%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET187-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 14:21:02 EDT 2024
% Result : Unsatisfiable 0.12s 0.53s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : SET187-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.04/0.07 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.26 % Computer : n019.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Sun Jun 23 11:11:38 EDT 2024
% 0.08/0.26 % CPUTime :
% 0.12/0.46 start to proof:theBenchmark
% 0.12/0.52 %-------------------------------------------
% 0.12/0.52 % File :CSE---1.7
% 0.12/0.52 % Problem :theBenchmark
% 0.12/0.52 % Transform :cnf
% 0.12/0.52 % Format :tptp:raw
% 0.12/0.52 % Command :java -jar mcs_scs.jar %d %s
% 0.12/0.52
% 0.12/0.52 % Result :Theorem 0.000000s
% 0.12/0.52 % Output :CNFRefutation 0.000000s
% 0.12/0.52 %-------------------------------------------
% 0.12/0.52 %--------------------------------------------------------------------------
% 0.12/0.52 % File : SET187-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.52 % Domain : Set Theory
% 0.12/0.52 % Problem : Subclass property 5
% 0.12/0.52 % Version : [Qua92] axioms.
% 0.12/0.52 % English :
% 0.12/0.53
% 0.12/0.53 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.12/0.53 % : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.12/0.53 % Source : [Quaife]
% 0.12/0.53 % Names : SU5 [Qua92]
% 0.12/0.53
% 0.12/0.53 % Status : Unsatisfiable
% 0.12/0.53 % Rating : 0.25 v8.2.0, 0.29 v8.1.0, 0.26 v7.5.0, 0.32 v7.4.0, 0.29 v7.3.0, 0.33 v7.0.0, 0.40 v6.3.0, 0.36 v6.2.0, 0.30 v6.1.0, 0.43 v6.0.0, 0.50 v5.5.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.69 v5.1.0, 0.71 v5.0.0, 0.64 v4.1.0, 0.69 v4.0.1, 0.73 v4.0.0, 0.64 v3.7.0, 0.40 v3.5.0, 0.55 v3.4.0, 0.58 v3.3.0, 0.64 v3.2.0, 0.54 v3.1.0, 0.45 v2.7.0, 0.50 v2.6.0, 0.33 v2.5.0, 0.45 v2.4.0, 0.38 v2.2.1, 0.50 v2.2.0, 0.00 v2.1.0
% 0.12/0.53 % Syntax : Number of clauses : 114 ( 39 unt; 8 nHn; 81 RR)
% 0.12/0.53 % Number of literals : 220 ( 50 equ; 101 neg)
% 0.12/0.53 % Maximal clause size : 5 ( 1 avg)
% 0.12/0.53 % Maximal term depth : 6 ( 2 avg)
% 0.12/0.53 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% 0.12/0.53 % Number of functors : 48 ( 48 usr; 14 con; 0-3 aty)
% 0.12/0.53 % Number of variables : 214 ( 32 sgn)
% 0.12/0.53 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.12/0.53
% 0.12/0.53 % Comments : Quaife proves all these problems by augmenting the axioms with
% 0.12/0.53 % all previously proved theorems. With a few exceptions (the
% 0.12/0.53 % problems that correspond to [BL+86] problems), the TPTP has
% 0.12/0.53 % retained the order in which Quaife presents the problems. The
% 0.12/0.53 % user may create an augmented version of this problem by adding
% 0.12/0.53 % all previously proved theorems (the ones that correspond to
% 0.12/0.53 % [BL+86] are easily identified and positioned using Quaife's
% 0.12/0.53 % naming scheme).
% 0.12/0.53 % Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% 0.12/0.53 % : v2.1.0 - Bugfix in SET004-0.ax.
% 0.12/0.53 %--------------------------------------------------------------------------
% 0.12/0.53 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.12/0.53 include('Axioms/SET004-0.ax').
% 0.12/0.53 %----Include von Neuman-Bernays-Godel Boolean Algebra definitions
% 0.12/0.53 include('Axioms/SET004-1.ax').
% 0.12/0.53 %--------------------------------------------------------------------------
% 0.12/0.53 cnf(prove_subclass_property5_1,negated_conjecture,
% 0.12/0.53 subclass(x,y) ).
