%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET071+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 14:20:29 EDT 2024
% Result : Theorem 0.52s 0.68s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET071+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.06/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jun 23 13:55:24 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.52/0.55 start to proof:theBenchmark
% 0.52/0.67 %-------------------------------------------
% 0.52/0.67 % File :CSE---1.7
% 0.52/0.67 % Problem :theBenchmark
% 0.52/0.67 % Transform :cnf
% 0.52/0.67 % Format :tptp:raw
% 0.52/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.52/0.67
% 0.52/0.67 % Result :Theorem 0.070000s
% 0.52/0.67 % Output :CNFRefutation 0.070000s
% 0.52/0.67 %-------------------------------------------
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 % File : SET071+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.52/0.68 % Domain : Set Theory
% 0.52/0.68 % Problem : If both arguments are proper classes, pair is null
% 0.52/0.68 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.52/0.68 % English :
% 0.52/0.68
% 0.52/0.68 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.52/0.68 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.52/0.68 % Source : [Qua92]
% 0.52/0.68 % Names :
% 0.52/0.68
% 0.52/0.68 % Status : Theorem
% 0.52/0.68 % Rating : 0.44 v8.1.0, 0.56 v7.5.0, 0.59 v7.4.0, 0.47 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.52 v7.0.0, 0.50 v6.4.0, 0.54 v6.2.0, 0.56 v6.1.0, 0.60 v6.0.0, 0.57 v5.5.0, 0.59 v5.4.0
% 0.52/0.68 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.52/0.68 % Number of atoms : 103 ( 20 equ)
% 0.52/0.68 % Maximal formula atoms : 4 ( 2 avg)
% 0.52/0.68 % Number of connectives : 66 ( 7 ~; 3 |; 27 &)
% 0.52/0.68 % ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% 0.52/0.68 % Maximal formula depth : 7 ( 4 avg)
% 0.52/0.68 % Maximal term depth : 4 ( 1 avg)
% 0.52/0.68 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.52/0.68 % Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% 0.52/0.68 % Number of variables : 88 ( 83 !; 5 ?)
% 0.52/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.52/0.68
% 0.52/0.68 % Comments :
% 0.52/0.68 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 %----Include set theory axioms
% 0.52/0.68 include('Axioms/SET005+0.ax').
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 %----UP3: If both arguments are proper classes, pair is null
% 0.52/0.68 fof(null_unordered_pair,conjecture,
% 0.52/0.68 ! [X,Y] :
% 0.52/0.68 ( ( ~ member(X,universal_class)
% 0.52/0.68 & ~ member(Y,universal_class) )
% 0.52/0.68 => unordered_pair(X,Y) = null_class ) ).
% 0.52/0.68
% 0.52/0.68 %--------------------------------------------------------------------------
