TSTP Solution File: SET163-6 by CSE---1.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE---1.6
% Problem  : SET163-6 : 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 : n007.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 14:29:02 EDT 2023

% Result   : Unsatisfiable 0.55s 0.87s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET163-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 14:49:41 EDT 2023
% 0.20/0.34  % CPUTime    : 
% 0.20/0.58  start to proof:theBenchmark
% 0.55/0.87  %-------------------------------------------
% 0.55/0.87  % File        :CSE---1.6
% 0.55/0.87  % Problem     :theBenchmark
% 0.55/0.87  % Transform   :cnf
% 0.55/0.87  % Format      :tptp:raw
% 0.55/0.87  % Command     :java -jar mcs_scs.jar %d %s
% 0.55/0.87  
% 0.55/0.87  % Result      :Theorem 0.210000s
% 0.55/0.87  % Output      :CNFRefutation 0.210000s
% 0.55/0.87  %-------------------------------------------
% 0.55/0.87  %--------------------------------------------------------------------------
% 0.55/0.87  % File     : SET163-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.55/0.87  % Domain   : Set Theory
% 0.55/0.87  % Problem  : Union with universal class
% 0.55/0.87  % Version  : [Qua92] axioms.
% 0.55/0.87  % English  :
% 0.55/0.87  
% 0.55/0.87  % Refs     : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.55/0.87  %          : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.55/0.87  % Source   : [Quaife]
% 0.55/0.87  % Names    : U5 [Qua92]
% 0.55/0.87  
% 0.55/0.87  % Status   : Unsatisfiable
% 0.55/0.87  % Rating   : 0.33 v8.1.0, 0.32 v7.5.0, 0.37 v7.4.0, 0.35 v7.3.0, 0.50 v7.1.0, 0.42 v7.0.0, 0.53 v6.3.0, 0.36 v6.2.0, 0.30 v6.1.0, 0.36 v6.0.0, 0.40 v5.5.0, 0.70 v5.4.0, 0.65 v5.3.0, 0.72 v5.2.0, 0.62 v5.1.0, 0.71 v5.0.0, 0.64 v4.1.0, 0.69 v4.0.1, 0.64 v4.0.0, 0.73 v3.7.0, 0.50 v3.5.0, 0.64 v3.4.0, 0.67 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, 0.55 v2.4.0, 0.50 v2.3.0, 0.62 v2.2.1, 0.67 v2.2.0, 0.33 v2.1.0
% 0.55/0.87  % Syntax   : Number of clauses     :  113 (  38 unt;   8 nHn;  80 RR)
% 0.55/0.87  %            Number of literals    :  219 (  50 equ; 101 neg)
% 0.55/0.87  %            Maximal clause size   :    5 (   1 avg)
% 0.55/0.87  %            Maximal term depth    :    6 (   2 avg)
% 0.55/0.87  %            Number of predicates  :   11 (  10 usr;   0 prp; 1-3 aty)
% 0.55/0.87  %            Number of functors    :   47 (  47 usr;  13 con; 0-3 aty)
% 0.55/0.87  %            Number of variables   :  214 (  32 sgn)
% 0.55/0.87  % SPC      : CNF_UNS_RFO_SEQ_NHN
% 0.55/0.87  
% 0.55/0.87  % Comments : Quaife proves all these problems by augmenting the axioms with
% 0.55/0.87  %            all previously proved theorems. With a few exceptions (the
% 0.55/0.87  %            problems that correspond to [BL+86] problems), the TPTP has
% 0.55/0.87  %            retained the order in which Quaife presents the problems. The
% 0.55/0.87  %            user may create an augmented version of this problem by adding
% 0.55/0.87  %            all previously proved theorems (the ones that correspond to
% 0.55/0.87  %            [BL+86] are easily identified and positioned using Quaife's
% 0.55/0.87  %            naming scheme).
% 0.55/0.87  %          : Used as a demodulator by Quaife.
