TSTP Solution File: SET204-6 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n008.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 14:29:14 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 15:13:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % File :CSE---1.6
% 0.20/0.64 % Problem :theBenchmark
% 0.20/0.64 % Transform :cnf
% 0.20/0.64 % Format :tptp:raw
% 0.20/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.64
% 0.20/0.64 % Result :Theorem 0.000000s
% 0.20/0.64 % Output :CNFRefutation 0.000000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 % File : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.20/0.64 % Domain : Set Theory
% 0.20/0.64 % Problem : Cross product property 2
% 0.20/0.64 % Version : [Qua92] axioms.
% 0.20/0.64 % English :
% 0.20/0.64
% 0.20/0.64 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.20/0.64 % : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.20/0.64 % Source : [Quaife]
% 0.20/0.64 % Names : CP2 [Qua92]
% 0.20/0.64
% 0.20/0.64 % Status : Unsatisfiable
% 0.20/0.64 % Rating : 0.10 v8.1.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.00 v7.0.0, 0.13 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.15 v5.3.0, 0.11 v5.2.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 0.18 v3.7.0, 0.20 v3.5.0, 0.18 v3.4.0, 0.08 v3.3.0, 0.07 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.4.0, 0.12 v2.3.0, 0.00 v2.2.1, 0.17 v2.2.0, 0.00 v2.1.0
% 0.20/0.64 % Syntax : Number of clauses : 114 ( 39 unt; 8 nHn; 81 RR)
% 0.20/0.64 % Number of literals : 220 ( 49 equ; 101 neg)
% 0.20/0.64 % Maximal clause size : 5 ( 1 avg)
% 0.20/0.64 % Maximal term depth : 6 ( 2 avg)
% 0.20/0.64 % Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% 0.20/0.64 % Number of functors : 50 ( 50 usr; 16 con; 0-3 aty)
% 0.20/0.64 % Number of variables : 214 ( 32 sgn)
% 0.20/0.64 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.64
% 0.20/0.64 % Comments : Quaife proves all these problems by augmenting the axioms with
% 0.20/0.64 % all previously proved theorems. With a few exceptions (the
% 0.20/0.64 % problems that correspond to [BL+86] problems), the TPTP has
% 0.20/0.64 % retained the order in which Quaife presents the problems. The
% 0.20/0.64 % user may create an augmented version of this problem by adding
% 0.20/0.64 % all previously proved theorems (the ones that correspond to
% 0.20/0.64 % [BL+86] are easily identified and positioned using Quaife's
% 0.20/0.64 % naming scheme).
% 0.20/0.64 % Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% 0.20/0.64 % : v2.1.0 - Bugfix in SET004-0.ax.
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.20/0.64 include('Axioms/SET004-0.ax').
% 0.20/0.64 %----Include von Neuman-Bernays-Godel Boolean Algebra definitions
% 0.20/0.64 include('Axioms/SET004-1.ax').
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 cnf(prove_cross_product_property2_1,negated_conjecture,
% 0.20/0.64 member(ordered_pair(u,v),cross_product(x,y)) ).
% 0.20/0.64
% 0.20/0.64 cnf(prove_cross_product_property2_2,negated_conjecture,
% 0.20/0.64 ~ member(ordered_pair(v,u),cross_product(y,x)) ).
