%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET166-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Mon Jun 24 14:20:58 EDT 2024
% Result : Unsatisfiable 3.50s 3.58s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET166-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Sun Jun 23 17:38:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.48/0.57 start to proof:theBenchmark
% 3.50/3.57 %-------------------------------------------
% 3.50/3.57 % File :CSE---1.7
% 3.50/3.57 % Problem :theBenchmark
% 3.50/3.57 % Transform :cnf
% 3.50/3.57 % Format :tptp:raw
% 3.50/3.57 % Command :java -jar mcs_scs.jar %d %s
% 3.50/3.57
% 3.50/3.57 % Result :Theorem 2.950000s
% 3.50/3.57 % Output :CNFRefutation 2.950000s
% 3.50/3.57 %-------------------------------------------
% 3.50/3.57 %--------------------------------------------------------------------------
% 3.50/3.57 % File : SET166-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 3.50/3.57 % Domain : Set Theory
% 3.50/3.57 % Problem : Members of union 1
% 3.50/3.57 % Version : [Qua92] axioms.
% 3.50/3.57 % English :
% 3.50/3.57
% 3.50/3.57 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 3.50/3.57 % : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 3.50/3.58 % Source : [Quaife]
% 3.50/3.58 % Names : U7.1 [Qua92]
% 3.50/3.58
% 3.50/3.58 % Status : Unsatisfiable
% 3.50/3.58 % Rating : 0.15 v8.2.0, 0.19 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.33 v6.3.0, 0.27 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.20 v5.5.0, 0.65 v5.3.0, 0.67 v5.2.0, 0.56 v5.1.0, 0.53 v5.0.0, 0.50 v4.1.0, 0.62 v4.0.1, 0.64 v4.0.0, 0.55 v3.7.0, 0.40 v3.5.0, 0.45 v3.4.0, 0.50 v3.2.0, 0.38 v3.1.0, 0.36 v2.7.0, 0.50 v2.6.0, 0.44 v2.5.0, 0.45 v2.4.0, 0.50 v2.3.0, 0.62 v2.2.1, 0.83 v2.2.0, 1.00 v2.1.0
% 3.50/3.58 % Syntax : Number of clauses : 115 ( 40 unt; 8 nHn; 82 RR)
% 3.50/3.58 % Number of literals : 221 ( 49 equ; 102 neg)
% 3.50/3.58 % Maximal clause size : 5 ( 1 avg)
% 3.50/3.58 % Maximal term depth : 6 ( 2 avg)
% 3.50/3.58 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% 3.50/3.58 % Number of functors : 49 ( 49 usr; 15 con; 0-3 aty)
% 3.50/3.58 % Number of variables : 214 ( 32 sgn)
% 3.50/3.58 % SPC : CNF_UNS_RFO_SEQ_NHN
% 3.50/3.58
% 3.50/3.58 % Comments : Quaife proves all these problems by augmenting the axioms with
% 3.50/3.58 % all previously proved theorems. With a few exceptions (the
% 3.50/3.58 % problems that correspond to [BL+86] problems), the TPTP has
% 3.50/3.58 % retained the order in which Quaife presents the problems. The
% 3.50/3.58 % user may create an augmented version of this problem by adding
% 3.50/3.58 % all previously proved theorems (the ones that correspond to
% 3.50/3.58 % [BL+86] are easily identified and positioned using Quaife's
% 3.50/3.58 % naming scheme).
% 3.50/3.58 % Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% 3.50/3.58 % : v2.1.0 - Bugfix in SET004-0.ax.
% 3.50/3.58 %--------------------------------------------------------------------------
% 3.50/3.58 %----Include von Neuman-Bernays-Godel set theory axioms
% 3.50/3.58 include('Axioms/SET004-0.ax').
% 3.50/3.58 %----Include von Neuman-Bernays-Godel Boolean Algebra definitions
% 3.50/3.58 include('Axioms/SET004-1.ax').
% 3.50/3.58 %--------------------------------------------------------------------------
% 3.50/3.58 cnf(prove_members_of_union1_1,negated_conjecture,
% 3.50/3.58 member(x,union(y,z)) ).
% 3.50/3.58
% 3.50/3.58 cnf(prove_members_of_union1_2,negated_conjecture,
% 3.50/3.58 ~ member(x,y) ).
% 3.50/3.58
% 3.50/3.58 cnf(prove_members_of_union1_3,negated_conjecture,
% 3.50/3.58 ~ member(x,z) ).
