%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET084+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 : 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 14:20:36 EDT 2024
% Result : Theorem 0.53s 0.69s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET084+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.04/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n019.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 : Sun Jun 23 12:56:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.47/0.56 start to proof:theBenchmark
% 0.53/0.68 %-------------------------------------------
% 0.53/0.68 % File :CSE---1.7
% 0.53/0.68 % Problem :theBenchmark
% 0.53/0.68 % Transform :cnf
% 0.53/0.68 % Format :tptp:raw
% 0.53/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.53/0.68
% 0.53/0.68 % Result :Theorem 0.040000s
% 0.53/0.68 % Output :CNFRefutation 0.040000s
% 0.53/0.68 %-------------------------------------------
% 0.53/0.68 %--------------------------------------------------------------------------
% 0.53/0.68 % File : SET084+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.53/0.68 % Domain : Set Theory
% 0.53/0.68 % Problem : A singleton set is determined by its element
% 0.53/0.68 % Version : [Qua92] axioms : Reduced & Augmented > Complete.
% 0.53/0.68 % English :
% 0.53/0.68
% 0.53/0.68 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.53/0.69 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.53/0.69 % Source : [Qua92]
% 0.53/0.69 % Names :
% 0.53/0.69
% 0.53/0.69 % Status : Theorem
% 0.53/0.69 % Rating : 0.22 v8.2.0, 0.19 v8.1.0, 0.25 v7.5.0, 0.28 v7.4.0, 0.17 v7.3.0, 0.24 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.27 v6.3.0, 0.33 v6.2.0, 0.44 v6.1.0, 0.40 v6.0.0, 0.43 v5.5.0, 0.37 v5.4.0
% 0.53/0.69 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.53/0.69 % Number of atoms : 103 ( 21 equ)
% 0.53/0.69 % Maximal formula atoms : 4 ( 2 avg)
% 0.53/0.69 % Number of connectives : 64 ( 5 ~; 3 |; 27 &)
% 0.53/0.69 % ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% 0.53/0.69 % Maximal formula depth : 7 ( 4 avg)
% 0.53/0.69 % Maximal term depth : 4 ( 1 avg)
% 0.53/0.69 % Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% 0.53/0.69 % Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% 0.53/0.69 % Number of variables : 88 ( 83 !; 5 ?)
% 0.53/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.53/0.69
% 0.53/0.69 % Comments :
% 0.53/0.69 % Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
% 0.53/0.69 %--------------------------------------------------------------------------
% 0.53/0.69 %----Include set theory axioms
% 0.53/0.69 include('Axioms/SET005+0.ax').
% 0.53/0.69 %--------------------------------------------------------------------------
% 0.53/0.69 %----SS5: A singleton set is determined by its element
% 0.53/0.69 fof(singleton_identified_by_element2,conjecture,
% 0.53/0.69 ! [X,Y] :
% 0.53/0.69 ( ( singleton(X) = singleton(Y)
% 0.53/0.69 & member(Y,universal_class) )
% 0.53/0.69 => X = Y ) ).
