TSTP Solution File: SEU672^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU672^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 : Tue May 21 03:29:01 EDT 2024

% Result   : Theorem 0.35s 0.57s
% Output   : CNFRefutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  220
% Syntax   : Number of formulae    :  244 (  18 unt; 211 typ;   0 def)
%            Number of atoms       :  765 (  56 equ;   0 cnn)
%            Maximal formula atoms :  242 (  23 avg)
%            Number of connectives : 1455 (  51   ~;  59   |; 233   &; 672   @)
%                                         (   8 <=>; 432  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  231 (  24 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  213 ( 211 usr; 194 con; 0-3 aty)
%            Number of variables   :  169 (  65   ^  82   !;  22   ?; 169   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_24,type,
    setextAx: $o ).

thf(decl_25,type,
    emptyset: $i ).

thf(decl_26,type,
    emptysetAx: $o ).

thf(decl_27,type,
    setadjoin: $i > $i > $i ).

thf(decl_28,type,
    setadjoinAx: $o ).

thf(decl_30,type,
    powersetAx: $o ).

thf(decl_32,type,
    setunionAx: $o ).

thf(decl_34,type,
    omega0Ax: $o ).

thf(decl_35,type,
    omegaSAx: $o ).

thf(decl_36,type,
    omegaIndAx: $o ).

thf(decl_37,type,
    replAx: $o ).

thf(decl_38,type,
    foundationAx: $o ).

thf(decl_39,type,
    wellorderingAx: $o ).

thf(decl_41,type,
    descrp: $o ).

thf(decl_42,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(decl_43,type,
    dsetconstrI: $o ).

thf(decl_44,type,
    dsetconstrEL: $o ).

thf(decl_45,type,
    dsetconstrER: $o ).

thf(decl_46,type,
    exuE1: $o ).

thf(decl_48,type,
    prop2setE: $o ).

thf(decl_49,type,
    emptysetE: $o ).

thf(decl_50,type,
    emptysetimpfalse: $o ).

thf(decl_51,type,
    notinemptyset: $o ).

thf(decl_52,type,
    exuE3e: $o ).

thf(decl_53,type,
    setext: $o ).

thf(decl_54,type,
    emptyI: $o ).

thf(decl_55,type,
    noeltsimpempty: $o ).

thf(decl_56,type,
    setbeta: $o ).

thf(decl_58,type,
    nonemptyE1: $o ).

thf(decl_59,type,
    nonemptyI: $o ).

thf(decl_60,type,
    nonemptyI1: $o ).

thf(decl_61,type,
    setadjoinIL: $o ).

thf(decl_62,type,
    emptyinunitempty: $o ).

thf(decl_63,type,
    setadjoinIR: $o ).

thf(decl_64,type,
    setadjoinE: $o ).

thf(decl_65,type,
    setadjoinOr: $o ).

thf(decl_66,type,
    setoftrueEq: $o ).

thf(decl_67,type,
    powersetI: $o ).

thf(decl_68,type,
    emptyinPowerset: $o ).

thf(decl_69,type,
    emptyInPowerset: $o ).

thf(decl_70,type,
    powersetE: $o ).

thf(decl_71,type,
    setunionI: $o ).

thf(decl_72,type,
    setunionE: $o ).

thf(decl_73,type,
    subPowSU: $o ).

thf(decl_74,type,
    exuE2: $o ).

thf(decl_75,type,
    nonemptyImpWitness: $o ).

thf(decl_76,type,
    uniqinunit: $o ).

thf(decl_77,type,
    notinsingleton: $o ).

thf(decl_78,type,
    eqinunit: $o ).

thf(decl_79,type,
    singletonsswitch: $o ).

thf(decl_80,type,
    upairsetE: $o ).

thf(decl_81,type,
    upairsetIL: $o ).

thf(decl_82,type,
    upairsetIR: $o ).

thf(decl_83,type,
    emptyE1: $o ).