% 0.55/0.87  % Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% 0.55/0.87  %          : v2.1.0 - Bugfix in SET004-0.ax.
% 0.55/0.87  %--------------------------------------------------------------------------
% 0.55/0.87  %----Include von Neuman-Bernays-Godel set theory axioms
% 0.55/0.87  include('Axioms/SET004-0.ax').
% 0.55/0.87  %----Include von Neuman-Bernays-Godel Boolean Algebra definitions
% 0.55/0.87  include('Axioms/SET004-1.ax').
% 0.55/0.87  %--------------------------------------------------------------------------
% 0.55/0.87  cnf(prove_union_with_universal_class_1,negated_conjecture,
% 0.55/0.87      union(universal_class,x) != universal_class ).
% 0.55/0.87  
% 0.55/0.87  %--------------------------------------------------------------------------
% 0.55/0.87  %-------------------------------------------
% 0.55/0.87  % Proof found
% 0.55/0.87  % SZS status Theorem for theBenchmark
% 0.55/0.87  % SZS output start Proof
% 0.55/0.87  %ClaNum:143(EqnAxiom:47)
% 0.55/0.87  %VarNum:892(SingletonVarNum:186)
% 0.55/0.87  %MaxLitNum:5
% 0.55/0.87  %MaxfuncDepth:24
% 0.55/0.87  %SharedTerms:48
% 0.55/0.87  %goalClause: 68
% 0.55/0.87  %singleGoalClaCount:1
% 0.55/0.87  [48]P1(a1)
% 0.55/0.87  [49]P2(a2)
% 0.55/0.87  [50]P5(a1,a21)
% 0.55/0.87  [52]P7(a5,f6(a21,a21))
% 0.55/0.87  [53]P7(a22,f6(a21,a21))
% 0.55/0.87  [54]P7(a11,f6(a21,a21))
% 0.55/0.87  [58]P7(a10,f6(a21,f6(a21,a21)))
% 0.55/0.87  [59]P7(a3,f6(a21,f6(a21,a21)))
% 0.55/0.87  [68]~E(f9(f16(f9(a21),f9(a30))),a21)
% 0.55/0.87  [60]E(f16(f9(f8(a5,f9(a13))),a5),a23)
% 0.55/0.87  [64]E(f16(f12(f14(f6(a28,a21))),a28),a13)
% 0.55/0.87  [65]E(f16(f6(a21,a21),f16(f6(a21,a21),f9(f8(f9(a5),f12(f14(f6(a5,a21))))))),a28)
% 0.55/0.87  [51]P7(x511,a21)
% 0.55/0.87  [56]P7(f7(x561),f6(a21,a21))
% 0.55/0.87  [62]P7(f24(x621),f6(f6(a21,a21),a21))
% 0.55/0.87  [63]P7(f14(x631),f6(f6(a21,a21),a21))
% 0.55/0.87  [66]E(f16(f12(x661),f9(f12(f16(f8(f12(f14(f6(a5,a21))),x661),a13)))),f4(x661))
% 0.55/0.88  [67]E(f15(f17(f16(x671,f6(f12(f12(f14(f6(f16(f12(f14(f6(x671,a21))),f6(f29(f15(f17(f8(x671,f12(f14(f6(x671,a21)))),a13)),f15(f17(f8(x671,f12(f14(f6(x671,a21)))),a13))),a21)),a21)))),f29(f26(f17(f8(x671,f12(f14(f6(x671,a21)))),a13)),f26(f17(f8(x671,f12(f14(f6(x671,a21)))),a13))))),a20)),f27(x671))
% 0.55/0.88  [55]P5(f29(x551,x552),a21)
% 0.55/0.88  [57]P7(f8(x571,x572),f6(a21,a21))
% 0.55/0.88  [61]E(f16(f6(x611,x612),x613),f16(x613,f6(x611,x612)))
% 0.55/0.88  [69]~P8(x691)+P2(x691)
% 0.55/0.88  [70]~P9(x701)+P2(x701)
% 0.55/0.88  [73]~P1(x731)+P7(a1,x731)
% 0.55/0.88  [74]~P1(x741)+P5(a20,x741)
% 0.55/0.88  [76]P5(f25(x761),x761)+E(x761,a20)