% 0.20/0.64
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.65 %ClaNum:144(EqnAxiom:47)
% 0.20/0.65 %VarNum:892(SingletonVarNum:186)
% 0.20/0.65 %MaxLitNum:5
% 0.20/0.65 %MaxfuncDepth:24
% 0.20/0.65 %SharedTerms:56
% 0.20/0.65 %goalClause: 65 69
% 0.20/0.65 %singleGoalClaCount:2
% 0.20/0.65 [48]P1(a1)
% 0.20/0.65 [49]P2(a2)
% 0.20/0.65 [50]P5(a1,a21)
% 0.20/0.65 [52]P7(a5,f6(a21,a21))
% 0.20/0.65 [53]P7(a22,f6(a21,a21))
% 0.20/0.65 [54]P7(a11,f6(a21,a21))
% 0.20/0.65 [58]P7(a10,f6(a21,f6(a21,a21)))
% 0.20/0.65 [59]P7(a3,f6(a21,f6(a21,a21)))
% 0.20/0.65 [65]P5(f30(f30(a29,a29),f30(a29,f30(a31,a31))),f6(a32,a33))
% 0.20/0.65 [69]~P5(f30(f30(a31,a31),f30(a31,f30(a29,a29))),f6(a33,a32))
% 0.20/0.65 [60]E(f16(f9(f8(a5,f9(a13))),a5),a23)
% 0.20/0.65 [64]E(f16(f12(f14(f6(a28,a21))),a28),a13)
% 0.20/0.65 [66]E(f16(f6(a21,a21),f16(f6(a21,a21),f9(f8(f9(a5),f12(f14(f6(a5,a21))))))),a28)
% 0.20/0.65 [51]P7(x511,a21)
% 0.20/0.65 [56]P7(f7(x561),f6(a21,a21))
% 0.20/0.65 [62]P7(f24(x621),f6(f6(a21,a21),a21))
% 0.20/0.65 [63]P7(f14(x631),f6(f6(a21,a21),a21))
% 0.20/0.65 [67]E(f16(f12(x671),f9(f12(f16(f8(f12(f14(f6(a5,a21))),x671),a13)))),f4(x671))
% 0.20/0.65 [68]E(f15(f17(f16(x681,f6(f12(f12(f14(f6(f16(f12(f14(f6(x681,a21))),f6(f30(f15(f17(f8(x681,f12(f14(f6(x681,a21)))),a13)),f15(f17(f8(x681,f12(f14(f6(x681,a21)))),a13))),a21)),a21)))),f30(f26(f17(f8(x681,f12(f14(f6(x681,a21)))),a13)),f26(f17(f8(x681,f12(f14(f6(x681,a21)))),a13))))),a20)),f27(x681))
% 0.20/0.65 [55]P5(f30(x551,x552),a21)
% 0.20/0.65 [57]P7(f8(x571,x572),f6(a21,a21))
% 0.20/0.65 [61]E(f16(f6(x611,x612),x613),f16(x613,f6(x611,x612)))
% 0.20/0.65 [70]~P8(x701)+P2(x701)
% 0.20/0.65 [71]~P9(x711)+P2(x711)
% 0.20/0.65 [74]~P1(x741)+P7(a1,x741)
% 0.20/0.65 [75]~P1(x751)+P5(a20,x751)
% 0.20/0.65 [77]P5(f25(x771),x771)+E(x771,a20)
% 0.20/0.65 [78]~P2(x781)+P7(x781,f6(a21,a21))
% 0.20/0.65 [76]E(x761,a20)+E(f16(x761,f25(x761)),a20)
% 0.20/0.65 [86]~P9(x861)+E(f6(f12(f12(x861)),f12(f12(x861))),f12(x861))
% 0.20/0.65 [98]~P8(x981)+P2(f12(f14(f6(x981,a21))))
% 0.20/0.65 [102]~P5(x1021,a21)+P5(f12(f16(a5,f6(a21,x1021))),a21)
% 0.20/0.65 [104]~P10(x1041)+P7(f8(x1041,f12(f14(f6(x1041,a21)))),a13)
% 0.20/0.65 [105]~P2(x1051)+P7(f8(x1051,f12(f14(f6(x1051,a21)))),a13)
% 0.20/0.65 [106]~P9(x1061)+P7(f12(f12(f14(f6(x1061,a21)))),f12(f12(x1061)))
% 0.20/0.65 [111]~P5(x1111,a21)+P5(f30(f30(x1111,x1111),f30(x1111,f30(f12(x1111),f12(x1111)))),a11)
% 0.20/0.65 [114]P10(x1141)+~P7(f8(x1141,f12(f14(f6(x1141,a21)))),a13)
% 0.20/0.65 [126]~P1(x1261)+P7(f12(f12(f14(f6(f16(a22,f6(x1261,a21)),a21)))),x1261)
% 0.20/0.65 [130]~P5(x1301,a21)+P5(f9(f12(f12(f14(f6(f16(a5,f6(f9(x1301),a21)),a21))))),a21)