% 0.52/0.68 %-------------------------------------------
% 0.52/0.68 % Proof found
% 0.52/0.68 % SZS status Theorem for theBenchmark
% 0.52/0.68 % SZS output start Proof
% 0.52/0.68 %ClaNum:121(EqnAxiom:37)
% 0.52/0.68 %VarNum:607(SingletonVarNum:169)
% 0.52/0.68 %MaxLitNum:4
% 0.52/0.68 %MaxfuncDepth:13
% 0.52/0.68 %SharedTerms:20
% 0.52/0.68 %goalClause: 48 49 50
% 0.52/0.68 %singleGoalClaCount:3
% 0.52/0.68 [38]P1(a1)
% 0.52/0.68 [39]P2(a8)
% 0.52/0.68 [40]P4(a1,a13)
% 0.52/0.68 [49]~P4(a17,a13)
% 0.52/0.68 [50]~P4(a18,a13)
% 0.52/0.68 [42]P5(a2,f3(a13,a13))
% 0.52/0.68 [43]P5(a14,f3(a13,a13))
% 0.52/0.68 [48]~E(f27(a17,a18),a20)
% 0.52/0.68 [41]P5(x411,a13)
% 0.52/0.68 [51]~P4(x511,a20)
% 0.52/0.68 [46]P5(f15(x461),f3(f3(a13,a13),a13))
% 0.52/0.68 [47]P5(f16(x471),f3(f3(a13,a13),a13))
% 0.52/0.68 [44]P4(f27(x441,x442),a13)
% 0.52/0.68 [45]P5(f4(x451,x452),f3(a13,a13))
% 0.52/0.68 [54]~P1(x541)+P5(a1,x541)
% 0.52/0.68 [55]~P1(x551)+P4(a20,x551)
% 0.52/0.68 [56]E(x561,a20)+P4(f9(x561),a13)
% 0.52/0.68 [57]P4(f9(x571),x571)+E(x571,a20)
% 0.52/0.68 [58]P3(f9(x581),x581)+E(x581,a20)
% 0.52/0.68 [59]~P4(x591,a13)+P4(f25(x591),a13)
% 0.52/0.68 [60]~P4(x601,a13)+P4(f23(x601),a13)
% 0.52/0.68 [61]~P4(x611,a21)+P4(f10(x611),a13)
% 0.52/0.68 [62]~P2(x621)+P5(x621,f3(a13,a13))
% 0.52/0.68 [93]~P4(x931,a21)+E(f27(f27(f10(x931),f10(x931)),f27(f10(x931),f27(f10(x931),f10(x931)))),x931)
% 0.52/0.68 [94]~P2(x941)+P5(f4(x941,f6(f16(f3(x941,a13)))),a21)
% 0.52/0.68 [110]~P1(x1101)+P5(f6(f6(f16(f3(f22(a14,f3(x1101,a13)),a13)))),x1101)
% 0.52/0.68 [53]~E(x531,x532)+P5(x531,x532)
% 0.52/0.68 [63]P4(x631,a13)+~P4(x631,f5(x632))
% 0.52/0.68 [64]P4(x641,a13)+~P4(x641,f6(x642))
% 0.52/0.68 [65]P4(x651,a13)+~P4(x651,f23(x652))
% 0.52/0.68 [66]P5(x661,x662)+~P4(x661,f23(x662))
% 0.52/0.68 [68]P5(x681,x682)+P4(f7(x681,x682),x681)
% 0.52/0.68 [69]P3(x691,x692)+P4(f12(x691,x692),x692)
% 0.52/0.68 [70]P3(x701,x702)+P4(f12(x701,x702),x701)
% 0.52/0.68 [71]~P4(x711,x712)+~P4(x711,f5(x712))
% 0.52/0.68 [82]~P4(x821,f25(x822))+P4(x821,f11(x821,x822))
% 0.52/0.68 [83]~P4(x831,f25(x832))+P4(f11(x831,x832),x832)
% 0.52/0.68 [87]P5(x871,x872)+~P4(f7(x871,x872),x872)
% 0.52/0.68 [91]~P4(x912,f6(x911))+~E(f22(x911,f3(f27(x912,x912),a13)),a20)
% 0.52/0.68 [101]P4(x1011,a13)+~P4(f27(f27(x1012,x1012),f27(x1012,f27(x1011,x1011))),a2)
% 0.52/0.68 [102]P4(x1021,a13)+~P4(f27(f27(x1022,x1022),f27(x1022,f27(x1021,x1021))),a14)
% 0.52/0.68 [103]P4(x1031,a13)+~P4(f27(f27(x1031,x1031),f27(x1031,f27(x1032,x1032))),a14)
% 0.52/0.68 [104]P4(x1041,x1042)+~P4(f27(f27(x1041,x1041),f27(x1041,f27(x1042,x1042))),a2)
% 0.52/0.68 [105]E(f26(x1051,f27(x1051,x1051)),x1052)+~P4(f27(f27(x1051,x1051),f27(x1051,f27(x1052,x1052))),a14)
% 0.52/0.68 [74]~P4(x741,x743)+P4(x741,f26(x742,x743))
% 0.52/0.68 [75]~P4(x751,x752)+P4(x751,f26(x752,x753))