% 0.55/0.88  [77]~P2(x771)+P7(x771,f6(a21,a21))
% 0.55/0.88  [75]E(x751,a20)+E(f16(x751,f25(x751)),a20)
% 0.55/0.88  [85]~P9(x851)+E(f6(f12(f12(x851)),f12(f12(x851))),f12(x851))
% 0.55/0.88  [97]~P8(x971)+P2(f12(f14(f6(x971,a21))))
% 0.55/0.88  [101]~P5(x1011,a21)+P5(f12(f16(a5,f6(a21,x1011))),a21)
% 0.55/0.88  [103]~P10(x1031)+P7(f8(x1031,f12(f14(f6(x1031,a21)))),a13)
% 0.55/0.88  [104]~P2(x1041)+P7(f8(x1041,f12(f14(f6(x1041,a21)))),a13)
% 0.55/0.88  [105]~P9(x1051)+P7(f12(f12(f14(f6(x1051,a21)))),f12(f12(x1051)))
% 0.55/0.88  [110]~P5(x1101,a21)+P5(f29(f29(x1101,x1101),f29(x1101,f29(f12(x1101),f12(x1101)))),a11)
% 0.55/0.88  [113]P10(x1131)+~P7(f8(x1131,f12(f14(f6(x1131,a21)))),a13)
% 0.55/0.88  [125]~P1(x1251)+P7(f12(f12(f14(f6(f16(a22,f6(x1251,a21)),a21)))),x1251)
% 0.55/0.88  [129]~P5(x1291,a21)+P5(f9(f12(f12(f14(f6(f16(a5,f6(f9(x1291),a21)),a21))))),a21)
% 0.55/0.88  [71]~E(x712,x711)+P7(x711,x712)
% 0.55/0.88  [72]~E(x721,x722)+P7(x721,x722)
% 0.55/0.88  [79]P7(x791,x792)+P5(f17(x791,x792),x791)
% 0.55/0.88  [80]~P5(x801,x802)+~P5(x801,f9(x802))
% 0.55/0.88  [83]~P5(x831,a21)+P5(x831,f29(x832,x831))
% 0.55/0.88  [84]~P5(x841,a21)+P5(x841,f29(x841,x842))
% 0.55/0.88  [89]P7(x891,x892)+~P5(f17(x891,x892),x892)
% 0.55/0.88  [100]~P5(x1002,f12(x1001))+~E(f16(x1001,f6(f29(x1002,x1002),a21)),a20)
% 0.55/0.88  [111]E(f12(x1111),x1112)+~P5(f29(f29(x1111,x1111),f29(x1111,f29(x1112,x1112))),a11)
% 0.55/0.88  [112]P5(x1121,x1122)+~P5(f29(f29(x1121,x1121),f29(x1121,f29(x1122,x1122))),a5)
% 0.55/0.88  [121]~P5(f29(f29(x1211,x1211),f29(x1211,f29(x1212,x1212))),a22)+E(f9(f16(f9(x1211),f9(f29(x1211,x1211)))),x1212)
% 0.55/0.88  [134]~P5(f29(f29(x1341,x1341),f29(x1341,f29(x1342,x1342))),f6(a21,a21))+P5(f29(f29(x1341,x1341),f29(x1341,f29(f29(f29(x1342,x1342),f29(x1342,f29(f8(x1341,x1342),f8(x1341,x1342)))),f29(f29(x1342,x1342),f29(x1342,f29(f8(x1341,x1342),f8(x1341,x1342))))))),a10)
% 0.55/0.88  [91]P2(x911)+~P3(x911,x912,x913)
% 0.55/0.88  [92]P2(x921)+~P6(x921,x922,x923)
% 0.55/0.88  [93]P9(x931)+~P4(x932,x933,x931)
% 0.55/0.88  [94]P9(x941)+~P4(x942,x941,x943)
% 0.55/0.88  [99]~P4(x991,x992,x993)+P3(x991,x992,x993)
% 0.55/0.88  [87]P5(x871,x872)+~P5(x871,f16(x873,x872))
% 0.55/0.88  [88]P5(x881,x882)+~P5(x881,f16(x882,x883))
% 0.55/0.88  [95]~P6(x951,x952,x953)+E(f12(x951),x952)
% 0.55/0.88  [96]~P3(x962,x961,x963)+E(f12(f12(x961)),f12(x962))
% 0.55/0.88  [114]E(f8(x1141,x1142),x1143)+~P5(f29(f29(x1142,x1142),f29(x1142,f29(x1143,x1143))),f7(x1141))
% 0.55/0.88  [106]~P5(x1061,f6(x1062,x1063))+E(f29(f29(f15(x1061),f15(x1061)),f29(f15(x1061),f29(f26(x1061),f26(x1061)))),x1061)