% 0.20/0.65 [72]~E(x722,x721)+P7(x721,x722)
% 0.20/0.65 [73]~E(x731,x732)+P7(x731,x732)
% 0.20/0.65 [80]P7(x801,x802)+P5(f17(x801,x802),x801)
% 0.20/0.65 [81]~P5(x811,x812)+~P5(x811,f9(x812))
% 0.20/0.65 [84]~P5(x841,a21)+P5(x841,f30(x842,x841))
% 0.20/0.65 [85]~P5(x851,a21)+P5(x851,f30(x851,x852))
% 0.20/0.65 [90]P7(x901,x902)+~P5(f17(x901,x902),x902)
% 0.20/0.65 [101]~P5(x1012,f12(x1011))+~E(f16(x1011,f6(f30(x1012,x1012),a21)),a20)
% 0.20/0.65 [112]E(f12(x1121),x1122)+~P5(f30(f30(x1121,x1121),f30(x1121,f30(x1122,x1122))),a11)
% 0.20/0.65 [113]P5(x1131,x1132)+~P5(f30(f30(x1131,x1131),f30(x1131,f30(x1132,x1132))),a5)
% 0.20/0.65 [122]~P5(f30(f30(x1221,x1221),f30(x1221,f30(x1222,x1222))),a22)+E(f9(f16(f9(x1221),f9(f30(x1221,x1221)))),x1222)
% 0.20/0.65 [135]~P5(f30(f30(x1351,x1351),f30(x1351,f30(x1352,x1352))),f6(a21,a21))+P5(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)
% 0.20/0.65 [92]P2(x921)+~P3(x921,x922,x923)
% 0.20/0.65 [93]P2(x931)+~P6(x931,x932,x933)
% 0.20/0.65 [94]P9(x941)+~P4(x942,x943,x941)
% 0.20/0.65 [95]P9(x951)+~P4(x952,x951,x953)
% 0.20/0.65 [100]~P4(x1001,x1002,x1003)+P3(x1001,x1002,x1003)
% 0.20/0.65 [88]P5(x881,x882)+~P5(x881,f16(x883,x882))
% 0.20/0.65 [89]P5(x891,x892)+~P5(x891,f16(x892,x893))
% 0.20/0.65 [96]~P6(x961,x962,x963)+E(f12(x961),x962)
% 0.20/0.65 [97]~P3(x972,x971,x973)+E(f12(f12(x971)),f12(x972))
% 0.20/0.65 [115]E(f8(x1151,x1152),x1153)+~P5(f30(f30(x1152,x1152),f30(x1152,f30(x1153,x1153))),f7(x1151))
% 0.20/0.65 [107]~P5(x1071,f6(x1072,x1073))+E(f30(f30(f15(x1071),f15(x1071)),f30(f15(x1071),f30(f26(x1071),f26(x1071)))),x1071)
% 0.20/0.65 [109]~P6(x1091,x1093,x1092)+P7(f12(f12(f14(f6(x1091,a21)))),x1092)
% 0.20/0.65 [110]~P3(x1101,x1103,x1102)+P7(f12(f12(f14(f6(x1101,a21)))),f12(f12(x1102)))
% 0.20/0.65 [131]E(f8(x1311,x1312),x1313)+~P5(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)
% 0.20/0.65 [132]P5(x1321,f12(x1322))+~P5(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)
% 0.20/0.65 [138]~P5(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(a21,f12(f12(f14(f6(f16(x1381,f6(f30(x1382,x1382),a21)),a21))))))),x1383)
% 0.20/0.65 [116]P5(x1161,x1162)+~P5(f30(f30(x1163,x1163),f30(x1163,f30(x1161,x1161))),f6(x1164,x1162))
% 0.20/0.65 [117]P5(x1171,x1172)+~P5(f30(f30(x1171,x1171),f30(x1171,f30(x1173,x1173))),f6(x1172,x1174))
% 0.20/0.65 [133]~P5(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))),f24(x1334))+P5(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)
% 0.20/0.65 [134]~P5(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))+P5(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)