% 3.50/3.58
% 3.50/3.58 %--------------------------------------------------------------------------
% 3.50/3.58 %-------------------------------------------
% 3.50/3.58 % Proof found
% 3.50/3.58 % SZS status Theorem for theBenchmark
% 3.50/3.58 % SZS output start Proof
% 3.50/3.58 %ClaNum:145(EqnAxiom:47)
% 3.50/3.58 %VarNum:892(SingletonVarNum:186)
% 3.50/3.58 %MaxLitNum:5
% 3.50/3.58 %MaxfuncDepth:24
% 3.50/3.58 %SharedTerms:52
% 3.50/3.58 %goalClause: 64 69 70
% 3.50/3.58 %singleGoalClaCount:3
% 3.50/3.58 [48]P1(a1)
% 3.50/3.58 [49]P2(a2)
% 3.50/3.58 [50]P5(a1,a21)
% 3.50/3.58 [69]~P5(a30,a31)
% 3.50/3.58 [70]~P5(a30,a32)
% 3.50/3.58 [52]P7(a5,f6(a21,a21))
% 3.50/3.58 [53]P7(a22,f6(a21,a21))
% 3.50/3.58 [54]P7(a11,f6(a21,a21))
% 3.50/3.58 [58]P7(a10,f6(a21,f6(a21,a21)))
% 3.50/3.58 [59]P7(a3,f6(a21,f6(a21,a21)))
% 3.50/3.58 [64]P5(a30,f9(f16(f9(a31),f9(a32))))
% 3.50/3.58 [60]E(f16(f9(f8(a5,f9(a13))),a5),a23)
% 3.50/3.58 [65]E(f16(f12(f14(f6(a28,a21))),a28),a13)
% 3.50/3.58 [66]E(f16(f6(a21,a21),f16(f6(a21,a21),f9(f8(f9(a5),f12(f14(f6(a5,a21))))))),a28)
% 3.50/3.58 [51]P7(x511,a21)
% 3.50/3.58 [56]P7(f7(x561),f6(a21,a21))
% 3.50/3.58 [62]P7(f24(x621),f6(f6(a21,a21),a21))
% 3.50/3.58 [63]P7(f14(x631),f6(f6(a21,a21),a21))
% 3.50/3.58 [67]E(f16(f12(x671),f9(f12(f16(f8(f12(f14(f6(a5,a21))),x671),a13)))),f4(x671))
% 3.50/3.58 [68]E(f15(f17(f16(x681,f6(f12(f12(f14(f6(f16(f12(f14(f6(x681,a21))),f6(f29(f15(f17(f8(x681,f12(f14(f6(x681,a21)))),a13)),f15(f17(f8(x681,f12(f14(f6(x681,a21)))),a13))),a21)),a21)))),f29(f26(f17(f8(x681,f12(f14(f6(x681,a21)))),a13)),f26(f17(f8(x681,f12(f14(f6(x681,a21)))),a13))))),a20)),f27(x681))
% 3.50/3.58 [55]P5(f29(x551,x552),a21)
% 3.50/3.58 [57]P7(f8(x571,x572),f6(a21,a21))
% 3.50/3.58 [61]E(f16(f6(x611,x612),x613),f16(x613,f6(x611,x612)))
% 3.50/3.58 [71]~P8(x711)+P2(x711)
% 3.50/3.58 [72]~P9(x721)+P2(x721)
% 3.50/3.58 [75]~P1(x751)+P7(a1,x751)
% 3.50/3.58 [76]~P1(x761)+P5(a20,x761)
% 3.50/3.58 [78]P5(f25(x781),x781)+E(x781,a20)
% 3.50/3.58 [79]~P2(x791)+P7(x791,f6(a21,a21))
% 3.50/3.58 [77]E(x771,a20)+E(f16(x771,f25(x771)),a20)
% 3.50/3.58 [87]~P9(x871)+E(f6(f12(f12(x871)),f12(f12(x871))),f12(x871))
% 3.50/3.58 [99]~P8(x991)+P2(f12(f14(f6(x991,a21))))
% 3.50/3.58 [103]~P5(x1031,a21)+P5(f12(f16(a5,f6(a21,x1031))),a21)
% 3.50/3.58 [105]~P10(x1051)+P7(f8(x1051,f12(f14(f6(x1051,a21)))),a13)
% 3.50/3.58 [106]~P2(x1061)+P7(f8(x1061,f12(f14(f6(x1061,a21)))),a13)
% 3.50/3.58 [107]~P9(x1071)+P7(f12(f12(f14(f6(x1071,a21)))),f12(f12(x1071)))
% 3.50/3.58 [112]~P5(x1121,a21)+P5(f29(f29(x1121,x1121),f29(x1121,f29(f12(x1121),f12(x1121)))),a11)
% 3.50/3.58 [115]P10(x1151)+~P7(f8(x1151,f12(f14(f6(x1151,a21)))),a13)
% 3.50/3.58 [127]~P1(x1271)+P7(f12(f12(f14(f6(f16(a22,f6(x1271,a21)),a21)))),x1271)
% 3.50/3.58 [131]~P5(x1311,a21)+P5(f9(f12(f12(f14(f6(f16(a5,f6(f9(x1311),a21)),a21))))),a21)