% 0.55/0.88  [108]~P6(x1081,x1083,x1082)+P7(f12(f12(f14(f6(x1081,a21)))),x1082)
% 0.55/0.88  [109]~P3(x1091,x1093,x1092)+P7(f12(f12(f14(f6(x1091,a21)))),f12(f12(x1092)))
% 0.55/0.88  [130]E(f8(x1301,x1302),x1303)+~P5(f29(f29(x1301,x1301),f29(x1301,f29(f29(f29(x1302,x1302),f29(x1302,f29(x1303,x1303))),f29(f29(x1302,x1302),f29(x1302,f29(x1303,x1303)))))),a10)
% 0.55/0.88  [131]P5(x1311,f12(x1312))+~P5(f29(f29(x1312,x1312),f29(x1312,f29(f29(f29(x1311,x1311),f29(x1311,f29(x1313,x1313))),f29(f29(x1311,x1311),f29(x1311,f29(x1313,x1313)))))),a3)
% 0.55/0.88  [137]~P5(f29(f29(x1371,x1371),f29(x1371,f29(f29(f29(x1372,x1372),f29(x1372,f29(x1373,x1373))),f29(f29(x1372,x1372),f29(x1372,f29(x1373,x1373)))))),a3)+E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1371,f6(f29(x1372,x1372),a21)),a21))))))),x1373)
% 0.55/0.88  [115]P5(x1151,x1152)+~P5(f29(f29(x1153,x1153),f29(x1153,f29(x1151,x1151))),f6(x1154,x1152))
% 0.55/0.88  [116]P5(x1161,x1162)+~P5(f29(f29(x1161,x1161),f29(x1161,f29(x1163,x1163))),f6(x1162,x1164))
% 0.55/0.88  [132]~P5(f29(f29(f29(f29(x1323,x1323),f29(x1323,f29(x1321,x1321))),f29(f29(x1323,x1323),f29(x1323,f29(x1321,x1321)))),f29(f29(f29(x1323,x1323),f29(x1323,f29(x1321,x1321))),f29(x1322,x1322))),f24(x1324))+P5(f29(f29(f29(f29(x1321,x1321),f29(x1321,f29(x1322,x1322))),f29(f29(x1321,x1321),f29(x1321,f29(x1322,x1322)))),f29(f29(f29(x1321,x1321),f29(x1321,f29(x1322,x1322))),f29(x1323,x1323))),x1324)
% 0.55/0.88  [133]~P5(f29(f29(f29(f29(x1332,x1332),f29(x1332,f29(x1331,x1331))),f29(f29(x1332,x1332),f29(x1332,f29(x1331,x1331)))),f29(f29(f29(x1332,x1332),f29(x1332,f29(x1331,x1331))),f29(x1333,x1333))),f14(x1334))+P5(f29(f29(f29(f29(x1331,x1331),f29(x1331,f29(x1332,x1332))),f29(f29(x1331,x1331),f29(x1331,f29(x1332,x1332)))),f29(f29(f29(x1331,x1331),f29(x1331,f29(x1332,x1332))),f29(x1333,x1333))),x1334)
% 0.55/0.88  [139]~P5(f29(f29(x1394,x1394),f29(x1394,f29(x1391,x1391))),f8(x1392,x1393))+P5(x1391,f12(f12(f14(f6(f16(x1392,f6(f12(f12(f14(f6(f16(x1393,f6(f29(x1394,x1394),a21)),a21)))),a21)),a21)))))
% 0.55/0.88  [102]~P2(x1021)+P8(x1021)+~P2(f12(f14(f6(x1021,a21))))
% 0.55/0.88  [118]P2(x1181)+~P7(x1181,f6(a21,a21))+~P7(f8(x1181,f12(f14(f6(x1181,a21)))),a13)
% 0.55/0.88  [127]P1(x1271)+~P5(a20,x1271)+~P7(f12(f12(f14(f6(f16(a22,f6(x1271,a21)),a21)))),x1271)
% 0.55/0.88  [138]~P5(x1381,a21)+E(x1381,a20)+P5(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(a2,f6(f29(x1381,x1381),a21)),a21))))))),x1381)
% 0.55/0.88  [78]~P7(x782,x781)+~P7(x781,x782)+E(x781,x782)
% 0.55/0.88  [81]P5(x811,x812)+P5(x811,f9(x812))+~P5(x811,a21)
% 0.55/0.88  [98]P5(x982,f12(x981))+~P5(x982,a21)+E(f16(x981,f6(f29(x982,x982),a21)),a20)
