)
% 0.76/0.84 [42]P5(x421,a13)
% 0.76/0.84 [49]~P4(x491,a20)
% 0.76/0.84 [47]P5(f17(x471),f3(f3(a13,a13),a13))
% 0.76/0.84 [48]P5(f18(x481),f3(f3(a13,a13),a13))
% 0.76/0.84 [45]P4(f27(x451,x452),a13)
% 0.76/0.84 [46]P5(f4(x461,x462),f3(a13,a13))
% 0.76/0.84 [53]~P1(x531)+P5(a1,x531)
% 0.76/0.84 [54]~P1(x541)+P4(a20,x541)
% 0.76/0.84 [55]E(x551,a20)+P4(f9(x551),a13)
% 0.76/0.84 [56]P4(f9(x561),x561)+E(x561,a20)
% 0.76/0.84 [57]P3(f9(x571),x571)+E(x571,a20)
% 0.76/0.84 [58]~P4(x581,a13)+P4(f25(x581),a13)
% 0.76/0.84 [59]~P4(x591,a13)+P4(f23(x591),a13)
% 0.76/0.84 [60]~P4(x601,a21)+P4(f10(x601),a13)
% 0.76/0.84 [61]~P2(x611)+P5(x611,f3(a13,a13))
% 0.76/0.84 [92]~P4(x921,a21)+E(f27(f27(f10(x921),f10(x921)),f27(f10(x921),f27(f10(x921),f10(x921)))),x921)
% 0.76/0.84 [93]~P2(x931)+P5(f4(x931,f6(f18(f3(x931,a13)))),a21)
% 0.76/0.84 [109]~P1(x1091)+P5(f6(f6(f18(f3(f22(a16,f3(x1091,a13)),a13)))),x1091)
% 0.76/0.84 [52]~E(x521,x522)+P5(x521,x522)
% 0.76/0.84 [62]P4(x621,a13)+~P4(x621,f5(x622))
% 0.76/0.84 [63]P4(x631,a13)+~P4(x631,f6(x632))
% 0.76/0.84 [64]P4(x641,a13)+~P4(x641,f23(x642))
% 0.76/0.84 [65]P5(x651,x652)+~P4(x651,f23(x652))
% 0.76/0.84 [67]P5(x671,x672)+P4(f7(x671,x672),x671)
% 0.76/0.84 [68]P3(x681,x682)+P4(f12(x681,x682),x682)
% 0.76/0.84 [69]P3(x691,x692)+P4(f12(x691,x692),x691)
% 0.76/0.84 [70]~P4(x701,x702)+~P4(x701,f5(x702))
% 0.76/0.84 [81]~P4(x811,f25(x812))+P4(x811,f11(x811,x812))
% 0.76/0.84 [82]~P4(x821,f25(x822))+P4(f11(x821,x822),x822)
% 0.76/0.84 [86]P5(x861,x862)+~P4(f7(x861,x862),x862)
% 0.76/0.84 [90]~P4(x902,f6(x901))+~E(f22(x901,f3(f27(x902,x902),a13)),a20)
% 0.76/0.84 [100]P4(x1001,a13)+~P4(f27(f27(x1002,x1002),f27(x1002,f27(x1001,x1001))),a2)
% 0.76/0.84 [101]P4(x1011,a13)+~P4(f27(f27(x1012,x1012),f27(x1012,f27(x1011,x1011))),a16)
% 0.76/0.84 [102]P4(x1021,a13)+~P4(f27(f27(x1021,x1021),f27(x1021,f27(x1022,x1022))),a16)
% 0.76/0.84 [103]P4(x1031,x1032)+~P4(f27(f27(x1031,x1031),f27(x1031,f27(x1032,x1032))),a2)
% 0.76/0.84 [104]E(f26(x1041,f27(x1041,x1041)),x1042)+~P4(f27(f27(x1041,x1041),f27(x1041,f27(x1042,x1042))),a16)
% 0.76/0.84 [73]~P4(x731,x733)+P4(x731,f26(x732,x733))
% 0.76/0.84 [74]~P4(x741,x742)+P4(x741,f26(x742,x743))
% 0.76/0.84 [83]P4(x831,a13)+~P4(x831,f27(x832,x833))
% 0.76/0.84 [84]P4(x841,x842)+~P4(x841,f22(x843,x842))
% 0.76/0.84 [85]P4(x851,x852)+~P4(x851,f22(x852,x853))
% 0.76/0.84 [94]~P4(x941,f3(x942,x943))+E(f27(f27(f19(x941),f19(x941)),f27(f19(x941),f27(f24(x941),f24(x941)))),x941)
% 0.76/0.84 [105]P4(x1051,a13)+~P4(f27(f27(x1051,x1051),f27(x1051,f27(x1052,x1052))),f4(x1053,x1054))
% 0.76/0.84 [106]P4(x1061,x1062)+~P4(f27(f27(x1063,x1063),f27(x1063,f27(x1061,x1061))),f3(x1064,x1062))