% 0.52/0.68 [84]P4(x841,a13)+~P4(x841,f27(x842,x843))
% 0.52/0.68 [85]P4(x851,x852)+~P4(x851,f22(x853,x852))
% 0.52/0.68 [86]P4(x861,x862)+~P4(x861,f22(x862,x863))
% 0.52/0.68 [95]~P4(x951,f3(x952,x953))+E(f27(f27(f19(x951),f19(x951)),f27(f19(x951),f27(f24(x951),f24(x951)))),x951)
% 0.52/0.68 [106]P4(x1061,a13)+~P4(f27(f27(x1061,x1061),f27(x1061,f27(x1062,x1062))),f4(x1063,x1064))
% 0.52/0.68 [107]P4(x1071,x1072)+~P4(f27(f27(x1073,x1073),f27(x1073,f27(x1071,x1071))),f3(x1074,x1072))
% 0.52/0.68 [108]P4(x1081,x1082)+~P4(f27(f27(x1081,x1081),f27(x1081,f27(x1083,x1083))),f3(x1082,x1084))
% 0.52/0.68 [114]~P4(f27(f27(f27(f27(x1143,x1143),f27(x1143,f27(x1141,x1141))),f27(f27(x1143,x1143),f27(x1143,f27(x1141,x1141)))),f27(f27(f27(x1143,x1143),f27(x1143,f27(x1141,x1141))),f27(x1142,x1142))),f15(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)
% 0.52/0.68 [115]~P4(f27(f27(f27(f27(x1152,x1152),f27(x1152,f27(x1151,x1151))),f27(f27(x1152,x1152),f27(x1152,f27(x1151,x1151)))),f27(f27(f27(x1152,x1152),f27(x1152,f27(x1151,x1151))),f27(x1153,x1153))),f16(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))),x1154)
% 0.52/0.68 [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))),f15(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))
% 0.52/0.68 [117]~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))),f16(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))
% 0.52/0.68 [120]~P4(f27(f27(x1204,x1204),f27(x1204,f27(x1201,x1201))),f4(x1202,x1203))+P4(x1201,f6(f6(f16(f3(f22(x1202,f3(f6(f6(f16(f3(f22(x1203,f3(f27(x1204,x1204),a13)),a13)))),a13)),a13)))))
% 0.52/0.68 [109]P2(x1091)+~P5(x1091,f3(a13,a13))+~P5(f4(x1091,f6(f16(f3(x1091,a13)))),a21)
% 0.52/0.68 [112]P1(x1121)+~P4(a20,x1121)+~P5(f6(f6(f16(f3(f22(a14,f3(x1121,a13)),a13)))),x1121)
% 0.52/0.68 [113]~P4(x1131,a13)+E(x1131,a20)+P4(f25(f6(f6(f16(f3(f22(a8,f3(f27(x1131,x1131),a13)),a13))))),x1131)
% 0.52/0.68 [67]~P5(x672,x671)+~P5(x671,x672)+E(x671,x672)
% 0.52/0.68 [72]P4(x721,x722)+P4(x721,f5(x722))+~P4(x721,a13)
% 0.52/0.68 [76]~P5(x761,x762)+~P4(x761,a13)+P4(x761,f23(x762))
% 0.52/0.68 [90]P4(x902,f6(x901))+~P4(x902,a13)+E(f22(x901,f3(f27(x902,x902),a13)),a20)
% 0.52/0.68 [92]~P4(x922,a13)+P4(x921,a21)+~E(x921,f27(f27(x922,x922),f27(x922,f27(x922,x922))))
% 0.52/0.68 [98]~P4(x981,x982)+~P4(x982,a13)+P4(f27(f27(x981,x981),f27(x981,f27(x982,x982))),a2)
% 0.52/0.68 [96]~P4(x962,a13)+~P4(x961,a13)+E(f19(f27(f27(x961,x961),f27(x961,f27(x962,x962)))),x961)
% 0.52/0.68 [97]~P4(x972,a13)+~P4(x971,a13)+E(f24(f27(f27(x971,x971),f27(x971,f27(x972,x972)))),x972)
% 0.52/0.68 [111]~P2(x1111)+~P4(x1112,a13)+P4(f6(f6(f16(f3(f22(x1111,f3(x1112,a13)),a13)))),a13)
% 0.52/0.68 [73]~P4(x731,x733)+P4(x731,x732)+~P5(x733,x732)
% 0.52/0.68 [81]~P3(x813,x812)+~P4(x811,x812)+~P4(x811,x813)
% 0.52/0.68 [77]~E(x771,x773)+~P4(x771,a13)+P4(x771,f27(x772,x773))