% 0.55/0.88  [122]~P5(x1221,x1222)+~P5(f29(f29(x1221,x1221),f29(x1221,f29(x1222,x1222))),f6(a21,a21))+P5(f29(f29(x1221,x1221),f29(x1221,f29(x1222,x1222))),a5)
% 0.55/0.88  [117]~P2(x1171)+P6(x1171,f12(x1171),x1172)+~P7(f12(f12(f14(f6(x1171,a21)))),x1172)
% 0.55/0.88  [124]~P5(f29(f29(x1241,x1241),f29(x1241,f29(x1242,x1242))),f6(a21,a21))+~E(f9(f16(f9(x1241),f9(f29(x1241,x1241)))),x1242)+P5(f29(f29(x1241,x1241),f29(x1241,f29(x1242,x1242))),a22)
% 0.55/0.88  [126]~P2(x1261)+~P5(x1262,a21)+P5(f12(f12(f14(f6(f16(x1261,f6(x1262,a21)),a21)))),a21)
% 0.55/0.88  [82]~P5(x821,x823)+P5(x821,x822)+~P7(x823,x822)
% 0.55/0.88  [86]E(x861,x862)+E(x861,x863)+~P5(x861,f29(x863,x862))
% 0.55/0.88  [90]~P5(x901,x903)+~P5(x901,x902)+P5(x901,f16(x902,x903))
% 0.55/0.88  [123]~E(f8(x1233,x1231),x1232)+P5(f29(f29(x1231,x1231),f29(x1231,f29(x1232,x1232))),f7(x1233))+~P5(f29(f29(x1231,x1231),f29(x1231,f29(x1232,x1232))),f6(a21,a21))
% 0.55/0.88  [141]~P5(x1412,f12(x1411))+~P5(f29(f29(x1411,x1411),f29(x1411,f29(f29(f29(x1412,x1412),f29(x1412,f29(x1413,x1413))),f29(f29(x1412,x1412),f29(x1412,f29(x1413,x1413)))))),f6(a21,f6(a21,a21)))+P5(f29(f29(x1411,x1411),f29(x1411,f29(f29(f29(x1412,x1412),f29(x1412,f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1411,f6(f29(x1412,x1412),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1411,f6(f29(x1412,x1412),a21)),a21)))))))))),f29(f29(x1412,x1412),f29(x1412,f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1411,f6(f29(x1412,x1412),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1411,f6(f29(x1412,x1412),a21)),a21))))))))))))),a3)
% 0.55/0.88  [107]~P5(x1072,x1074)+~P5(x1071,x1073)+P5(f29(f29(x1071,x1071),f29(x1071,f29(x1072,x1072))),f6(x1073,x1074))
% 0.55/0.88  [135]~P5(f29(f29(f29(f29(x1352,x1352),f29(x1352,f29(x1353,x1353))),f29(f29(x1352,x1352),f29(x1352,f29(x1353,x1353)))),f29(f29(f29(x1352,x1352),f29(x1352,f29(x1353,x1353))),f29(x1351,x1351))),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))),f24(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))),f6(f6(a21,a21),a21))
% 0.55/0.88  [136]~P5(f29(f29(f29(f29(x1362,x1362),f29(x1362,f29(x1361,x1361))),f29(f29(x1362,x1362),f29(x1362,f29(x1361,x1361)))),f29(f29(f29(x1362,x1362),f29(x1362,f29(x1361,x1361))),f29(x1363,x1363))),x1364)+P5(f29(f29(f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362))),f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362)))),f29(f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362))),f29(x1363,x1363))),f14(x1364))+~P5(f29(f29(f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362))),f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362)))),f29(f29(f29(x1361,x1361),f29(x1361,f29(x1362,x1362))),f29(x1363,x1363))),f6(f6(a21,a21),a21))