% 3.50/3.58 [73]~E(x732,x731)+P7(x731,x732)
% 3.50/3.58 [74]~E(x741,x742)+P7(x741,x742)
% 3.50/3.58 [81]P7(x811,x812)+P5(f17(x811,x812),x811)
% 3.50/3.58 [82]~P5(x821,x822)+~P5(x821,f9(x822))
% 3.50/3.58 [85]~P5(x851,a21)+P5(x851,f29(x852,x851))
% 3.50/3.58 [86]~P5(x861,a21)+P5(x861,f29(x861,x862))
% 3.50/3.58 [91]P7(x911,x912)+~P5(f17(x911,x912),x912)
% 3.50/3.58 [102]~P5(x1022,f12(x1021))+~E(f16(x1021,f6(f29(x1022,x1022),a21)),a20)
% 3.50/3.58 [113]E(f12(x1131),x1132)+~P5(f29(f29(x1131,x1131),f29(x1131,f29(x1132,x1132))),a11)
% 3.50/3.58 [114]P5(x1141,x1142)+~P5(f29(f29(x1141,x1141),f29(x1141,f29(x1142,x1142))),a5)
% 3.50/3.58 [123]~P5(f29(f29(x1231,x1231),f29(x1231,f29(x1232,x1232))),a22)+E(f9(f16(f9(x1231),f9(f29(x1231,x1231)))),x1232)
% 3.50/3.58 [136]~P5(f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362))),f6(a21,a21))+P5(f29(f29(x1361,x1361),f29(x1361,f29(f29(f29(x1362,x1362),f29(x1362,f29(f8(x1361,x1362),f8(x1361,x1362)))),f29(f29(x1362,x1362),f29(x1362,f29(f8(x1361,x1362),f8(x1361,x1362))))))),a10)
% 3.50/3.58 [93]P2(x931)+~P3(x931,x932,x933)
% 3.50/3.58 [94]P2(x941)+~P6(x941,x942,x943)
% 3.50/3.58 [95]P9(x951)+~P4(x952,x953,x951)
% 3.50/3.58 [96]P9(x961)+~P4(x962,x961,x963)
% 3.50/3.58 [101]~P4(x1011,x1012,x1013)+P3(x1011,x1012,x1013)
% 3.50/3.58 [89]P5(x891,x892)+~P5(x891,f16(x893,x892))
% 3.50/3.58 [90]P5(x901,x902)+~P5(x901,f16(x902,x903))
% 3.50/3.58 [97]~P6(x971,x972,x973)+E(f12(x971),x972)
% 3.50/3.58 [98]~P3(x982,x981,x983)+E(f12(f12(x981)),f12(x982))
% 3.50/3.58 [116]E(f8(x1161,x1162),x1163)+~P5(f29(f29(x1162,x1162),f29(x1162,f29(x1163,x1163))),f7(x1161))
% 3.50/3.58 [108]~P5(x1081,f6(x1082,x1083))+E(f29(f29(f15(x1081),f15(x1081)),f29(f15(x1081),f29(f26(x1081),f26(x1081)))),x1081)
% 3.50/3.58 [110]~P6(x1101,x1103,x1102)+P7(f12(f12(f14(f6(x1101,a21)))),x1102)
% 3.50/3.58 [111]~P3(x1111,x1113,x1112)+P7(f12(f12(f14(f6(x1111,a21)))),f12(f12(x1112)))
% 3.50/3.58 [132]E(f8(x1321,x1322),x1323)+~P5(f29(f29(x1321,x1321),f29(x1321,f29(f29(f29(x1322,x1322),f29(x1322,f29(x1323,x1323))),f29(f29(x1322,x1322),f29(x1322,f29(x1323,x1323)))))),a10)
% 3.50/3.58 [133]P5(x1331,f12(x1332))+~P5(f29(f29(x1332,x1332),f29(x1332,f29(f29(f29(x1331,x1331),f29(x1331,f29(x1333,x1333))),f29(f29(x1331,x1331),f29(x1331,f29(x1333,x1333)))))),a3)
% 3.50/3.58 [139]~P5(f29(f29(x1391,x1391),f29(x1391,f29(f29(f29(x1392,x1392),f29(x1392,f29(x1393,x1393))),f29(f29(x1392,x1392),f29(x1392,f29(x1393,x1393)))))),a3)+E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1391,f6(f29(x1392,x1392),a21)),a21))))))),x1393)
% 3.50/3.58 [117]P5(x1171,x1172)+~P5(f29(f29(x1173,x1173),f29(x1173,f29(x1171,x1171))),f6(x1174,x1172))
% 3.50/3.58 [118]P5(x1181,x1182)+~P5(f29(f29(x1181,x1181),f29(x1181,f29(x1183,x1183))),f6(x1182,x1184))