% 0.12/0.53
% 0.12/0.53 cnf(prove_subclass_property5_2,negated_conjecture,
% 0.12/0.53 intersection(complement(y),x) != null_class ).
% 0.12/0.53
% 0.12/0.53 %--------------------------------------------------------------------------
% 0.12/0.53 %-------------------------------------------
% 0.12/0.53 % Proof found
% 0.12/0.53 % SZS status Theorem for theBenchmark
% 0.12/0.53 % SZS output start Proof
% 0.12/0.53 %ClaNum:144(EqnAxiom:47)
% 0.12/0.53 %VarNum:892(SingletonVarNum:186)
% 0.12/0.53 %MaxLitNum:5
% 0.12/0.53 %MaxfuncDepth:24
% 0.12/0.53 %SharedTerms:48
% 0.12/0.53 %goalClause: 50 69
% 0.12/0.53 %singleGoalClaCount:2
% 0.12/0.53 [48]P1(a1)
% 0.12/0.53 [49]P2(a2)
% 0.12/0.53 [50]P5(a21,a31)
% 0.12/0.53 [51]P6(a1,a22)
% 0.12/0.53 [53]P5(a5,f6(a22,a22))
% 0.12/0.53 [54]P5(a23,f6(a22,a22))
% 0.12/0.53 [55]P5(a11,f6(a22,a22))
% 0.12/0.53 [59]P5(a10,f6(a22,f6(a22,a22)))
% 0.12/0.53 [60]P5(a3,f6(a22,f6(a22,a22)))
% 0.12/0.53 [69]~E(f16(f9(a31),a21),a20)
% 0.12/0.53 [61]E(f16(f9(f8(a5,f9(a13))),a5),a24)
% 0.12/0.53 [65]E(f16(f12(f14(f6(a29,a22))),a29),a13)
% 0.12/0.53 [66]E(f16(f6(a22,a22),f16(f6(a22,a22),f9(f8(f9(a5),f12(f14(f6(a5,a22))))))),a29)
% 0.12/0.53 [52]P5(x521,a22)
% 0.12/0.53 [57]P5(f7(x571),f6(a22,a22))
% 0.12/0.53 [63]P5(f25(x631),f6(f6(a22,a22),a22))
% 0.12/0.53 [64]P5(f14(x641),f6(f6(a22,a22),a22))
% 0.12/0.53 [67]E(f16(f12(x671),f9(f12(f16(f8(f12(f14(f6(a5,a22))),x671),a13)))),f4(x671))
% 0.12/0.53 [68]E(f15(f17(f16(x681,f6(f12(f12(f14(f6(f16(f12(f14(f6(x681,a22))),f6(f30(f15(f17(f8(x681,f12(f14(f6(x681,a22)))),a13)),f15(f17(f8(x681,f12(f14(f6(x681,a22)))),a13))),a22)),a22)))),f30(f27(f17(f8(x681,f12(f14(f6(x681,a22)))),a13)),f27(f17(f8(x681,f12(f14(f6(x681,a22)))),a13))))),a20)),f28(x681))
% 0.12/0.53 [56]P6(f30(x561,x562),a22)
% 0.12/0.53 [58]P5(f8(x581,x582),f6(a22,a22))
% 0.12/0.53 [62]E(f16(f6(x621,x622),x623),f16(x623,f6(x621,x622)))
% 0.12/0.53 [70]~P8(x701)+P2(x701)
% 0.12/0.53 [71]~P9(x711)+P2(x711)
% 0.12/0.53 [74]~P1(x741)+P5(a1,x741)
% 0.12/0.53 [75]~P1(x751)+P6(a20,x751)
% 0.12/0.53 [77]P6(f26(x771),x771)+E(x771,a20)
% 0.12/0.53 [78]~P2(x781)+P5(x781,f6(a22,a22))
% 0.12/0.53 [76]E(x761,a20)+E(f16(x761,f26(x761)),a20)
% 0.12/0.53 [86]~P9(x861)+E(f6(f12(f12(x861)),f12(f12(x861))),f12(x861))
% 0.12/0.53 [98]~P8(x981)+P2(f12(f14(f6(x981,a22))))
% 0.12/0.53 [102]~P6(x1021,a22)+P6(f12(f16(a5,f6(a22,x1021))),a22)
% 0.12/0.53 [104]~P10(x1041)+P5(f8(x1041,f12(f14(f6(x1041,a22)))),a13)
% 0.12/0.53 [105]~P2(x1051)+P5(f8(x1051,f12(f14(f6(x1051,a22)))),a13)
% 0.12/0.53 [106]~P9(x1061)+P5(f12(f12(f14(f6(x1061,a22)))),f12(f12(x1061)))
% 0.12/0.53 [111]~P6(x1111,a22)+P6(f30(f30(x1111,x1111),f30(x1111,f30(f12(x1111),f12(x1111)))),a11)
% 0.12/0.53 [114]P10(x1141)+~P5(f8(x1141,f12(f14(f6(x1141,a22)))),a13)
% 0.12/0.53 [126]~P1(x1261)+P5(f12(f12(f14(f6(f16(a23,f6(x1261,a22)),a22)))),x1261)