% 0.55/0.88  [140]P5(f29(f29(x1401,x1401),f29(x1401,f29(x1402,x1402))),f8(x1403,x1404))+~P5(f29(f29(x1401,x1401),f29(x1401,f29(x1402,x1402))),f6(a21,a21))+~P5(x1402,f12(f12(f14(f6(f16(x1403,f6(f12(f12(f14(f6(f16(x1404,f6(f29(x1401,x1401),a21)),a21)))),a21)),a21)))))
% 0.55/0.88  [142]~P4(x1422,x1425,x1421)+~P5(f29(f29(x1423,x1423),f29(x1423,f29(x1424,x1424))),f12(x1425))+E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1421,f6(f29(f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1424,x1424),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1424,x1424),a21)),a21)))))))))),f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1423,x1423),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1424,x1424),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(x1424,x1424),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1422,f6(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1425,f6(f29(f29(f29(x1423,x1423),f29(x1423,f29(x1424,x1424))),f29(f29(x1423,x1423),f29(x1423,f29(x1424,x1424)))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1425,f6(f29(f29(f29(x1423,x1423),f29(x1423,f29(x1424,x1424))),f29(f29(x1423,x1423),f29(x1423,f29(x1424,x1424)))),a21)),a21)))))))),a21)),a21))))))))
% 0.55/0.88  [120]~P2(x1201)+P9(x1201)+~E(f6(f12(f12(x1201)),f12(f12(x1201))),f12(x1201))+~P7(f12(f12(f14(f6(x1201,a21)))),f12(f12(x1201)))
% 0.55/0.88  [119]~P2(x1191)+P3(x1191,x1192,x1193)+~E(f12(f12(x1192)),f12(x1191))+~P7(f12(f12(f14(f6(x1191,a21)))),f12(f12(x1193)))
% 0.55/0.88  [128]~P9(x1283)+~P9(x1282)+~P3(x1281,x1282,x1283)+P4(x1281,x1282,x1283)+P5(f29(f29(f18(x1281,x1282,x1283),f18(x1281,x1282,x1283)),f29(f18(x1281,x1282,x1283),f29(f19(x1281,x1282,x1283),f19(x1281,x1282,x1283)))),f12(x1282))
% 0.55/0.88  [143]~P9(x1433)+~P9(x1432)+~P3(x1431,x1432,x1433)+P4(x1431,x1432,x1433)+~E(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1433,f6(f29(f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)),a21)),a21)))))))))),f29(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21)))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),a21)),a21))))))),f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)),a21)),a21))))))))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1431,f6(f29(f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f29(f29(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),f29(f18(x1431,x1432,x1433),f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)))),f29(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),f29(f18(x1431,x1432,x1433),f