% 3.50/3.58 [134]~P5(f29(f29(f29(f29(x1343,x1343),f29(x1343,f29(x1341,x1341))),f29(f29(x1343,x1343),f29(x1343,f29(x1341,x1341)))),f29(f29(f29(x1343,x1343),f29(x1343,f29(x1341,x1341))),f29(x1342,x1342))),f24(x1344))+P5(f29(f29(f29(f29(x1341,x1341),f29(x1341,f29(x1342,x1342))),f29(f29(x1341,x1341),f29(x1341,f29(x1342,x1342)))),f29(f29(f29(x1341,x1341),f29(x1341,f29(x1342,x1342))),f29(x1343,x1343))),x1344)
% 3.50/3.58 [135]~P5(f29(f29(f29(f29(x1352,x1352),f29(x1352,f29(x1351,x1351))),f29(f29(x1352,x1352),f29(x1352,f29(x1351,x1351)))),f29(f29(f29(x1352,x1352),f29(x1352,f29(x1351,x1351))),f29(x1353,x1353))),f14(x1354))+P5(f29(f29(f29(f29(x1351,x1351),f29(x1351,f29(x1352,x1352))),f29(f29(x1351,x1351),f29(x1351,f29(x1352,x1352)))),f29(f29(f29(x1351,x1351),f29(x1351,f29(x1352,x1352))),f29(x1353,x1353))),x1354)
% 3.50/3.58 [141]~P5(f29(f29(x1414,x1414),f29(x1414,f29(x1411,x1411))),f8(x1412,x1413))+P5(x1411,f12(f12(f14(f6(f16(x1412,f6(f12(f12(f14(f6(f16(x1413,f6(f29(x1414,x1414),a21)),a21)))),a21)),a21)))))
% 3.50/3.58 [104]~P2(x1041)+P8(x1041)+~P2(f12(f14(f6(x1041,a21))))
% 3.50/3.58 [120]P2(x1201)+~P7(x1201,f6(a21,a21))+~P7(f8(x1201,f12(f14(f6(x1201,a21)))),a13)
% 3.50/3.58 [129]P1(x1291)+~P5(a20,x1291)+~P7(f12(f12(f14(f6(f16(a22,f6(x1291,a21)),a21)))),x1291)
% 3.50/3.58 [140]~P5(x1401,a21)+E(x1401,a20)+P5(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(a2,f6(f29(x1401,x1401),a21)),a21))))))),x1401)
% 3.50/3.58 [80]~P7(x802,x801)+~P7(x801,x802)+E(x801,x802)
% 3.50/3.58 [83]P5(x831,x832)+P5(x831,f9(x832))+~P5(x831,a21)
% 3.50/3.58 [100]P5(x1002,f12(x1001))+~P5(x1002,a21)+E(f16(x1001,f6(f29(x1002,x1002),a21)),a20)
% 3.50/3.58 [124]~P5(x1241,x1242)+~P5(f29(f29(x1241,x1241),f29(x1241,f29(x1242,x1242))),f6(a21,a21))+P5(f29(f29(x1241,x1241),f29(x1241,f29(x1242,x1242))),a5)
% 3.50/3.58 [119]~P2(x1191)+P6(x1191,f12(x1191),x1192)+~P7(f12(f12(f14(f6(x1191,a21)))),x1192)
% 3.50/3.58 [126]~P5(f29(f29(x1261,x1261),f29(x1261,f29(x1262,x1262))),f6(a21,a21))+~E(f9(f16(f9(x1261),f9(f29(x1261,x1261)))),x1262)+P5(f29(f29(x1261,x1261),f29(x1261,f29(x1262,x1262))),a22)
% 3.50/3.58 [128]~P2(x1281)+~P5(x1282,a21)+P5(f12(f12(f14(f6(f16(x1281,f6(x1282,a21)),a21)))),a21)
% 3.50/3.58 [84]~P5(x841,x843)+P5(x841,x842)+~P7(x843,x842)
% 3.50/3.58 [88]E(x881,x882)+E(x881,x883)+~P5(x881,f29(x883,x882))
% 3.50/3.58 [92]~P5(x921,x923)+~P5(x921,x922)+P5(x921,f16(x922,x923))
% 3.50/3.58 [125]~E(f8(x1253,x1251),x1252)+P5(f29(f29(x1251,x1251),f29(x1251,f29(x1252,x1252))),f7(x1253))+~P5(f29(f29(x1251,x1251),f29(x1251,f29(x1252,x1252))),f6(a21,a21))
% 3.50/3.58 [143]~P5(x1432,f12(x1431))+~P5(f29(f29(x1431,x1431),f29(x1431,f29(f29(f29(x1432,x1432),f29(x1432,f29(x1433,x1433))),f29(f29(x1432,x1432),f29(x1432,f29(x1433,x1433)))))),f6(a21,f6(a21,a21)))+P5(f29(f29(x1431,x1431),f29(x1431,f29(f29(f29(x1432,x1432),f29(x1432,f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(x1432,x1432),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(x1432,x1432),a21)),a21)))))))))),f29(f29(x1432,x1432),f29(x1432,f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(x1432,x1432),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(x1432,x1432),a21)),a21))))))))))))),a3)