% 0.76/0.84 [107]P4(x1071,x1072)+~P4(f27(f27(x1071,x1071),f27(x1071,f27(x1073,x1073))),f3(x1072,x1074))
% 0.76/0.84 [113]~P4(f27(f27(f27(f27(x1133,x1133),f27(x1133,f27(x1131,x1131))),f27(f27(x1133,x1133),f27(x1133,f27(x1131,x1131)))),f27(f27(f27(x1133,x1133),f27(x1133,f27(x1131,x1131))),f27(x1132,x1132))),f17(x1134))+P4(f27(f27(f27(f27(x1131,x1131),f27(x1131,f27(x1132,x1132))),f27(f27(x1131,x1131),f27(x1131,f27(x1132,x1132)))),f27(f27(f27(x1131,x1131),f27(x1131,f27(x1132,x1132))),f27(x1133,x1133))),x1134)
% 0.76/0.84 [114]~P4(f27(f27(f27(f27(x1142,x1142),f27(x1142,f27(x1141,x1141))),f27(f27(x1142,x1142),f27(x1142,f27(x1141,x1141)))),f27(f27(f27(x1142,x1142),f27(x1142,f27(x1141,x1141))),f27(x1143,x1143))),f18(x1144))+P4(f27(f27(f27(f27(x1141,x1141),f27(x1141,f27(x1142,x1142))),f27(f27(x1141,x1141),f27(x1141,f27(x1142,x1142)))),f27(f27(f27(x1141,x1141),f27(x1141,f27(x1142,x1142))),f27(x1143,x1143))),x1144)
% 0.76/0.84 [115]~P4(f27(f27(f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152))),f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152)))),f27(f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152))),f27(x1153,x1153))),f17(x1154))+P4(f27(f27(f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152))),f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152)))),f27(f27(f27(x1151,x1151),f27(x1151,f27(x1152,x1152))),f27(x1153,x1153))),f3(f3(a13,a13),a13))
% 0.76/0.84 [116]~P4(f27(f27(f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162))),f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162)))),f27(f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162))),f27(x1163,x1163))),f18(x1164))+P4(f27(f27(f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162))),f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162)))),f27(f27(f27(x1161,x1161),f27(x1161,f27(x1162,x1162))),f27(x1163,x1163))),f3(f3(a13,a13),a13))
% 0.76/0.84 [119]~P4(f27(f27(x1194,x1194),f27(x1194,f27(x1191,x1191))),f4(x1192,x1193))+P4(x1191,f6(f6(f18(f3(f22(x1192,f3(f6(f6(f18(f3(f22(x1193,f3(f27(x1194,x1194),a13)),a13)))),a13)),a13)))))
% 0.76/0.84 [108]P2(x1081)+~P5(x1081,f3(a13,a13))+~P5(f4(x1081,f6(f18(f3(x1081,a13)))),a21)
% 0.76/0.84 [111]P1(x1111)+~P4(a20,x1111)+~P5(f6(f6(f18(f3(f22(a16,f3(x1111,a13)),a13)))),x1111)
% 0.76/0.84 [112]~P4(x1121,a13)+E(x1121,a20)+P4(f25(f6(f6(f18(f3(f22(a8,f3(f27(x1121,x1121),a13)),a13))))),x1121)
% 0.76/0.84 [66]~P5(x662,x661)+~P5(x661,x662)+E(x661,x662)
% 0.76/0.84 [71]P4(x711,x712)+P4(x711,f5(x712))+~P4(x711,a13)
% 0.76/0.84 [75]~P5(x751,x752)+~P4(x751,a13)+P4(x751,f23(x752))
% 0.76/0.84 [89]P4(x892,f6(x891))+~P4(x892,a13)+E(f22(x891,f3(f27(x892,x892),a13)),a20)