% 0.53/0.69
% 0.53/0.69 %--------------------------------------------------------------------------
% 0.53/0.69 %-------------------------------------------
% 0.53/0.69 % Proof found
% 0.53/0.69 % SZS status Theorem for theBenchmark
% 0.53/0.69 % SZS output start Proof
% 0.53/0.69 %ClaNum:121(EqnAxiom:37)
% 0.53/0.69 %VarNum:607(SingletonVarNum:169)
% 0.53/0.69 %MaxLitNum:4
% 0.53/0.69 %MaxfuncDepth:13
% 0.53/0.69 %SharedTerms:21
% 0.53/0.69 %goalClause: 41 43 50
% 0.53/0.69 %singleGoalClaCount:3
% 0.53/0.69 [38]P1(a1)
% 0.53/0.69 [39]P2(a8)
% 0.53/0.69 [40]P4(a1,a13)
% 0.53/0.69 [41]P4(a14,a13)
% 0.53/0.69 [50]~E(a15,a14)
% 0.53/0.69 [43]E(f27(a15,a15),f27(a14,a14))
% 0.53/0.69 [44]P5(a2,f3(a13,a13))
% 0.53/0.69 [45]P5(a16,f3(a13,a13))
% 0.53/0.69 [42]P5(x421,a13)
% 0.53/0.69 [51]~P4(x511,a20)
% 0.53/0.69 [48]P5(f17(x481),f3(f3(a13,a13),a13))
% 0.53/0.69 [49]P5(f18(x491),f3(f3(a13,a13),a13))
% 0.53/0.69 [46]P4(f27(x461,x462),a13)
% 0.53/0.69 [47]P5(f4(x471,x472),f3(a13,a13))
% 0.53/0.69 [54]~P1(x541)+P5(a1,x541)
% 0.53/0.69 [55]~P1(x551)+P4(a20,x551)
% 0.53/0.69 [56]E(x561,a20)+P4(f9(x561),a13)
% 0.53/0.69 [57]P4(f9(x571),x571)+E(x571,a20)
% 0.53/0.69 [58]P3(f9(x581),x581)+E(x581,a20)
% 0.53/0.69 [59]~P4(x591,a13)+P4(f25(x591),a13)
% 0.53/0.69 [60]~P4(x601,a13)+P4(f23(x601),a13)
% 0.53/0.69 [61]~P4(x611,a21)+P4(f10(x611),a13)
% 0.53/0.69 [62]~P2(x621)+P5(x621,f3(a13,a13))
% 0.53/0.69 [93]~P4(x931,a21)+E(f27(f27(f10(x931),f10(x931)),f27(f10(x931),f27(f10(x931),f10(x931)))),x931)
% 0.53/0.69 [94]~P2(x941)+P5(f4(x941,f6(f18(f3(x941,a13)))),a21)
% 0.53/0.69 [110]~P1(x1101)+P5(f6(f6(f18(f3(f22(a16,f3(x1101,a13)),a13)))),x1101)
% 0.53/0.69 [53]~E(x531,x532)+P5(x531,x532)
% 0.53/0.69 [63]P4(x631,a13)+~P4(x631,f5(x632))
% 0.53/0.69 [64]P4(x641,a13)+~P4(x641,f6(x642))
% 0.53/0.69 [65]P4(x651,a13)+~P4(x651,f23(x652))
% 0.53/0.69 [66]P5(x661,x662)+~P4(x661,f23(x662))
% 0.53/0.69 [68]P5(x681,x682)+P4(f7(x681,x682),x681)
% 0.53/0.69 [69]P3(x691,x692)+P4(f12(x691,x692),x692)
% 0.53/0.69 [70]P3(x701,x702)+P4(f12(x701,x702),x701)
% 0.53/0.69 [71]~P4(x711,x712)+~P4(x711,f5(x712))
% 0.53/0.69 [82]~P4(x821,f25(x822))+P4(x821,f11(x821,x822))
% 0.53/0.69 [83]~P4(x831,f25(x832))+P4(f11(x831,x832),x832)
% 0.53/0.69 [87]P5(x871,x872)+~P4(f7(x871,x872),x872)
% 0.53/0.69 [91]~P4(x912,f6(x911))+~E(f22(x911,f3(f27(x912,x912),a13)),a20)
% 0.53/0.69 [101]P4(x1011,a13)+~P4(f27(f27(x1012,x1012),f27(x1012,f27(x1011,x1011))),a2)
% 0.53/0.69 [102]P4(x1021,a13)+~P4(f27(f27(x1022,x1022),f27(x1022,f27(x1021,x1021))),a16)
% 0.53/0.69 [103]P4(x1031,a13)+~P4(f27(f27(x1031,x1031),f27(x1031,f27(x1032,x1032))),a16)
% 0.53/0.69 [104]P4(x1041,x1042)+~P4(f27(f27(x1041,x1041),f27(x1041,f27(x1042,x1042))),a2)
% 0.53/0.69 [105]E(f26(x1051,f27(x1051,x1051)),x1052)+~P4(f27(f27(x1051,x1051),f27(x1051,f27(x1052,x1052))),a16)
% 0.53/0.69 [74]~P4(x741,x743)+P4(x741,f26(x742,x743))
% 0.53/0.69 [75]~P4(x751,x752)+P4(x751,f26(x752,x753))
% 0.53/0.69 [84]P4(x841,a13)+~P4(x841,f27(x842,x843))