thf(decl_84,type,
    vacuousDall: $o ).

thf(decl_85,type,
    quantDeMorgan1: $o ).

thf(decl_86,type,
    quantDeMorgan2: $o ).

thf(decl_87,type,
    quantDeMorgan3: $o ).

thf(decl_88,type,
    quantDeMorgan4: $o ).

thf(decl_89,type,
    prop2setI: $o ).

thf(decl_91,type,
    prop2set2propI: $o ).

thf(decl_92,type,
    notdexE: $o ).

thf(decl_93,type,
    notdallE: $o ).

thf(decl_94,type,
    exuI1: $o ).

thf(decl_95,type,
    exuI3: $o ).

thf(decl_96,type,
    exuI2: $o ).

thf(decl_97,type,
    inCongP: $o ).

thf(decl_98,type,
    in__Cong: $o ).

thf(decl_99,type,
    exuE3u: $o ).

thf(decl_100,type,
    exu__Cong: $o ).

thf(decl_101,type,
    emptyset__Cong: $o ).

thf(decl_102,type,
    setadjoin__Cong: $o ).

thf(decl_103,type,
    powerset__Cong: $o ).

thf(decl_104,type,
    setunion__Cong: $o ).

thf(decl_105,type,
    omega__Cong: $o ).

thf(decl_106,type,
    exuEu: $o ).

thf(decl_107,type,
    descr__Cong: $o ).

thf(decl_108,type,
    dsetconstr__Cong: $o ).

thf(decl_109,type,
    subset: $i > $i > $o ).

thf(decl_112,type,
    subsetI1: $o ).

thf(decl_113,type,
    eqimpsubset2: $o ).

thf(decl_114,type,
    eqimpsubset1: $o ).

thf(decl_115,type,
    subsetI2: $o ).

thf(decl_116,type,
    emptysetsubset: $o ).

thf(decl_117,type,
    subsetE: $o ).

thf(decl_118,type,
    subsetE2: $o ).

thf(decl_119,type,
    notsubsetI: $o ).

thf(decl_120,type,
    notequalI1: $o ).

thf(decl_121,type,
    notequalI2: $o ).

thf(decl_122,type,
    subsetRefl: $o ).

thf(decl_123,type,
    subsetTrans: $o ).

thf(decl_124,type,
    setadjoinSub: $o ).

thf(decl_125,type,
    setadjoinSub2: $o ).

thf(decl_126,type,
    subset2powerset: $o ).

thf(decl_127,type,
    setextsub: $o ).

thf(decl_128,type,
    subsetemptysetimpeq: $o ).

thf(decl_129,type,
    powersetI1: $o ).

thf(decl_130,type,
    powersetE1: $o ).

thf(decl_131,type,
    inPowerset: $o ).

thf(decl_132,type,
    powersetsubset: $o ).

thf(decl_133,type,
    sepInPowerset: $o ).

thf(decl_134,type,
    sepSubset: $o ).

thf(decl_136,type,
    binunionIL: $o ).

thf(decl_137,type,
    upairset2IR: $o ).

thf(decl_138,type,
    binunionIR: $o ).

thf(decl_139,type,
    binunionEcases: $o ).

thf(decl_140,type,
    binunionE: $o ).

thf(decl_141,type,
    binunionLsub: $o ).

thf(decl_142,type,
    binunionRsub: $o ).

thf(decl_144,type,
    binintersectI: $o ).

thf(decl_145,type,
    binintersectSubset5: $o ).

thf(decl_146,type,
    binintersectEL: $o ).

thf(decl_147,type,
    binintersectLsub: $o ).

thf(decl_148,type,
    binintersectSubset2: $o ).

thf(decl_149,type,
    binintersectSubset3: $o ).

thf(decl_150,type,
    binintersectER: $o ).

thf(decl_151,type,
    disjointsetsI1: $o ).

thf(decl_152,type,
    binintersectRsub: $o ).