% 0.12/0.53 [130]~P6(x1301,a22)+P6(f9(f12(f12(f14(f6(f16(a5,f6(f9(x1301),a22)),a22))))),a22)
% 0.12/0.53 [72]~E(x722,x721)+P5(x721,x722)
% 0.12/0.53 [73]~E(x731,x732)+P5(x731,x732)
% 0.12/0.53 [80]P5(x801,x802)+P6(f17(x801,x802),x801)
% 0.12/0.53 [81]~P6(x811,x812)+~P6(x811,f9(x812))
% 0.12/0.53 [84]~P6(x841,a22)+P6(x841,f30(x842,x841))
% 0.12/0.53 [85]~P6(x851,a22)+P6(x851,f30(x851,x852))
% 0.12/0.53 [90]P5(x901,x902)+~P6(f17(x901,x902),x902)
% 0.12/0.53 [101]~P6(x1012,f12(x1011))+~E(f16(x1011,f6(f30(x1012,x1012),a22)),a20)
% 0.12/0.53 [112]E(f12(x1121),x1122)+~P6(f30(f30(x1121,x1121),f30(x1121,f30(x1122,x1122))),a11)
% 0.12/0.53 [113]P6(x1131,x1132)+~P6(f30(f30(x1131,x1131),f30(x1131,f30(x1132,x1132))),a5)
% 0.12/0.53 [122]~P6(f30(f30(x1221,x1221),f30(x1221,f30(x1222,x1222))),a23)+E(f9(f16(f9(x1221),f9(f30(x1221,x1221)))),x1222)
% 0.12/0.53 [135]~P6(f30(f30(x1351,x1351),f30(x1351,f30(x1352,x1352))),f6(a22,a22))+P6(f30(f30(x1351,x1351),f30(x1351,f30(f30(f30(x1352,x1352),f30(x1352,f30(f8(x1351,x1352),f8(x1351,x1352)))),f30(f30(x1352,x1352),f30(x1352,f30(f8(x1351,x1352),f8(x1351,x1352))))))),a10)
% 0.12/0.53 [92]P2(x921)+~P3(x921,x922,x923)
% 0.12/0.53 [93]P2(x931)+~P7(x931,x932,x933)
% 0.12/0.53 [94]P9(x941)+~P4(x942,x943,x941)
% 0.12/0.53 [95]P9(x951)+~P4(x952,x951,x953)
% 0.12/0.53 [100]~P4(x1001,x1002,x1003)+P3(x1001,x1002,x1003)
% 0.12/0.53 [88]P6(x881,x882)+~P6(x881,f16(x883,x882))
% 0.12/0.53 [89]P6(x891,x892)+~P6(x891,f16(x892,x893))
% 0.12/0.53 [96]~P7(x961,x962,x963)+E(f12(x961),x962)
% 0.12/0.53 [97]~P3(x972,x971,x973)+E(f12(f12(x971)),f12(x972))
% 0.12/0.53 [115]E(f8(x1151,x1152),x1153)+~P6(f30(f30(x1152,x1152),f30(x1152,f30(x1153,x1153))),f7(x1151))
% 0.12/0.53 [107]~P6(x1071,f6(x1072,x1073))+E(f30(f30(f15(x1071),f15(x1071)),f30(f15(x1071),f30(f27(x1071),f27(x1071)))),x1071)
% 0.12/0.53 [109]~P7(x1091,x1093,x1092)+P5(f12(f12(f14(f6(x1091,a22)))),x1092)
% 0.12/0.53 [110]~P3(x1101,x1103,x1102)+P5(f12(f12(f14(f6(x1101,a22)))),f12(f12(x1102)))
% 0.12/0.53 [131]E(f8(x1311,x1312),x1313)+~P6(f30(f30(x1311,x1311),f30(x1311,f30(f30(f30(x1312,x1312),f30(x1312,f30(x1313,x1313))),f30(f30(x1312,x1312),f30(x1312,f30(x1313,x1313)))))),a10)
% 0.12/0.53 [132]P6(x1321,f12(x1322))+~P6(f30(f30(x1322,x1322),f30(x1322,f30(f30(f30(x1321,x1321),f30(x1321,f30(x1323,x1323))),f30(f30(x1321,x1321),f30(x1321,f30(x1323,x1323)))))),a3)
% 0.12/0.53 [138]~P6(f30(f30(x1381,x1381),f30(x1381,f30(f30(f30(x1382,x1382),f30(x1382,f30(x1383,x1383))),f30(f30(x1382,x1382),f30(x1382,f30(x1383,x1383)))))),a3)+E(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1381,f6(f30(x1382,x1382),a22)),a22))))))),x1383)
% 0.12/0.53 [116]P6(x1161,x1162)+~P6(f30(f30(x1163,x1163),f30(x1163,f30(x1161,x1161))),f6(x1164,x1162))
% 0.12/0.53 [117]P6(x1171,x1172)+~P6(f30(f30(x1171,x1171),f30(x1171,f30(x1173,x1173))),f6(x1172,x1174))