% 0.52/0.68 [78]~E(x781,x782)+~P4(x781,a13)+P4(x781,f27(x782,x783))
% 0.52/0.68 [79]~P4(x791,x793)+~P4(x793,x792)+P4(x791,f25(x792))
% 0.52/0.68 [80]E(x801,x802)+E(x801,x803)+~P4(x801,f27(x803,x802))
% 0.52/0.68 [88]~P4(x881,x883)+~P4(x881,x882)+P4(x881,f22(x882,x883))
% 0.52/0.68 [89]P4(x891,x892)+P4(x891,x893)+~P4(x891,f26(x893,x892))
% 0.52/0.68 [99]~P4(x992,x994)+~P4(x991,x993)+P4(f27(f27(x991,x991),f27(x991,f27(x992,x992))),f3(x993,x994))
% 0.52/0.68 [118]~P4(f27(f27(f27(f27(x1182,x1182),f27(x1182,f27(x1183,x1183))),f27(f27(x1182,x1182),f27(x1182,f27(x1183,x1183)))),f27(f27(f27(x1182,x1182),f27(x1182,f27(x1183,x1183))),f27(x1181,x1181))),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))),f15(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))
% 0.52/0.68 [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))),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))),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))),f3(f3(a13,a13),a13))
% 0.52/0.68 [121]~P4(x1211,a13)+P4(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f4(x1213,x1214))+~P4(x1212,f6(f6(f16(f3(f22(x1213,f3(f6(f6(f16(f3(f22(x1214,f3(f27(x1211,x1211),a13)),a13)))),a13)),a13)))))
% 0.52/0.68 [100]~P4(x1002,a13)+~P4(x1001,a13)+~E(f26(x1001,f27(x1001,x1001)),x1002)+P4(f27(f27(x1001,x1001),f27(x1001,f27(x1002,x1002))),a14)
% 0.52/0.68 %EqnAxiom
% 0.52/0.68 [1]E(x11,x11)
% 0.52/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.52/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.52/0.68 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.52/0.68 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.52/0.68 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.52/0.68 [7]~E(x71,x72)+E(f27(x71,x73),f27(x72,x73))
% 0.52/0.68 [8]~E(x81,x82)+E(f27(x83,x81),f27(x83,x82))
% 0.52/0.68 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.52/0.68 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.52/0.68 [11]~E(x111,x112)+E(f16(x111),f16(x112))
% 0.52/0.68 [12]~E(x121,x122)+E(f15(x121),f15(x122))
% 0.52/0.68 [13]~E(x131,x132)+E(f19(x131),f19(x132))
% 0.52/0.68 [14]~E(x141,x142)+E(f22(x141,x143),f22(x142,x143))
% 0.52/0.68 [15]~E(x151,x152)+E(f22(x153,x151),f22(x153,x152))
% 0.52/0.68 [16]~E(x161,x162)+E(f26(x161,x163),f26(x162,x163))
% 0.52/0.68 [17]~E(x171,x172)+E(f26(x173,x171),f26(x173,x172))
% 0.52/0.68 [18]~E(x181,x182)+E(f10(x181),f10(x182))
% 0.52/0.68 [19]~E(x191,x192)+E(f25(x191),f25(x192))
% 0.52/0.68 [20]~E(x201,x202)+E(f11(x201,x203),f11(x202,x203))
% 0.52/0.68 [21]~E(x211,x212)+E(f11(x213,x211),f11(x213,x212))
% 0.52/0.68 [22]~E(x221,x222)+E(f9(x221),f9(x222))
% 0.52/0.68 [23]~E(x231,x232)+E(f7(x231,x233),f7(x232,x233))
% 0.52/0.68 [24]~E(x241,x242)+E(f7(x243,x241),f7(x243,x242))
% 0.52/0.68 [25]~E(x251,x252)+E(f5(x251),f5(x252))