% 3.50/3.58 [109]~P5(x1092,x1094)+~P5(x1091,x1093)+P5(f29(f29(x1091,x1091),f29(x1091,f29(x1092,x1092))),f6(x1093,x1094))
% 3.50/3.58 [137]~P5(f29(f29(f29(f29(x1372,x1372),f29(x1372,f29(x1373,x1373))),f29(f29(x1372,x1372),f29(x1372,f29(x1373,x1373)))),f29(f29(f29(x1372,x1372),f29(x1372,f29(x1373,x1373))),f29(x1371,x1371))),x1374)+P5(f29(f29(f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372))),f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372)))),f29(f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372))),f29(x1373,x1373))),f24(x1374))+~P5(f29(f29(f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372))),f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372)))),f29(f29(f29(x1371,x1371),f29(x1371,f29(x1372,x1372))),f29(x1373,x1373))),f6(f6(a21,a21),a21))
% 3.50/3.58 [138]~P5(f29(f29(f29(f29(x1382,x1382),f29(x1382,f29(x1381,x1381))),f29(f29(x1382,x1382),f29(x1382,f29(x1381,x1381)))),f29(f29(f29(x1382,x1382),f29(x1382,f29(x1381,x1381))),f29(x1383,x1383))),x1384)+P5(f29(f29(f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382))),f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382)))),f29(f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382))),f29(x1383,x1383))),f14(x1384))+~P5(f29(f29(f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382))),f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382)))),f29(f29(f29(x1381,x1381),f29(x1381,f29(x1382,x1382))),f29(x1383,x1383))),f6(f6(a21,a21),a21))
% 3.50/3.58 [142]P5(f29(f29(x1421,x1421),f29(x1421,f29(x1422,x1422))),f8(x1423,x1424))+~P5(f29(f29(x1421,x1421),f29(x1421,f29(x1422,x1422))),f6(a21,a21))+~P5(x1422,f12(f12(f14(f6(f16(x1423,f6(f12(f12(f14(f6(f16(x1424,f6(f29(x1421,x1421),a21)),a21)))),a21)),a21)))))
% 3.50/3.58 [144]~P4(x1442,x1445,x1441)+~P5(f29(f29(x1443,x1443),f29(x1443,f29(x1444,x1444))),f12(x1445))+E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f29(f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1444,x1444),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1444,x1444),a21)),a21)))))))))),f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1443,x1443),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1444,x1444),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(x1444,x1444),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1442,f6(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1445,f6(f29(f29(f29(x1443,x1443),f29(x1443,f29(x1444,x1444))),f29(f29(x1443,x1443),f29(x1443,f29(x1444,x1444)))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1445,f6(f29(f29(f29(x1443,x1443),f29(x1443,f29(x1444,x1444))),f29(f29(x1443,x1443),f29(x1443,f29(x1444,x1444)))),a21)),a21)))))))),a21)),a21))))))))