% 0.53/0.69 [85]P4(x851,x852)+~P4(x851,f22(x853,x852))
% 0.53/0.69 [86]P4(x861,x862)+~P4(x861,f22(x862,x863))
% 0.53/0.69 [95]~P4(x951,f3(x952,x953))+E(f27(f27(f19(x951),f19(x951)),f27(f19(x951),f27(f24(x951),f24(x951)))),x951)
% 0.53/0.69 [106]P4(x1061,a13)+~P4(f27(f27(x1061,x1061),f27(x1061,f27(x1062,x1062))),f4(x1063,x1064))
% 0.53/0.69 [107]P4(x1071,x1072)+~P4(f27(f27(x1073,x1073),f27(x1073,f27(x1071,x1071))),f3(x1074,x1072))
% 0.53/0.69 [108]P4(x1081,x1082)+~P4(f27(f27(x1081,x1081),f27(x1081,f27(x1083,x1083))),f3(x1082,x1084))
% 0.53/0.69 [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))),f17(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)
% 0.53/0.69 [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))),f18(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)
% 0.53/0.69 [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))),f17(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))
% 0.53/0.69 [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))),f18(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))
% 0.53/0.69 [120]~P4(f27(f27(x1204,x1204),f27(x1204,f27(x1201,x1201))),f4(x1202,x1203))+P4(x1201,f6(f6(f18(f3(f22(x1202,f3(f6(f6(f18(f3(f22(x1203,f3(f27(x1204,x1204),a13)),a13)))),a13)),a13)))))
% 0.53/0.69 [109]P2(x1091)+~P5(x1091,f3(a13,a13))+~P5(f4(x1091,f6(f18(f3(x1091,a13)))),a21)
% 0.53/0.69 [112]P1(x1121)+~P4(a20,x1121)+~P5(f6(f6(f18(f3(f22(a16,f3(x1121,a13)),a13)))),x1121)
% 0.53/0.69 [113]~P4(x1131,a13)+E(x1131,a20)+P4(f25(f6(f6(f18(f3(f22(a8,f3(f27(x1131,x1131),a13)),a13))))),x1131)
% 0.53/0.69 [67]~P5(x672,x671)+~P5(x671,x672)+E(x671,x672)
% 0.53/0.69 [72]P4(x721,x722)+P4(x721,f5(x722))+~P4(x721,a13)
% 0.53/0.69 [76]~P5(x761,x762)+~P4(x761,a13)+P4(x761,f23(x762))
% 0.53/0.69 [90]P4(x902,f6(x901))+~P4(x902,a13)+E(f22(x901,f3(f27(x902,x902),a13)),a20)
% 0.53/0.69 [92]~P4(x922,a13)+P4(x921,a21)+~E(x921,f27(f27(x922,x922),f27(x922,f27(x922,x922))))
% 0.53/0.69 [98]~P4(x981,x982)+~P4(x982,a13)+P4(f27(f27(x981,x981),f27(x981,f27(x982,x982))),a2)
% 0.53/0.69 [96]~P4(x962,a13)+~P4(x961,a13)+E(f19(f27(f27(x961,x961),f27(x961,f27(x962,x962)))),x961)
% 0.53/0.69 [97]~P4(x972,a13)+~P4(x971,a13)+E(f24(f27(f27(x971,x971),f27(x971,f27(x972,x972)))),x972)
% 0.53/0.69 [111]~P2(x1111)+~P4(x1112,a13)+P4(f6(f6(f18(f3(f22(x1111,f3(x1112,a13)),a13)))),a13)
% 0.53/0.69 [73]~P4(x731,x733)+P4(x731,x732)+~P5(x733,x732)
% 0.53/0.69 [81]~P3(x813,x812)+~P4(x811,x812)+~P4(x811,x813)
% 0.53/0.69 [77]~E(x771,x773)+~P4(x771,a13)+P4(x771,f27(x772,x773))
% 0.53/0.69 [78]~E(x781,x782)+~P4(x781,a13)+P4(x781,f27(x782,x783))
% 0.53/0.69 [79]~P4(x791,x793)+~P4(x793,x792)+P4(x791,f25(x792))
% 0.53/0.69 [80]E(x801,x802)+E(x801,x803)+~P4(x801,f27(x803,x802))
% 0.53/0.69 [88]~P4(x881,x883)+~P4(x881,x882)+P4(x881,f22(x882,x883))
% 0.53/0.69 [89]P4(x891,x892)+P4(x891,x893)+~P4(x891,f26(x893,x892))
% 0.53/0.69 [99]~P4(x992,x994)+~P4(x991,x993)+P4(f27(f27(x991,x991),f27(x991,f27(x992,x992))),f3(x993,x994))
% 0.53/0.69 [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))),f17(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))