% 0.12/0.53 [133]~P6(f30(f30(f30(f30(x1333,x1333),f30(x1333,f30(x1331,x1331))),f30(f30(x1333,x1333),f30(x1333,f30(x1331,x1331)))),f30(f30(f30(x1333,x1333),f30(x1333,f30(x1331,x1331))),f30(x1332,x1332))),f25(x1334))+P6(f30(f30(f30(f30(x1331,x1331),f30(x1331,f30(x1332,x1332))),f30(f30(x1331,x1331),f30(x1331,f30(x1332,x1332)))),f30(f30(f30(x1331,x1331),f30(x1331,f30(x1332,x1332))),f30(x1333,x1333))),x1334)
% 0.12/0.53 [134]~P6(f30(f30(f30(f30(x1342,x1342),f30(x1342,f30(x1341,x1341))),f30(f30(x1342,x1342),f30(x1342,f30(x1341,x1341)))),f30(f30(f30(x1342,x1342),f30(x1342,f30(x1341,x1341))),f30(x1343,x1343))),f14(x1344))+P6(f30(f30(f30(f30(x1341,x1341),f30(x1341,f30(x1342,x1342))),f30(f30(x1341,x1341),f30(x1341,f30(x1342,x1342)))),f30(f30(f30(x1341,x1341),f30(x1341,f30(x1342,x1342))),f30(x1343,x1343))),x1344)
% 0.12/0.53 [140]~P6(f30(f30(x1404,x1404),f30(x1404,f30(x1401,x1401))),f8(x1402,x1403))+P6(x1401,f12(f12(f14(f6(f16(x1402,f6(f12(f12(f14(f6(f16(x1403,f6(f30(x1404,x1404),a22)),a22)))),a22)),a22)))))
% 0.12/0.53 [103]~P2(x1031)+P8(x1031)+~P2(f12(f14(f6(x1031,a22))))
% 0.12/0.53 [119]P2(x1191)+~P5(x1191,f6(a22,a22))+~P5(f8(x1191,f12(f14(f6(x1191,a22)))),a13)
% 0.12/0.53 [128]P1(x1281)+~P6(a20,x1281)+~P5(f12(f12(f14(f6(f16(a23,f6(x1281,a22)),a22)))),x1281)
% 0.12/0.53 [139]~P6(x1391,a22)+E(x1391,a20)+P6(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(a2,f6(f30(x1391,x1391),a22)),a22))))))),x1391)
% 0.12/0.53 [79]~P5(x792,x791)+~P5(x791,x792)+E(x791,x792)
% 0.12/0.53 [82]P6(x821,x822)+P6(x821,f9(x822))+~P6(x821,a22)
% 0.12/0.53 [99]P6(x992,f12(x991))+~P6(x992,a22)+E(f16(x991,f6(f30(x992,x992),a22)),a20)
% 0.12/0.53 [123]~P6(x1231,x1232)+~P6(f30(f30(x1231,x1231),f30(x1231,f30(x1232,x1232))),f6(a22,a22))+P6(f30(f30(x1231,x1231),f30(x1231,f30(x1232,x1232))),a5)
% 0.12/0.53 [118]~P2(x1181)+P7(x1181,f12(x1181),x1182)+~P5(f12(f12(f14(f6(x1181,a22)))),x1182)
% 0.12/0.53 [125]~P6(f30(f30(x1251,x1251),f30(x1251,f30(x1252,x1252))),f6(a22,a22))+~E(f9(f16(f9(x1251),f9(f30(x1251,x1251)))),x1252)+P6(f30(f30(x1251,x1251),f30(x1251,f30(x1252,x1252))),a23)
% 0.12/0.53 [127]~P2(x1271)+~P6(x1272,a22)+P6(f12(f12(f14(f6(f16(x1271,f6(x1272,a22)),a22)))),a22)
% 0.12/0.53 [83]~P6(x831,x833)+P6(x831,x832)+~P5(x833,x832)
% 0.12/0.53 [87]E(x871,x872)+E(x871,x873)+~P6(x871,f30(x873,x872))
% 0.12/0.53 [91]~P6(x911,x913)+~P6(x911,x912)+P6(x911,f16(x912,x913))
% 0.12/0.53 [124]~E(f8(x1243,x1241),x1242)+P6(f30(f30(x1241,x1241),f30(x1241,f30(x1242,x1242))),f7(x1243))+~P6(f30(f30(x1241,x1241),f30(x1241,f30(x1242,x1242))),f6(a22,a22))
% 0.12/0.53 [142]~P6(x1422,f12(x1421))+~P6(f30(f30(x1421,x1421),f30(x1421,f30(f30(f30(x1422,x1422),f30(x1422,f30(x1423,x1423))),f30(f30(x1422,x1422),f30(x1422,f30(x1423,x1423)))))),f6(a22,f6(a22,a22)))+P6(f30(f30(x1421,x1421),f30(x1421,f30(f30(f30(x1422,x1422),f30(x1422,f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a22)),a22)))))))))),f30(f30(x1422,x1422),f30(x1422,f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a22)),a22))))))))))))),a3)