% 0.76/0.84 [91]~P4(x912,a13)+P4(x911,a21)+~E(x911,f27(f27(x912,x912),f27(x912,f27(x912,x912))))
% 0.76/0.84 [97]~P4(x971,x972)+~P4(x972,a13)+P4(f27(f27(x971,x971),f27(x971,f27(x972,x972))),a2)
% 0.76/0.84 [95]~P4(x952,a13)+~P4(x951,a13)+E(f19(f27(f27(x951,x951),f27(x951,f27(x952,x952)))),x951)
% 0.76/0.84 [96]~P4(x962,a13)+~P4(x961,a13)+E(f24(f27(f27(x961,x961),f27(x961,f27(x962,x962)))),x962)
% 0.76/0.84 [110]~P2(x1101)+~P4(x1102,a13)+P4(f6(f6(f18(f3(f22(x1101,f3(x1102,a13)),a13)))),a13)
% 0.76/0.84 [72]~P4(x721,x723)+P4(x721,x722)+~P5(x723,x722)
% 0.76/0.84 [80]~P3(x803,x802)+~P4(x801,x802)+~P4(x801,x803)
% 0.76/0.84 [76]~E(x761,x763)+~P4(x761,a13)+P4(x761,f27(x762,x763))
% 0.76/0.84 [77]~E(x771,x772)+~P4(x771,a13)+P4(x771,f27(x772,x773))
% 0.76/0.84 [78]~P4(x781,x783)+~P4(x783,x782)+P4(x781,f25(x782))
% 0.76/0.84 [79]E(x791,x792)+E(x791,x793)+~P4(x791,f27(x793,x792))
% 0.76/0.84 [87]~P4(x871,x873)+~P4(x871,x872)+P4(x871,f22(x872,x873))
% 0.76/0.84 [88]P4(x881,x882)+P4(x881,x883)+~P4(x881,f26(x883,x882))
% 0.76/0.84 [98]~P4(x982,x984)+~P4(x981,x983)+P4(f27(f27(x981,x981),f27(x981,f27(x982,x982))),f3(x983,x984))
% 0.76/0.84 [117]~P4(f27(f27(f27(f27(x1172,x1172),f27(x1172,f27(x1173,x1173))),f27(f27(x1172,x1172),f27(x1172,f27(x1173,x1173)))),f27(f27(f27(x1172,x1172),f27(x1172,f27(x1173,x1173))),f27(x1171,x1171))),x1174)+P4(f27(f27(f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172))),f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172)))),f27(f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172))),f27(x1173,x1173))),f17(x1174))+~P4(f27(f27(f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172))),f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172)))),f27(f27(f27(x1171,x1171),f27(x1171,f27(x1172,x1172))),f27(x1173,x1173))),f3(f3(a13,a13),a13))
% 0.76/0.84 [118]~P4(f27(f27(f27(f27(x1182,x1182),f27(x1182,f27(x1181,x1181))),f27(f27(x1182,x1182),f27(x1182,f27(x1181,x1181)))),f27(f27(f27(x1182,x1182),f27(x1182,f27(x1181,x1181))),f27(x1183,x1183))),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))),f18(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))),f3(f3(a13,a13),a13))
% 0.76/0.84 [120]~P4(x1201,a13)+P4(f27(f27(x1201,x1201),f27(x1201,f27(x1202,x1202))),f4(x1203,x1204))+~P4(x1202,f6(f6(f18(f3(f22(x1203,f3(f6(f6(f18(f3(f22(x1204,f3(f27(x1201,x1201),a13)),a13)))),a13)),a13)))))
% 0.76/0.84 [99]~P4(x992,a13)+~P4(x991,a13)+~E(f26(x991,f27(x991,x991)),x992)+P4(f27(f27(x991,x991),f27(x991,f27(x992,x992))),a16)
% 0.76/0.84 %EqnAxiom
% 0.76/0.84 [1]E(x11,x11)
% 0.76/0.84 [2]E(x22,x21)+~E(x21,x22)