% 0.53/0.69 [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))),f18(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))
% 0.53/0.69 [121]~P4(x1211,a13)+P4(f27(f27(x1211,x1211),f27(x1211,f27(x1212,x1212))),f4(x1213,x1214))+~P4(x1212,f6(f6(f18(f3(f22(x1213,f3(f6(f6(f18(f3(f22(x1214,f3(f27(x1211,x1211),a13)),a13)))),a13)),a13)))))
% 0.53/0.69 [100]~P4(x1002,a13)+~P4(x1001,a13)+~E(f26(x1001,f27(x1001,x1001)),x1002)+P4(f27(f27(x1001,x1001),f27(x1001,f27(x1002,x1002))),a16)
% 0.53/0.69 %EqnAxiom
% 0.53/0.69 [1]E(x11,x11)
% 0.53/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.53/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.53/0.69 [4]~E(x41,x42)+E(f27(x41,x43),f27(x42,x43))
% 0.53/0.69 [5]~E(x51,x52)+E(f27(x53,x51),f27(x53,x52))
% 0.53/0.69 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.53/0.69 [7]~E(x71,x72)+E(f3(x71,x73),f3(x72,x73))
% 0.53/0.69 [8]~E(x81,x82)+E(f3(x83,x81),f3(x83,x82))
% 0.53/0.69 [9]~E(x91,x92)+E(f18(x91),f18(x92))
% 0.53/0.69 [10]~E(x101,x102)+E(f22(x101,x103),f22(x102,x103))
% 0.53/0.69 [11]~E(x111,x112)+E(f22(x113,x111),f22(x113,x112))
% 0.53/0.69 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.53/0.69 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.53/0.69 [14]~E(x141,x142)+E(f19(x141),f19(x142))
% 0.53/0.69 [15]~E(x151,x152)+E(f17(x151),f17(x152))
% 0.53/0.69 [16]~E(x161,x162)+E(f24(x161),f24(x162))
% 0.53/0.69 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.53/0.69 [18]~E(x181,x182)+E(f7(x181,x183),f7(x182,x183))
% 0.53/0.69 [19]~E(x191,x192)+E(f7(x193,x191),f7(x193,x192))
% 0.53/0.69 [20]~E(x201,x202)+E(f25(x201),f25(x202))
% 0.53/0.69 [21]~E(x211,x212)+E(f26(x211,x213),f26(x212,x213))
% 0.53/0.69 [22]~E(x221,x222)+E(f26(x223,x221),f26(x223,x222))
% 0.53/0.69 [23]~E(x231,x232)+E(f9(x231),f9(x232))
% 0.53/0.69 [24]~E(x241,x242)+E(f12(x241,x243),f12(x242,x243))
% 0.53/0.69 [25]~E(x251,x252)+E(f12(x253,x251),f12(x253,x252))
% 0.53/0.69 [26]~E(x261,x262)+E(f11(x261,x263),f11(x262,x263))
% 0.53/0.69 [27]~E(x271,x272)+E(f11(x273,x271),f11(x273,x272))
% 0.53/0.69 [28]~E(x281,x282)+E(f5(x281),f5(x282))
% 0.53/0.69 [29]~E(x291,x292)+E(f23(x291),f23(x292))
% 0.53/0.69 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.53/0.69 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.53/0.69 [32]P4(x322,x323)+~E(x321,x322)+~P4(x321,x323)
% 0.53/0.69 [33]P4(x333,x332)+~E(x331,x332)+~P4(x333,x331)
% 0.53/0.69 [34]P5(x342,x343)+~E(x341,x342)+~P5(x341,x343)
% 0.53/0.69 [35]P5(x353,x352)+~E(x351,x352)+~P5(x353,x351)
% 0.53/0.69 [36]P3(x362,x363)+~E(x361,x362)+~P3(x361,x363)
% 0.53/0.69 [37]P3(x373,x372)+~E(x371,x372)+~P3(x373,x371)
% 0.53/0.69
% 0.53/0.69 %-------------------------------------------
% 0.53/0.69 cnf(122,plain,
% 0.53/0.69 (P5(x1221,x1221)),
% 0.53/0.69 inference(equality_inference,[],[53])).
% 0.53/0.70 cnf(123,plain,
% 0.53/0.70 (~P4(x1231,a13)+P4(x1231,f27(x1232,x1231))),
% 0.53/0.70 inference(equality_inference,[],[77])).