% 3.50/3.58 [122]~P2(x1221)+P9(x1221)+~E(f6(f12(f12(x1221)),f12(f12(x1221))),f12(x1221))+~P7(f12(f12(f14(f6(x1221,a21)))),f12(f12(x1221)))
% 3.50/3.58 [121]~P2(x1211)+P3(x1211,x1212,x1213)+~E(f12(f12(x1212)),f12(x1211))+~P7(f12(f12(f14(f6(x1211,a21)))),f12(f12(x1213)))
% 3.50/3.58 [130]~P9(x1303)+~P9(x1302)+~P3(x1301,x1302,x1303)+P4(x1301,x1302,x1303)+P5(f29(f29(f18(x1301,x1302,x1303),f18(x1301,x1302,x1303)),f29(f18(x1301,x1302,x1303),f29(f19(x1301,x1302,x1303),f19(x1301,x1302,x1303)))),f12(x1302))
% 3.50/3.58 [145]~P9(x1453)+~P9(x1452)+~P3(x1451,x1452,x1453)+P4(x1451,x1452,x1453)+~E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1453,f6(f29(f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)),a21)),a21)))))))))),f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1451,f6(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1452,f6(f29(f29(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),f29(f18(x1451,x1452,x1453),f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)))),f29(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),f29(f18(x1451,x1452,x1453),f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1452,f6(f29(f29(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),f29(f18(x1451,x1452,x1453),f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453)))),f29(f29(f18(x1451,x1452,x1453),f18(x1451,x1452,x1453)),f29(f18(x1451,x1452,x1453),f29(f19(x1451,x1452,x1453),f19(x1451,x1452,x1453))))),a21)),a21)))))))),a21)),a21))))))))
% 3.50/3.58 %EqnAxiom
% 3.50/3.58 [1]E(x11,x11)
% 3.50/3.58 [2]E(x22,x21)+~E(x21,x22)
% 3.50/3.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 3.50/3.58 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 3.50/3.58 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 3.50/3.58 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 3.50/3.58 [7]~E(x71,x72)+E(f16(x71,x73),f16(x72,x73))
% 3.50/3.58 [8]~E(x81,x82)+E(f16(x83,x81),f16(x83,x82))
% 3.50/3.59 [9]~E(x91,x92)+E(f29(x91,x93),f29(x92,x93))
% 3.50/3.59 [10]~E(x101,x102)+E(f29(x103,x101),f29(x103,x102))
% 3.50/3.59 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 3.50/3.59 [12]~E(x121,x122)+E(f8(x121,x123),f8(x122,x123))
% 3.50/3.59 [13]~E(x131,x132)+E(f8(x133,x131),f8(x133,x132))
% 3.50/3.59 [14]~E(x141,x142)+E(f19(x141,x143,x144),f19(x142,x143,x144))
% 3.50/3.59 [15]~E(x151,x152)+E(f19(x153,x151,x154),f19(x153,x152,x154))
% 3.50/3.59 [16]~E(x161,x162)+E(f19(x163,x164,x161),f19(x163,x164,x162))
% 3.50/3.59 [17]~E(x171,x172)+E(f18(x171,x173,x174),f18(x172,x173,x174))
% 3.50/3.59 [18]~E(x181,x182)+E(f18(x183,x181,x184),f18(x183,x182,x184))
% 3.50/3.59 [19]~E(x191,x192)+E(f18(x193,x194,x191),f18(x193,x194,x192))
% 3.50/3.59 [20]~E(x201,x202)+E(f14(x201),f14(x202))
% 3.50/3.59 [21]~E(x211,x212)+E(f17(x211,x213),f17(x212,x213))