% 0.52/0.68 [26]~E(x261,x262)+E(f24(x261),f24(x262))
% 0.52/0.68 [27]~E(x271,x272)+E(f23(x271),f23(x272))
% 0.52/0.68 [28]~E(x281,x282)+E(f12(x281,x283),f12(x282,x283))
% 0.52/0.68 [29]~E(x291,x292)+E(f12(x293,x291),f12(x293,x292))
% 0.52/0.68 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.52/0.68 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.52/0.68 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.52/0.68 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.52/0.68 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.52/0.68 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.52/0.68 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363)
% 0.52/0.68 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371)
% 0.52/0.68
% 0.52/0.68 %-------------------------------------------
% 0.52/0.68 cnf(122,plain,
% 0.52/0.68 (P5(x1221,x1221)),
% 0.52/0.68 inference(equality_inference,[],[53])).
% 0.52/0.68 cnf(123,plain,
% 0.52/0.68 (~P4(x1231,a13)+P4(x1231,f27(x1232,x1231))),
% 0.52/0.68 inference(equality_inference,[],[77])).
% 0.52/0.68 cnf(124,plain,
% 0.52/0.69 (~P4(x1241,a13)+P4(x1241,f27(x1241,x1242))),
% 0.52/0.69 inference(equality_inference,[],[78])).
% 0.52/0.69 cnf(127,plain,
% 0.52/0.69 (P4(f9(f27(a17,a18)),f27(a17,a18))),
% 0.52/0.69 inference(scs_inference,[],[48,57])).
% 0.52/0.69 cnf(137,plain,
% 0.52/0.69 (~P4(a17,f27(x1371,x1372))),
% 0.52/0.69 inference(scs_inference,[],[48,49,57,58,63,64,65,84])).
% 0.52/0.69 cnf(144,plain,
% 0.52/0.69 (~P4(x1441,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(147,plain,
% 0.52/0.69 (~P4(x1471,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(150,plain,
% 0.52/0.69 (~P4(x1501,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(153,plain,
% 0.52/0.69 (~P4(x1531,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(155,plain,
% 0.52/0.69 (~P4(x1551,f25(a20))),
% 0.52/0.69 inference(scs_inference,[],[48,49,51,144,147,150,153,40,57,58,63,64,65,84,123,124,55,68,69,70,83])).
% 0.52/0.69 cnf(156,plain,
% 0.52/0.69 (~P4(x1561,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(159,plain,
% 0.52/0.69 (~P4(x1591,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(162,plain,
% 0.52/0.69 (~P4(x1621,a20)),
% 0.52/0.69 inference(rename_variables,[],[51])).
% 0.52/0.69 cnf(164,plain,
% 0.52/0.69 (~P4(f27(f27(x1641,x1641),f27(x1641,f27(a17,a17))),f4(x1642,x1643))),
% 0.52/0.69 inference(scs_inference,[],[48,49,51,144,147,150,153,156,159,40,57,58,63,64,65,84,123,124,55,68,69,70,83,114,115,120])).
% 0.52/0.69 cnf(167,plain,
% 0.52/0.69 (~E(a13,a20)),
% 0.52/0.69 inference(scs_inference,[],[48,49,51,144,147,150,153,156,159,162,40,57,58,63,64,65,84,123,124,55,68,69,70,83,114,115,120,32,33])).
% 0.52/0.69 cnf(179,plain,
% 0.52/0.69 (~P4(x1791,f25(f25(a20)))),
% 0.52/0.69 inference(scs_inference,[],[155,83])).