% 0.20/0.65 [140]~P5(f30(f30(x1404,x1404),f30(x1404,f30(x1401,x1401))),f8(x1402,x1403))+P5(x1401,f12(f12(f14(f6(f16(x1402,f6(f12(f12(f14(f6(f16(x1403,f6(f30(x1404,x1404),a21)),a21)))),a21)),a21)))))
% 0.20/0.65 [103]~P2(x1031)+P8(x1031)+~P2(f12(f14(f6(x1031,a21))))
% 0.20/0.65 [119]P2(x1191)+~P7(x1191,f6(a21,a21))+~P7(f8(x1191,f12(f14(f6(x1191,a21)))),a13)
% 0.20/0.65 [128]P1(x1281)+~P5(a20,x1281)+~P7(f12(f12(f14(f6(f16(a22,f6(x1281,a21)),a21)))),x1281)
% 0.20/0.65 [139]~P5(x1391,a21)+E(x1391,a20)+P5(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(a2,f6(f30(x1391,x1391),a21)),a21))))))),x1391)
% 0.20/0.65 [79]~P7(x792,x791)+~P7(x791,x792)+E(x791,x792)
% 0.20/0.65 [82]P5(x821,x822)+P5(x821,f9(x822))+~P5(x821,a21)
% 0.20/0.65 [99]P5(x992,f12(x991))+~P5(x992,a21)+E(f16(x991,f6(f30(x992,x992),a21)),a20)
% 0.20/0.65 [123]~P5(x1231,x1232)+~P5(f30(f30(x1231,x1231),f30(x1231,f30(x1232,x1232))),f6(a21,a21))+P5(f30(f30(x1231,x1231),f30(x1231,f30(x1232,x1232))),a5)
% 0.20/0.65 [118]~P2(x1181)+P6(x1181,f12(x1181),x1182)+~P7(f12(f12(f14(f6(x1181,a21)))),x1182)
% 0.20/0.65 [125]~P5(f30(f30(x1251,x1251),f30(x1251,f30(x1252,x1252))),f6(a21,a21))+~E(f9(f16(f9(x1251),f9(f30(x1251,x1251)))),x1252)+P5(f30(f30(x1251,x1251),f30(x1251,f30(x1252,x1252))),a22)
% 0.20/0.65 [127]~P2(x1271)+~P5(x1272,a21)+P5(f12(f12(f14(f6(f16(x1271,f6(x1272,a21)),a21)))),a21)
% 0.20/0.65 [83]~P5(x831,x833)+P5(x831,x832)+~P7(x833,x832)
% 0.20/0.65 [87]E(x871,x872)+E(x871,x873)+~P5(x871,f30(x873,x872))
% 0.20/0.65 [91]~P5(x911,x913)+~P5(x911,x912)+P5(x911,f16(x912,x913))
% 0.20/0.65 [124]~E(f8(x1243,x1241),x1242)+P5(f30(f30(x1241,x1241),f30(x1241,f30(x1242,x1242))),f7(x1243))+~P5(f30(f30(x1241,x1241),f30(x1241,f30(x1242,x1242))),f6(a21,a21))
% 0.20/0.65 [142]~P5(x1422,f12(x1421))+~P5(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(a21,f6(a21,a21)))+P5(f30(f30(x1421,x1421),f30(x1421,f30(f30(f30(x1422,x1422),f30(x1422,f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a21)),a21)))))))))),f30(f30(x1422,x1422),f30(x1422,f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1421,f6(f30(x1422,x1422),a21)),a21))))))))))))),a3)
% 0.20/0.65 [108]~P5(x1082,x1084)+~P5(x1081,x1083)+P5(f30(f30(x1081,x1081),f30(x1081,f30(x1082,x1082))),f6(x1083,x1084))
% 0.20/0.65 [136]~P5(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)+P5(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))),f24(x1364))+~P5(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(a21,a21),a21))
% 0.20/0.65 [137]~P5(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)+P5(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))+~P5(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(a21,a21),a21))