% 0.76/0.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.76/0.84 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.76/0.84 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.76/0.84 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.76/0.84 [7]~E(x71,x72)+E(f27(x71,x73),f27(x72,x73))
% 0.76/0.84 [8]~E(x81,x82)+E(f27(x83,x81),f27(x83,x82))
% 0.76/0.84 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.76/0.84 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.76/0.84 [11]~E(x111,x112)+E(f18(x111),f18(x112))
% 0.76/0.84 [12]~E(x121,x122)+E(f17(x121),f17(x122))
% 0.76/0.84 [13]~E(x131,x132)+E(f19(x131),f19(x132))
% 0.76/0.84 [14]~E(x141,x142)+E(f22(x141,x143),f22(x142,x143))
% 0.76/0.84 [15]~E(x151,x152)+E(f22(x153,x151),f22(x153,x152))
% 0.76/0.84 [16]~E(x161,x162)+E(f26(x161,x163),f26(x162,x163))
% 0.76/0.84 [17]~E(x171,x172)+E(f26(x173,x171),f26(x173,x172))
% 0.76/0.84 [18]~E(x181,x182)+E(f10(x181),f10(x182))
% 0.76/0.84 [19]~E(x191,x192)+E(f25(x191),f25(x192))
% 0.76/0.84 [20]~E(x201,x202)+E(f11(x201,x203),f11(x202,x203))
% 0.76/0.84 [21]~E(x211,x212)+E(f11(x213,x211),f11(x213,x212))
% 0.76/0.84 [22]~E(x221,x222)+E(f9(x221),f9(x222))
% 0.76/0.84 [23]~E(x231,x232)+E(f7(x231,x233),f7(x232,x233))
% 0.76/0.84 [24]~E(x241,x242)+E(f7(x243,x241),f7(x243,x242))
% 0.76/0.84 [25]~E(x251,x252)+E(f5(x251),f5(x252))
% 0.76/0.84 [26]~E(x261,x262)+E(f24(x261),f24(x262))
% 0.76/0.84 [27]~E(x271,x272)+E(f23(x271),f23(x272))
% 0.76/0.84 [28]~E(x281,x282)+E(f12(x281,x283),f12(x282,x283))
% 0.76/0.84 [29]~E(x291,x292)+E(f12(x293,x291),f12(x293,x292))
% 0.76/0.84 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.76/0.84 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.76/0.84 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.76/0.84 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.76/0.84 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.76/0.84 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.76/0.84 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363)
% 0.76/0.84 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371)
% 0.76/0.84
% 0.76/0.84 %-------------------------------------------
% 0.76/0.84 cnf(121,plain,
% 0.76/0.84 (~P1(a20)),
% 0.76/0.84 inference(scs_inference,[],[49,54])).
% 0.76/0.84 cnf(122,plain,
% 0.76/0.84 (~P4(x1221,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(126,plain,
% 0.76/0.84 (~P4(x1261,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(128,plain,
% 0.76/0.84 (P3(x1281,a20)),
% 0.76/0.84 inference(scs_inference,[],[49,122,126,50,54,52,69,68])).
% 0.76/0.84 cnf(129,plain,
% 0.76/0.84 (~P4(x1291,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(131,plain,
% 0.76/0.84 (P5(a20,x1311)),
% 0.76/0.84 inference(scs_inference,[],[49,122,126,129,50,54,52,69,68,67])).