% 0.52/0.69 cnf(180,plain,
% 0.52/0.69 (~P4(x1801,f25(a20))),
% 0.52/0.69 inference(rename_variables,[],[155])).
% 0.52/0.69 cnf(191,plain,
% 0.52/0.69 (~P4(x1911,f25(a20))),
% 0.52/0.69 inference(rename_variables,[],[155])).
% 0.52/0.69 cnf(200,plain,
% 0.52/0.69 (~P4(x2001,f25(a20))),
% 0.52/0.69 inference(rename_variables,[],[155])).
% 0.52/0.69 cnf(203,plain,
% 0.52/0.69 (~P4(f27(f27(x2031,x2031),f27(x2031,f27(a17,a17))),f4(x2032,x2033))),
% 0.52/0.69 inference(rename_variables,[],[164])).
% 0.52/0.69 cnf(206,plain,
% 0.52/0.69 (~P4(x2061,f25(a20))),
% 0.52/0.69 inference(rename_variables,[],[155])).
% 0.52/0.69 cnf(208,plain,
% 0.52/0.69 (~P4(f27(f27(f27(f27(x2081,x2081),f27(x2081,f27(x2082,x2082))),f27(f27(x2081,x2081),f27(x2081,f27(x2082,x2082)))),f27(f27(f27(x2081,x2081),f27(x2081,f27(x2082,x2082))),f27(a17,a17))),f16(f4(x2083,x2084)))),
% 0.52/0.69 inference(scs_inference,[],[50,167,44,164,203,155,180,191,200,83,65,84,58,63,69,124,64,57,68,114,55,115])).
% 0.52/0.69 cnf(214,plain,
% 0.52/0.69 (~P4(x2141,f25(a20))),
% 0.52/0.69 inference(rename_variables,[],[155])).
% 0.52/0.69 cnf(219,plain,
% 0.52/0.69 (P4(f9(f27(a17,a18)),a13)),
% 0.52/0.69 inference(scs_inference,[],[50,127,167,122,41,44,164,203,155,180,191,200,206,83,65,84,58,63,69,124,64,57,68,114,55,115,123,70,76,73])).
% 0.52/0.69 cnf(220,plain,
% 0.52/0.69 (P5(x2201,a13)),
% 0.52/0.69 inference(rename_variables,[],[41])).
% 0.52/0.69 cnf(231,plain,
% 0.52/0.69 (E(f9(f27(a17,a18)),a18)),
% 0.52/0.69 inference(scs_inference,[],[50,127,137,167,122,41,220,44,164,203,155,180,191,200,206,214,83,65,84,58,63,69,124,64,57,68,114,55,115,123,70,76,73,33,32,120,112,80])).
% 0.52/0.69 cnf(253,plain,
% 0.52/0.69 (~P4(x2531,f25(f25(a20)))),
% 0.52/0.69 inference(rename_variables,[],[179])).
% 0.52/0.69 cnf(256,plain,
% 0.52/0.69 (~P4(x2561,f25(f25(a20)))),
% 0.52/0.69 inference(rename_variables,[],[179])).
% 0.52/0.69 cnf(263,plain,
% 0.52/0.69 (~P4(x2631,f25(f25(a20)))),
% 0.52/0.69 inference(rename_variables,[],[179])).
% 0.52/0.69 cnf(270,plain,
% 0.52/0.69 (~P4(x2701,f25(f25(a20)))),
% 0.52/0.69 inference(rename_variables,[],[179])).
% 0.52/0.69 cnf(278,plain,
% 0.52/0.69 ($false),
% 0.52/0.69 inference(scs_inference,[],[50,219,231,122,208,179,253,256,263,270,69,83,115,114,68,124,123,55,70,76,32]),
% 0.52/0.69 ['proof']).
% 0.52/0.69 % SZS output end Proof
% 0.52/0.69 % Total time :0.070000s
%------------------------------------------------------------------------------