% 3.50/3.59 [22]~E(x221,x222)+E(f17(x223,x221),f17(x223,x222))
% 3.50/3.59 [23]~E(x231,x232)+E(f9(x231),f9(x232))
% 3.50/3.59 [24]~E(x241,x242)+E(f15(x241),f15(x242))
% 3.50/3.59 [25]~E(x251,x252)+E(f26(x251),f26(x252))
% 3.50/3.59 [26]~E(x261,x262)+E(f4(x261),f4(x262))
% 3.50/3.59 [27]~E(x271,x272)+E(f24(x271),f24(x272))
% 3.50/3.59 [28]~E(x281,x282)+E(f27(x281),f27(x282))
% 3.50/3.59 [29]~E(x291,x292)+E(f25(x291),f25(x292))
% 3.50/3.59 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 3.50/3.59 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 3.50/3.59 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 3.50/3.59 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 3.50/3.59 [34]P7(x342,x343)+~E(x341,x342)+~P7(x341,x343)
% 3.50/3.59 [35]P7(x353,x352)+~E(x351,x352)+~P7(x353,x351)
% 3.50/3.59 [36]P3(x362,x363,x364)+~E(x361,x362)+~P3(x361,x363,x364)
% 3.50/3.59 [37]P3(x373,x372,x374)+~E(x371,x372)+~P3(x373,x371,x374)
% 3.50/3.59 [38]P3(x383,x384,x382)+~E(x381,x382)+~P3(x383,x384,x381)
% 3.50/3.59 [39]P6(x392,x393,x394)+~E(x391,x392)+~P6(x391,x393,x394)
% 3.50/3.59 [40]P6(x403,x402,x404)+~E(x401,x402)+~P6(x403,x401,x404)
% 3.50/3.59 [41]P6(x413,x414,x412)+~E(x411,x412)+~P6(x413,x414,x411)
% 3.50/3.59 [42]P4(x422,x423,x424)+~E(x421,x422)+~P4(x421,x423,x424)
% 3.50/3.59 [43]P4(x433,x432,x434)+~E(x431,x432)+~P4(x433,x431,x434)
% 3.50/3.59 [44]P4(x443,x444,x442)+~E(x441,x442)+~P4(x443,x444,x441)
% 3.50/3.59 [45]~P9(x451)+P9(x452)+~E(x451,x452)
% 3.50/3.59 [46]~P8(x461)+P8(x462)+~E(x461,x462)
% 3.50/3.59 [47]~P10(x471)+P10(x472)+~E(x471,x472)
% 3.50/3.59
% 3.50/3.59 %-------------------------------------------
% 3.50/3.59 cnf(146,plain,
% 3.50/3.59 (P7(x1461,x1461)),
% 3.50/3.59 inference(equality_inference,[],[73])).
% 3.50/3.59 cnf(154,plain,
% 3.50/3.59 (P5(a30,a21)),
% 3.50/3.59 inference(scs_inference,[],[64,51,61,82,2,84])).
% 3.50/3.59 cnf(160,plain,
% 3.50/3.59 (P7(x1601,x1601)),
% 3.50/3.59 inference(rename_variables,[],[146])).
% 3.50/3.59 cnf(161,plain,
% 3.50/3.59 (E(f16(f6(x1611,x1612),x1613),f16(x1613,f6(x1611,x1612)))),
% 3.50/3.59 inference(rename_variables,[],[61])).
% 3.50/3.59 cnf(163,plain,
% 3.50/3.59 (P7(x1631,x1631)),
% 3.50/3.59 inference(rename_variables,[],[146])).
% 3.50/3.59 cnf(167,plain,
% 3.50/3.59 (~P5(a30,f9(a32))+~P5(a30,f9(a31))),
% 3.50/3.59 inference(scs_inference,[],[64,69,146,160,163,51,61,161,66,49,82,2,84,33,3,34,35,119,92])).
% 3.50/3.59 cnf(1330,plain,
% 3.50/3.59 (~P5(a30,f9(a31))),
% 3.50/3.59 inference(scs_inference,[],[154,70,167,83])).
% 3.50/3.59 cnf(1331,plain,
% 3.50/3.59 ($false),
% 3.50/3.59 inference(scs_inference,[],[69,154,1330,83]),
% 3.50/3.59 ['proof']).
% 3.50/3.59 % SZS output end Proof
% 3.50/3.59 % Total time :2.950000s
%------------------------------------------------------------------------------