% 0.53/0.70 cnf(124,plain,
% 0.53/0.70 (~P4(x1241,a13)+P4(x1241,f27(x1241,x1242))),
% 0.53/0.70 inference(equality_inference,[],[78])).
% 0.53/0.70 cnf(127,plain,
% 0.53/0.70 (P4(a14,f27(x1271,a14))),
% 0.53/0.70 inference(scs_inference,[],[41,123])).
% 0.53/0.70 cnf(133,plain,
% 0.53/0.70 (~P4(x1331,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(136,plain,
% 0.53/0.70 (~P4(x1361,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(139,plain,
% 0.53/0.70 (~P4(x1391,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(142,plain,
% 0.53/0.70 (~P4(x1421,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(144,plain,
% 0.53/0.70 (~P4(x1441,f25(a20))),
% 0.53/0.70 inference(scs_inference,[],[41,43,51,133,136,139,142,123,124,2,55,68,69,70,83])).
% 0.53/0.70 cnf(145,plain,
% 0.53/0.70 (~P4(x1451,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(147,plain,
% 0.53/0.70 (~P4(f27(f27(f27(f27(x1471,x1471),f27(x1471,f27(x1472,x1472))),f27(f27(x1471,x1471),f27(x1471,f27(x1472,x1472)))),f27(f27(f27(x1471,x1471),f27(x1471,f27(x1472,x1472))),f27(x1473,x1473))),f17(a20))),
% 0.53/0.70 inference(scs_inference,[],[41,43,51,133,136,139,142,145,123,124,2,55,68,69,70,83,114])).
% 0.53/0.70 cnf(148,plain,
% 0.53/0.70 (~P4(x1481,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(151,plain,
% 0.53/0.70 (~P4(x1511,a20)),
% 0.53/0.70 inference(rename_variables,[],[51])).
% 0.53/0.70 cnf(154,plain,
% 0.53/0.70 (P5(x1541,x1541)),
% 0.53/0.70 inference(rename_variables,[],[122])).
% 0.53/0.70 cnf(157,plain,
% 0.53/0.70 (P4(f27(x1571,x1572),a13)),
% 0.53/0.70 inference(rename_variables,[],[46])).
% 0.53/0.70 cnf(165,plain,
% 0.53/0.70 (P5(f27(a14,a14),f27(a15,a15))),
% 0.53/0.70 inference(scs_inference,[],[41,43,122,154,51,133,136,139,142,145,148,151,46,157,123,124,2,55,68,69,70,83,114,115,76,77,78,32,33,34])).
% 0.53/0.70 cnf(166,plain,
% 0.53/0.70 (P5(x1661,x1661)),
% 0.53/0.70 inference(rename_variables,[],[122])).
% 0.53/0.70 cnf(169,plain,
% 0.53/0.70 (P4(f9(a13),a13)),
% 0.53/0.70 inference(scs_inference,[],[41,43,122,154,166,51,133,136,139,142,145,148,151,46,157,123,124,2,55,68,69,70,83,114,115,76,77,78,32,33,34,35,57])).
% 0.53/0.70 cnf(183,plain,
% 0.53/0.70 (~P4(x1831,f25(a20))),
% 0.53/0.70 inference(rename_variables,[],[144])).
% 0.53/0.70 cnf(188,plain,
% 0.53/0.70 (~P4(x1881,f25(a20))),
% 0.53/0.70 inference(rename_variables,[],[144])).
% 0.53/0.70 cnf(191,plain,
% 0.53/0.70 (~P4(x1911,f25(a20))),
% 0.53/0.70 inference(rename_variables,[],[144])).
% 0.53/0.70 cnf(194,plain,
% 0.53/0.70 (~P4(x1941,f25(a20))),
% 0.53/0.70 inference(rename_variables,[],[144])).
% 0.53/0.70 cnf(201,plain,
% 0.53/0.70 (~P4(x2011,f25(a20))),
% 0.53/0.70 inference(rename_variables,[],[144])).
% 0.53/0.70 cnf(218,plain,
% 0.53/0.70 ($false),
% 0.53/0.70 inference(scs_inference,[],[41,50,127,122,147,144,183,188,191,194,201,165,169,68,114,55,69,70,115,124,83,123,73,80,76,78,32,33,2]),
% 0.53/0.70 ['proof']).
% 0.53/0.70 % SZS output end Proof
% 0.53/0.70 % Total time :0.040000s
%------------------------------------------------------------------------------