% 0.76/0.84 cnf(132,plain,
% 0.76/0.84 (~P4(x1321,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(134,plain,
% 0.76/0.84 (~P4(x1341,f25(a20))),
% 0.76/0.84 inference(scs_inference,[],[49,122,126,129,132,50,54,52,69,68,67,82])).
% 0.76/0.84 cnf(135,plain,
% 0.76/0.84 (~P4(x1351,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(138,plain,
% 0.76/0.84 (~P4(x1381,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(141,plain,
% 0.76/0.84 (~P4(x1411,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(143,plain,
% 0.76/0.84 (~E(a13,a15)),
% 0.76/0.84 inference(scs_inference,[],[42,49,122,126,129,132,135,138,50,54,52,69,68,67,82,114,113,35])).
% 0.76/0.84 cnf(144,plain,
% 0.76/0.84 (~E(a20,f27(a14,a14))),
% 0.76/0.84 inference(scs_inference,[],[42,49,122,126,129,132,135,138,50,54,52,69,68,67,82,114,113,35,34])).
% 0.76/0.84 cnf(145,plain,
% 0.76/0.84 (~E(a15,a20)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,50,54,52,69,68,67,82,114,113,35,34,33])).
% 0.76/0.84 cnf(146,plain,
% 0.76/0.84 (~P4(x1461,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(149,plain,
% 0.76/0.84 (P5(x1491,a13)),
% 0.76/0.84 inference(rename_variables,[],[42])).
% 0.76/0.84 cnf(151,plain,
% 0.76/0.84 (~E(a15,f27(a14,a14))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2])).
% 0.76/0.84 cnf(152,plain,
% 0.76/0.84 (P5(a1,a1)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,38,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53])).
% 0.76/0.84 cnf(160,plain,
% 0.76/0.84 (~P4(x1601,f22(x1602,a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84])).
% 0.76/0.84 cnf(174,plain,
% 0.76/0.84 (E(f25(a20),a20)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56])).
% 0.76/0.84 cnf(178,plain,
% 0.76/0.84 (E(f12(x1781,f25(a20)),f12(x1781,a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29])).
% 0.76/0.84 cnf(179,plain,
% 0.76/0.84 (E(f12(f25(a20),x1791),f12(a20,x1791))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28])).
% 0.76/0.84 cnf(188,plain,
% 0.76/0.84 (E(f25(f25(a20)),f25(a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19])).
% 0.76/0.84 cnf(192,plain,
% 0.76/0.84 (E(f22(x1921,f25(a20)),f22(x1921,a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15])).
% 0.76/0.84 cnf(202,plain,
% 0.76/0.84 (E(f3(x2021,f25(a20)),f3(x2021,a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5])).
% 0.76/0.84 cnf(206,plain,
% 0.76/0.84 (~P4(f7(f27(a14,a14),a15),a15)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86])).
% 0.76/0.84 cnf(208,plain,
% 0.76/0.84 (~P4(f27(f27(x2081,x2081),f27(x2081,f27(x2082,x2082))),f3(x2083,a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106])).
% 0.76/0.84 cnf(215,plain,
% 0.76/0.84 (~E(a1,a20)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30])).
% 0.76/0.84 cnf(216,plain,
% 0.76/0.84 (~E(a15,f25(a20))),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3])).
% 0.76/0.84 cnf(217,plain,
% 0.76/0.84 (~P5(a15,a20)),
% 0.76/0.84 inference(scs_inference,[],[41,42,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72])).
% 0.76/0.84 cnf(218,plain,
% 0.76/0.84 (~P4(x2181,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(220,plain,
% 0.76/0.84 (~P5(a13,a15)),
% 0.76/0.84 inference(scs_inference,[],[41,42,149,49,122,126,129,132,135,138,141,146,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72,66])).
% 0.76/0.84 cnf(224,plain,
% 0.76/0.84 (~P4(x2241,a20)),
% 0.76/0.84 inference(rename_variables,[],[49])).