% 0.12/0.53 [108]~P6(x1082,x1084)+~P6(x1081,x1083)+P6(f30(f30(x1081,x1081),f30(x1081,f30(x1082,x1082))),f6(x1083,x1084))
% 0.12/0.53 [136]~P6(f30(f30(f30(f30(x1362,x1362),f30(x1362,f30(x1363,x1363))),f30(f30(x1362,x1362),f30(x1362,f30(x1363,x1363)))),f30(f30(f30(x1362,x1362),f30(x1362,f30(x1363,x1363))),f30(x1361,x1361))),x1364)+P6(f30(f30(f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362))),f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362)))),f30(f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362))),f30(x1363,x1363))),f25(x1364))+~P6(f30(f30(f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362))),f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362)))),f30(f30(f30(x1361,x1361),f30(x1361,f30(x1362,x1362))),f30(x1363,x1363))),f6(f6(a22,a22),a22))
% 0.12/0.53 [137]~P6(f30(f30(f30(f30(x1372,x1372),f30(x1372,f30(x1371,x1371))),f30(f30(x1372,x1372),f30(x1372,f30(x1371,x1371)))),f30(f30(f30(x1372,x1372),f30(x1372,f30(x1371,x1371))),f30(x1373,x1373))),x1374)+P6(f30(f30(f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372))),f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372)))),f30(f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372))),f30(x1373,x1373))),f14(x1374))+~P6(f30(f30(f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372))),f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372)))),f30(f30(f30(x1371,x1371),f30(x1371,f30(x1372,x1372))),f30(x1373,x1373))),f6(f6(a22,a22),a22))
% 0.12/0.53 [141]P6(f30(f30(x1411,x1411),f30(x1411,f30(x1412,x1412))),f8(x1413,x1414))+~P6(f30(f30(x1411,x1411),f30(x1411,f30(x1412,x1412))),f6(a22,a22))+~P6(x1412,f12(f12(f14(f6(f16(x1413,f6(f12(f12(f14(f6(f16(x1414,f6(f30(x1411,x1411),a22)),a22)))),a22)),a22)))))
% 0.12/0.53 [143]~P4(x1432,x1435,x1431)+~P6(f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434))),f12(x1435))+E(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1431,f6(f30(f30(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22)))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a22)),a22)))))))))),f30(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22)))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a22)),a22))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a22)),a22))))))))))),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1432,f6(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1435,f6(f30(f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434))),f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434)))),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1435,f6(f30(f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434))),f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434)))),a22)),a22)))))))),a22)),a22))))))))