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433))))),a21)),a21))))))),f12(f16(a5,f6(a21,f12(f12(f14(f6(f16(x1432,f6(f29(f29(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),f29(f18(x1431,x1432,x1433),f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433)))),f29(f29(f18(x1431,x1432,x1433),f18(x1431,x1432,x1433)),f29(f18(x1431,x1432,x1433),f29(f19(x1431,x1432,x1433),f19(x1431,x1432,x1433))))),a21)),a21)))))))),a21)),a21))))))))
% 0.55/0.88  %EqnAxiom
% 0.55/0.88  [1]E(x11,x11)
% 0.55/0.88  [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.88  [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.88  [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.55/0.88  [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.55/0.88  [6]~E(x61,x62)+E(f12(x61),f12(x62))
% 0.55/0.88  [7]~E(x71,x72)+E(f16(x71,x73),f16(x72,x73))
% 0.55/0.88  [8]~E(x81,x82)+E(f16(x83,x81),f16(x83,x82))
% 0.55/0.88  [9]~E(x91,x92)+E(f29(x91,x93),f29(x92,x93))
% 0.55/0.88  [10]~E(x101,x102)+E(f29(x103,x101),f29(x103,x102))
% 0.55/0.88  [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.55/0.88  [12]~E(x121,x122)+E(f8(x121,x123),f8(x122,x123))
% 0.55/0.88  [13]~E(x131,x132)+E(f8(x133,x131),f8(x133,x132))
% 0.55/0.88  [14]~E(x141,x142)+E(f19(x141,x143,x144),f19(x142,x143,x144))
% 0.55/0.88  [15]~E(x151,x152)+E(f19(x153,x151,x154),f19(x153,x152,x154))
% 0.55/0.88  [16]~E(x161,x162)+E(f19(x163,x164,x161),f19(x163,x164,x162))
% 0.55/0.88  [17]~E(x171,x172)+E(f18(x171,x173,x174),f18(x172,x173,x174))
% 0.55/0.88  [18]~E(x181,x182)+E(f18(x183,x181,x184),f18(x183,x182,x184))
% 0.55/0.88  [19]~E(x191,x192)+E(f18(x193,x194,x191),f18(x193,x194,x192))
% 0.55/0.88  [20]~E(x201,x202)+E(f14(x201),f14(x202))
% 0.55/0.88  [21]~E(x211,x212)+E(f17(x211,x213),f17(x212,x213))
% 0.55/0.88  [22]~E(x221,x222)+E(f17(x223,x221),f17(x223,x222))
% 0.55/0.88  [23]~E(x231,x232)+E(f9(x231),f9(x232))
% 0.55/0.88  [24]~E(x241,x242)+E(f15(x241),f15(x242))
% 0.55/0.88  [25]~E(x251,x252)+E(f24(x251),f24(x252))
% 0.55/0.88  [26]~E(x261,x262)+E(f26(x261),f26(x262))
% 0.55/0.88  [27]~E(x271,x272)+E(f27(x271),f27(x272))
% 0.55/0.88  [28]~E(x281,x282)+E(f4(x281),f4(x282))
% 0.55/0.88  [29]~E(x291,x292)+E(f25(x291),f25(x292))
% 0.55/0.88  [30]~P1(x301)+P1(x302)+~E(x301,x302)
% 0.55/0.88  [31]~P2(x311)+P2(x312)+~E(x311,x312)
% 0.55/0.88  [32]P5(x322,x323)+~E(x321,x322)+~P5(x321,x323)
% 0.55/0.88  [33]P5(x333,x332)+~E(x331,x332)+~P5(x333,x331)
% 0.55/0.88  [34]P7(x342,x343)+~E(x341,x342)+~P7(x341,x343)
% 0.55/0.88  [35]P7(x353,x352)+~E(x351,x352)+~P7(x353,x351)
% 0.55/0.88  [36]P3(x362,x363,x364)+~E(x361,x362)+~P3(x361,x363,x364)