% 0.76/0.84 cnf(234,plain,
% 0.76/0.84 (P4(f25(f6(f6(f18(f3(f22(a8,f3(f27(a1,a1),a13)),a13))))),a1)),
% 0.76/0.84 inference(scs_inference,[],[41,42,149,49,122,126,129,132,135,138,141,146,218,224,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72,66,71,110,88,87,79,112])).
% 0.76/0.84 cnf(240,plain,
% 0.76/0.84 (P4(f27(f27(a14,a14),f27(a14,f27(a14,a14))),f3(a15,a15))),
% 0.76/0.84 inference(scs_inference,[],[41,42,149,49,122,126,129,132,135,138,141,146,218,224,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72,66,71,110,88,87,79,112,96,95,98])).
% 0.76/0.84 cnf(242,plain,
% 0.76/0.84 (P3(f9(a15),a15)),
% 0.76/0.84 inference(scs_inference,[],[41,42,149,49,122,126,129,132,135,138,141,146,218,224,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72,66,71,110,88,87,79,112,96,95,98,57])).
% 0.76/0.84 cnf(244,plain,
% 0.76/0.84 (~P3(a15,a15)),
% 0.76/0.84 inference(scs_inference,[],[41,42,149,49,122,126,129,132,135,138,141,146,218,224,38,39,40,50,45,54,52,69,68,67,82,114,113,35,34,33,75,2,53,61,109,85,84,74,73,70,65,59,58,56,55,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,93,86,106,107,103,32,30,3,72,66,71,110,88,87,79,112,96,95,98,57,80])).
% 0.76/0.84 cnf(267,plain,
% 0.76/0.84 (~E(a20,a15)),
% 0.76/0.84 inference(scs_inference,[],[240,128,244,94,37])).
% 0.76/0.84 cnf(270,plain,
% 0.76/0.84 (P5(f12(x2701,f25(a20)),f12(x2701,a20))),
% 0.76/0.84 inference(scs_inference,[],[240,178,128,242,244,94,37,36,52])).
% 0.76/0.84 cnf(274,plain,
% 0.76/0.84 (P4(f7(f27(a14,a14),a15),f27(a14,a14))),
% 0.76/0.84 inference(scs_inference,[],[50,240,178,128,242,145,244,94,37,36,52,56,67])).
% 0.76/0.84 cnf(280,plain,
% 0.76/0.84 (~P4(a15,f27(f27(a14,a14),f27(a14,a14)))),
% 0.76/0.84 inference(scs_inference,[],[45,39,50,208,240,178,128,151,242,145,244,94,37,36,52,56,67,110,88,79])).
% 0.76/0.84 cnf(282,plain,
% 0.76/0.84 (E(f24(f27(f27(f27(x2821,x2822),f27(x2821,x2822)),f27(f27(x2821,x2822),f27(f27(x2821,x2822),f27(x2821,x2822))))),f27(x2821,x2822))),
% 0.76/0.84 inference(scs_inference,[],[45,39,50,208,240,178,128,151,242,145,244,94,37,36,52,56,67,110,88,79,96])).
% 0.76/0.84 cnf(284,plain,
% 0.76/0.84 (E(f19(f27(f27(f27(x2841,x2842),f27(x2841,x2842)),f27(f27(x2841,x2842),f27(f27(x2841,x2842),f27(x2841,x2842))))),f27(x2841,x2842))),
% 0.76/0.84 inference(scs_inference,[],[45,39,50,208,240,178,128,151,242,145,244,94,37,36,52,56,67,110,88,79,96,95])).
% 0.76/0.84 cnf(290,plain,
% 0.76/0.84 (E(f12(x2901,a20),f12(x2901,f25(a20)))),
% 0.76/0.84 inference(scs_inference,[],[45,38,39,50,208,240,178,128,151,242,145,244,94,37,36,52,56,67,110,88,79,96,95,54,69,2])).