% 0.12/0.53 [121]~P2(x1211)+P9(x1211)+~E(f6(f12(f12(x1211)),f12(f12(x1211))),f12(x1211))+~P5(f12(f12(f14(f6(x1211,a22)))),f12(f12(x1211)))
% 0.12/0.53 [120]~P2(x1201)+P3(x1201,x1202,x1203)+~E(f12(f12(x1202)),f12(x1201))+~P5(f12(f12(f14(f6(x1201,a22)))),f12(f12(x1203)))
% 0.12/0.53 [129]~P9(x1293)+~P9(x1292)+~P3(x1291,x1292,x1293)+P4(x1291,x1292,x1293)+P6(f30(f30(f18(x1291,x1292,x1293),f18(x1291,x1292,x1293)),f30(f18(x1291,x1292,x1293),f30(f19(x1291,x1292,x1293),f19(x1291,x1292,x1293)))),f12(x1292))
% 0.12/0.53 [144]~P9(x1443)+~P9(x1442)+~P3(x1441,x1442,x1443)+P4(x1441,x1442,x1443)+~E(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1443,f6(f30(f30(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22)))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a22)),a22)))))))))),f30(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22)))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a22)),a22))))))),f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a22)),a22))))))))))),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1441,f6(f30(f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1442,f6(f30(f30(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),f30(f18(x1441,x1442,x1443),f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)))),f30(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),f30(f18(x1441,x1442,x1443),f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443))))),a22)),a22))))))),f12(f16(a5,f6(a22,f12(f12(f14(f6(f16(x1442,f6(f30(f30(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),f30(f18(x1441,x1442,x1443),f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)))),f30(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),f30(f18(x1441,x1442,x1443),f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443))))),a22)),a22)))))))),a22)),a22))))))))
% 0.12/0.53 %EqnAxiom
% 0.12/0.53 [1]E(x11,x11)
% 0.12/0.53 [2]E(x22,x21)+~E(x21,x22)
% 0.12/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.12/0.53 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.12/0.53 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.12/0.53 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.12/0.53 [7]~E(x71,x72)+E(f16(x71,x73),f16(x72,x73))
% 0.12/0.53 [8]~E(x81,x82)+E(f16(x83,x81),f16(x83,x82))
% 0.12/0.53 [9]~E(x91,x92)+E(f30(x91,x93),f30(x92,x93))
% 0.12/0.53 [10]~E(x101,x102)+E(f30(x103,x101),f30(x103,x102))
% 0.12/0.53 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.12/0.53 [12]~E(x121,x122)+E(f8(x121,x123),f8(x122,x123))
% 0.12/0.53 [13]~E(x131,x132)+E(f8(x133,x131),f8(x133,x132))
% 0.12/0.53 [14]~E(x141,x142)+E(f19(x141,x143,x144),f19(x142,x143,x144))
% 0.12/0.53 [15]~E(x151,x152)+E(f19(x153,x151,x154),f19(x153,x152,x154))