% 0.20/0.65 [141]P5(f30(f30(x1411,x1411),f30(x1411,f30(x1412,x1412))),f8(x1413,x1414))+~P5(f30(f30(x1411,x1411),f30(x1411,f30(x1412,x1412))),f6(a21,a21))+~P5(x1412,f12(f12(f14(f6(f16(x1413,f6(f12(f12(f14(f6(f16(x1414,f6(f30(x1411,x1411),a21)),a21)))),a21)),a21)))))
% 0.20/0.65 [143]~P4(x1432,x1435,x1431)+~P5(f30(f30(x1433,x1433),f30(x1433,f30(x1434,x1434))),f12(x1435))+E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f30(f30(f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21)))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a21)),a21)))))))))),f30(f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21)))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1433,x1433),a21)),a21))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(x1434,x1434),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f30(f12(f16(a5,f6(a21,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)))),a21)),a21))))))),f12(f16(a5,f6(a21,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)))),a21)),a21)))))))),a21)),a21))))))))
% 0.20/0.65 [121]~P2(x1211)+P9(x1211)+~E(f6(f12(f12(x1211)),f12(f12(x1211))),f12(x1211))+~P7(f12(f12(f14(f6(x1211,a21)))),f12(f12(x1211)))
% 0.20/0.65 [120]~P2(x1201)+P3(x1201,x1202,x1203)+~E(f12(f12(x1202)),f12(x1201))+~P7(f12(f12(f14(f6(x1201,a21)))),f12(f12(x1203)))
% 0.20/0.65 [129]~P9(x1293)+~P9(x1292)+~P3(x1291,x1292,x1293)+P4(x1291,x1292,x1293)+P5(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))
% 0.20/0.65 [144]~P9(x1443)+~P9(x1442)+~P3(x1441,x1442,x1443)+P4(x1441,x1442,x1443)+~E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1443,f6(f30(f30(f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21)))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a21)),a21)))))))))),f30(f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21)))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f18(x1441,x1442,x1443),f18(x1441,x1442,x1443)),a21)),a21))))))),f30(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f19(x1441,x1442,x1443),f19(x1441,x1442,x1443)),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1441,f6(f30(f12(f16(a5,f6(a21,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))))),a21)),a21))))))),f12(f16(a5,f6(a21,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))))),a21)),a21)))))))),a21)),a21))))))))
% 0.20/0.65 %EqnAxiom
% 0.20/0.65 [1]E(x11,x11)
% 0.20/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.65 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.20/0.65 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.20/0.65 [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.20/0.65 [7]~E(x71,x72)+E(f16(x71,x73),f16(x72,x73))
% 0.20/0.65 [8]~E(x81,x82)+E(f16(x83,x81),f16(x83,x82))
% 0.20/0.65 [9]~E(x91,x92)+E(f30(x91,x93),f30(x92,x93))