% 0.76/0.84 cnf(296,plain,
% 0.76/0.84 (~P5(f24(f27(f27(f27(a14,a14),f27(a14,a14)),f27(f27(a14,a14),f27(f27(a14,a14),f27(a14,a14))))),a15)),
% 0.76/0.84 inference(scs_inference,[],[49,45,38,39,50,208,240,178,128,151,174,242,121,145,217,244,94,37,36,52,56,67,110,88,79,96,95,54,69,2,30,71,35,34])).
% 0.76/0.84 cnf(299,plain,
% 0.76/0.84 (E(f12(f25(a20),f25(a20)),f12(a20,a20))),
% 0.76/0.84 inference(scs_inference,[],[49,45,38,39,50,208,240,178,179,202,128,151,174,242,121,145,217,244,94,37,36,52,56,67,110,88,79,96,95,54,69,2,30,71,35,34,33,3])).
% 0.76/0.84 cnf(312,plain,
% 0.76/0.84 (~E(a14,f7(f27(a14,a14),a15))),
% 0.76/0.84 inference(scs_inference,[],[41,49,45,42,38,39,50,40,208,240,178,179,202,128,151,206,174,242,121,145,152,217,244,94,37,36,52,56,67,110,88,79,96,95,54,69,2,30,71,35,34,33,3,31,80,72,75,97,32])).
% 0.76/0.84 cnf(332,plain,
% 0.76/0.84 (E(f24(f27(f27(f27(x3321,x3322),f27(x3321,x3322)),f27(f27(x3321,x3322),f27(f27(x3321,x3322),f27(x3321,x3322))))),f27(x3321,x3322))),
% 0.76/0.84 inference(rename_variables,[],[282])).
% 0.76/0.84 cnf(335,plain,
% 0.76/0.84 (~P4(x3351,f22(x3352,a20))),
% 0.76/0.84 inference(rename_variables,[],[160])).
% 0.76/0.84 cnf(338,plain,
% 0.76/0.84 (~P4(x3381,f22(x3382,a20))),
% 0.76/0.84 inference(rename_variables,[],[160])).
% 0.76/0.84 cnf(341,plain,
% 0.76/0.84 (~P4(x3411,f22(x3412,a20))),
% 0.76/0.84 inference(rename_variables,[],[160])).
% 0.76/0.84 cnf(345,plain,
% 0.76/0.84 (E(f7(f27(a14,a14),a15),a14)),
% 0.76/0.84 inference(scs_inference,[],[45,282,274,160,335,338,296,91,56,67,69,52,79])).
% 0.76/0.84 cnf(360,plain,
% 0.76/0.84 (P5(f12(x3601,f25(a20)),f12(x3601,f25(a20)))),
% 0.76/0.84 inference(scs_inference,[],[49,45,282,274,160,335,338,341,192,270,290,143,296,91,56,67,69,52,79,54,80,58,30,72,2,35])).
% 0.76/0.84 cnf(363,plain,
% 0.76/0.84 (E(f24(f27(f27(f27(x3631,x3632),f27(x3631,x3632)),f27(f27(x3631,x3632),f27(f27(x3631,x3632),f27(x3631,x3632))))),f27(x3631,x3632))),
% 0.76/0.84 inference(rename_variables,[],[282])).
% 0.76/0.84 cnf(364,plain,
% 0.76/0.84 (~E(a20,f24(f27(f27(f27(a14,a14),f27(a14,a14)),f27(f27(a14,a14),f27(f27(a14,a14),f27(a14,a14))))))),
% 0.76/0.84 inference(scs_inference,[],[49,45,282,332,363,274,160,335,338,341,192,270,290,143,296,280,144,91,56,67,69,52,79,54,80,58,30,72,2,35,33,3])).
% 0.76/0.84 cnf(408,plain,
% 0.76/0.84 ($false),
% 0.76/0.84 inference(scs_inference,[],[42,40,267,360,234,220,364,345,312,216,215,134,131,188,299,284,91,67,56,52,68,79,66,72,35,3,2]),
% 0.76/0.84 ['proof']).
% 0.76/0.85 % SZS output end Proof
% 0.76/0.85 % Total time :0.210000s
%------------------------------------------------------------------------------