% 0.12/0.53 [16]~E(x161,x162)+E(f19(x163,x164,x161),f19(x163,x164,x162))
% 0.12/0.53 [17]~E(x171,x172)+E(f18(x171,x173,x174),f18(x172,x173,x174))
% 0.12/0.54 [18]~E(x181,x182)+E(f18(x183,x181,x184),f18(x183,x182,x184))
% 0.12/0.54 [19]~E(x191,x192)+E(f18(x193,x194,x191),f18(x193,x194,x192))
% 0.12/0.54 [20]~E(x201,x202)+E(f14(x201),f14(x202))
% 0.12/0.54 [21]~E(x211,x212)+E(f17(x211,x213),f17(x212,x213))
% 0.12/0.54 [22]~E(x221,x222)+E(f17(x223,x221),f17(x223,x222))
% 0.12/0.54 [23]~E(x231,x232)+E(f9(x231),f9(x232))
% 0.12/0.54 [24]~E(x241,x242)+E(f27(x241),f27(x242))
% 0.12/0.54 [25]~E(x251,x252)+E(f15(x251),f15(x252))
% 0.12/0.54 [26]~E(x261,x262)+E(f25(x261),f25(x262))
% 0.12/0.54 [27]~E(x271,x272)+E(f26(x271),f26(x272))
% 0.12/0.54 [28]~E(x281,x282)+E(f28(x281),f28(x282))
% 0.12/0.54 [29]~E(x291,x292)+E(f4(x291),f4(x292))
% 0.12/0.54 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.12/0.54 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.12/0.54 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.12/0.54 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.12/0.54 [34]P6(x342,x343)+~E(x341,x342)+~P6(x341,x343)
% 0.12/0.54 [35]P6(x353,x352)+~E(x351,x352)+~P6(x353,x351)
% 0.12/0.54 [36]~P9(x361)+P9(x362)+~E(x361,x362)
% 0.12/0.54 [37]P3(x372,x373,x374)+~E(x371,x372)+~P3(x371,x373,x374)
% 0.12/0.54 [38]P3(x383,x382,x384)+~E(x381,x382)+~P3(x383,x381,x384)
% 0.12/0.54 [39]P3(x393,x394,x392)+~E(x391,x392)+~P3(x393,x394,x391)
% 0.12/0.54 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.12/0.54 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.12/0.54 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.12/0.54 [43]P7(x432,x433,x434)+~E(x431,x432)+~P7(x431,x433,x434)
% 0.12/0.54 [44]P7(x443,x442,x444)+~E(x441,x442)+~P7(x443,x441,x444)
% 0.12/0.54 [45]P7(x453,x454,x452)+~E(x451,x452)+~P7(x453,x454,x451)
% 0.12/0.54 [46]~P10(x461)+P10(x462)+~E(x461,x462)
% 0.12/0.54 [47]~P8(x471)+P8(x472)+~E(x471,x472)
% 0.12/0.54
% 0.12/0.54 %-------------------------------------------
% 0.12/0.54 cnf(145,plain,
% 0.12/0.54 (P5(x1451,x1451)),
% 0.12/0.54 inference(equality_inference,[],[72])).
% 0.12/0.54 cnf(161,plain,
% 0.12/0.54 (P5(x1611,x1611)),
% 0.12/0.54 inference(rename_variables,[],[145])).
% 0.12/0.54 cnf(162,plain,
% 0.12/0.54 (E(f16(f6(x1621,x1622),x1623),f16(x1623,f6(x1621,x1622)))),
% 0.12/0.54 inference(rename_variables,[],[62])).
% 0.12/0.54 cnf(164,plain,
% 0.12/0.54 (P5(x1641,x1641)),
% 0.12/0.54 inference(rename_variables,[],[145])).
% 0.12/0.54 cnf(168,plain,
% 0.12/0.54 ($false),
% 0.12/0.54 inference(scs_inference,[],[50,69,145,161,164,49,62,162,66,77,2,88,89,83,3,32,33,118,81]),
% 0.12/0.54 ['proof']).
% 0.12/0.54 % SZS output end Proof
% 0.12/0.54 % Total time :0.000000s
%------------------------------------------------------------------------------