% 0.55/0.88  [37]P3(x373,x372,x374)+~E(x371,x372)+~P3(x373,x371,x374)
% 0.55/0.88  [38]P3(x383,x384,x382)+~E(x381,x382)+~P3(x383,x384,x381)
% 0.55/0.88  [39]~P8(x391)+P8(x392)+~E(x391,x392)
% 0.55/0.88  [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.55/0.88  [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.55/0.88  [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.55/0.88  [43]~P9(x431)+P9(x432)+~E(x431,x432)
% 0.55/0.88  [44]P6(x442,x443,x444)+~E(x441,x442)+~P6(x441,x443,x444)
% 0.55/0.88  [45]P6(x453,x452,x454)+~E(x451,x452)+~P6(x453,x451,x454)
% 0.55/0.88  [46]P6(x463,x464,x462)+~E(x461,x462)+~P6(x463,x464,x461)
% 0.55/0.88  [47]~P10(x471)+P10(x472)+~E(x471,x472)
% 0.55/0.88  
% 0.55/0.88  %-------------------------------------------
% 0.55/0.88  cnf(144,plain,
% 0.55/0.88     (E(a13,f16(f12(f14(f6(a28,a21))),a28))),
% 0.55/0.88     inference(scs_inference,[],[64,2])).
% 0.55/0.88  cnf(146,plain,
% 0.55/0.88     (P7(x1461,a21)),
% 0.55/0.88     inference(rename_variables,[],[51])).
% 0.55/0.88  cnf(183,plain,
% 0.55/0.88     (E(f18(x1831,x1832,f16(f12(f14(f6(a28,a21))),a28)),f18(x1831,x1832,a13))),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19])).
% 0.55/0.88  cnf(184,plain,
% 0.55/0.88     (E(f18(x1841,f16(f12(f14(f6(a28,a21))),a28),x1842),f18(x1841,a13,x1842))),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19,18])).
% 0.55/0.88  cnf(199,plain,
% 0.55/0.88     (P7(f8(a2,f12(f14(f6(a2,a21)))),a13)),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,104])).
% 0.55/0.88  cnf(201,plain,
% 0.55/0.88     (~P5(f17(a21,f9(f16(f9(a21),f9(a30)))),f9(f16(f9(a21),f9(a30))))),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,104,89])).
% 0.55/0.88  cnf(203,plain,
% 0.55/0.88     (P5(f17(a21,f9(f16(f9(a21),f9(a30)))),a21)),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,104,89,79])).
% 0.55/0.88  cnf(211,plain,
% 0.55/0.88     (P5(f29(f29(a1,a1),f29(a1,f29(f12(a1),f12(a1)))),a11)),
% 0.55/0.88     inference(scs_inference,[],[68,51,146,48,49,50,64,2,78,117,74,73,72,71,77,129,125,101,84,83,80,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,104,89,79,115,116,112,110])).
% 0.55/0.88  cnf(314,plain,
% 0.55/0.88     (P5(f17(a21,f9(f16(f9(a21),f9(a30)))),f9(a21))),
% 0.55/0.88     inference(scs_inference,[],[48,54,60,144,183,184,201,203,199,211,72,82,71,2,81,35,3,106,134,30,88])).
% 0.55/0.88  cnf(369,plain,
% 0.55/0.88     ($false),
% 0.55/0.88     inference(scs_inference,[],[314,203,80]),
% 0.55/0.88     ['proof']).
% 0.55/0.88  % SZS output end Proof
% 0.55/0.88  % Total time :0.210000s
%------------------------------------------------------------------------------