% 0.20/0.65 [10]~E(x101,x102)+E(f30(x103,x101),f30(x103,x102))
% 0.20/0.65 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.20/0.65 [12]~E(x121,x122)+E(f14(x121),f14(x122))
% 0.20/0.65 [13]~E(x131,x132)+E(f8(x131,x133),f8(x132,x133))
% 0.20/0.65 [14]~E(x141,x142)+E(f8(x143,x141),f8(x143,x142))
% 0.20/0.65 [15]~E(x151,x152)+E(f19(x151,x153,x154),f19(x152,x153,x154))
% 0.20/0.65 [16]~E(x161,x162)+E(f19(x163,x161,x164),f19(x163,x162,x164))
% 0.20/0.65 [17]~E(x171,x172)+E(f19(x173,x174,x171),f19(x173,x174,x172))
% 0.20/0.65 [18]~E(x181,x182)+E(f26(x181),f26(x182))
% 0.20/0.65 [19]~E(x191,x192)+E(f18(x191,x193,x194),f18(x192,x193,x194))
% 0.20/0.65 [20]~E(x201,x202)+E(f18(x203,x201,x204),f18(x203,x202,x204))
% 0.20/0.65 [21]~E(x211,x212)+E(f18(x213,x214,x211),f18(x213,x214,x212))
% 0.20/0.65 [22]~E(x221,x222)+E(f17(x221,x223),f17(x222,x223))
% 0.20/0.65 [23]~E(x231,x232)+E(f17(x233,x231),f17(x233,x232))
% 0.20/0.65 [24]~E(x241,x242)+E(f27(x241),f27(x242))
% 0.20/0.65 [25]~E(x251,x252)+E(f9(x251),f9(x252))
% 0.20/0.65 [26]~E(x261,x262)+E(f15(x261),f15(x262))
% 0.20/0.65 [27]~E(x271,x272)+E(f25(x271),f25(x272))
% 0.20/0.65 [28]~E(x281,x282)+E(f24(x281),f24(x282))
% 0.20/0.65 [29]~E(x291,x292)+E(f4(x291),f4(x292))
% 0.20/0.65 [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.20/0.65 [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.20/0.65 [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.20/0.65 [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.20/0.65 [34]P7(x342,x343)+~E(x341,x342)+~P7(x341,x343)
% 0.20/0.65 [35]P7(x353,x352)+~E(x351,x352)+~P7(x353,x351)
% 0.20/0.65 [36]~P8(x361)+P8(x362)+~E(x361,x362)
% 0.20/0.65 [37]P3(x372,x373,x374)+~E(x371,x372)+~P3(x371,x373,x374)
% 0.20/0.65 [38]P3(x383,x382,x384)+~E(x381,x382)+~P3(x383,x381,x384)
% 0.20/0.65 [39]P3(x393,x394,x392)+~E(x391,x392)+~P3(x393,x394,x391)
% 0.20/0.65 [40]P6(x402,x403,x404)+~E(x401,x402)+~P6(x401,x403,x404)
% 0.20/0.65 [41]P6(x413,x412,x414)+~E(x411,x412)+~P6(x413,x411,x414)
% 0.20/0.65 [42]P6(x423,x424,x422)+~E(x421,x422)+~P6(x423,x424,x421)
% 0.20/0.65 [43]~P9(x431)+P9(x432)+~E(x431,x432)
% 0.20/0.65 [44]P4(x442,x443,x444)+~E(x441,x442)+~P4(x441,x443,x444)
% 0.20/0.65 [45]P4(x453,x452,x454)+~E(x451,x452)+~P4(x453,x451,x454)
% 0.20/0.65 [46]P4(x463,x464,x462)+~E(x461,x462)+~P4(x463,x464,x461)
% 0.20/0.65 [47]~P10(x471)+P10(x472)+~E(x471,x472)
% 0.20/0.65
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 cnf(155,plain,
% 0.20/0.65 ($false),
% 0.20/0.65 inference(scs_inference,[],[65,51,49,64,69,55,2,116,117,33,118,108]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.000000s
%------------------------------------------------------------------------------