thf(decl_153,type,
    binintersectSubset4: $o ).

thf(decl_154,type,
    binintersectSubset1: $o ).

thf(decl_155,type,
    bs114d: $o ).

thf(decl_158,type,
    setminusI: $o ).

thf(decl_159,type,
    setminusEL: $o ).

thf(decl_160,type,
    setminusER: $o ).

thf(decl_161,type,
    setminusSubset2: $o ).

thf(decl_162,type,
    setminusERneg: $o ).

thf(decl_163,type,
    setminusELneg: $o ).

thf(decl_164,type,
    setminusILneg: $o ).

thf(decl_165,type,
    setminusIRneg: $o ).

thf(decl_166,type,
    setminusLsub: $o ).

thf(decl_167,type,
    setminusSubset1: $o ).

thf(decl_169,type,
    symdiffE: $o ).

thf(decl_170,type,
    symdiffI1: $o ).

thf(decl_171,type,
    symdiffI2: $o ).

thf(decl_172,type,
    symdiffIneg1: $o ).

thf(decl_173,type,
    symdiffIneg2: $o ).

thf(decl_175,type,
    secondinupair: $o ).

thf(decl_176,type,
    setukpairIL: $o ).

thf(decl_177,type,
    setukpairIR: $o ).

thf(decl_178,type,
    kpairiskpair: $o ).

thf(decl_179,type,
    kpair: $i > $i > $i ).

thf(decl_180,type,
    kpairp: $o ).

thf(decl_181,type,
    cartprod: $i > $i > $i ).

thf(decl_182,type,
    singletonsubset: $o ).

thf(decl_183,type,
    singletoninpowerset: $o ).

thf(decl_184,type,
    singletoninpowunion: $o ).

thf(decl_185,type,
    upairset2E: $o ).

thf(decl_186,type,
    upairsubunion: $o ).

thf(decl_187,type,
    upairinpowunion: $o ).

thf(decl_188,type,
    ubforcartprodlem1: $o ).

thf(decl_189,type,
    ubforcartprodlem2: $o ).

thf(decl_190,type,
    ubforcartprodlem3: $o ).

thf(decl_191,type,
    cartprodpairin: $o ).

thf(decl_192,type,
    cartprodmempair1: $o ).

thf(decl_193,type,
    cartprodmempair: $o ).

thf(decl_194,type,
    setunionE2: $o ).

thf(decl_195,type,
    setunionsingleton1: $o ).

thf(decl_196,type,
    setunionsingleton2: $o ).

thf(decl_197,type,
    setunionsingleton: $o ).

thf(decl_198,type,
    singleton: $i > $o ).

thf(decl_199,type,
    singletonprop: $o ).

thf(decl_200,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(decl_201,type,
    ex1E1: $o ).

thf(decl_202,type,
    ex1I: $o ).

thf(decl_203,type,
    ex1I2: $o ).

thf(decl_204,type,
    singletonsuniq: $o ).

thf(decl_209,type,
    setukpairinjL1: $o ).

thf(decl_210,type,
    kfstsingleton: $o ).

thf(decl_211,type,
    theprop: $o ).

thf(decl_213,type,
    kfstpairEq: $o ).

thf(decl_214,type,
    cartprodfstin: $o ).

thf(decl_215,type,
    setukpairinjL2: $o ).

thf(decl_216,type,
    setukpairinjL: $o ).

thf(decl_217,type,
    setukpairinjR11: $o ).

thf(decl_218,type,
    setukpairinjR12: $o ).

thf(decl_219,type,
    setukpairinjR1: $o ).

thf(decl_220,type,
    upairequniteq: $o ).

thf(decl_221,type,
    setukpairinjR2: $o ).

thf(decl_222,type,
    setukpairinjR: $o ).

thf(decl_223,type,
    ksndsingleton: $o ).

thf(decl_225,type,
    ksndpairEq: $o ).

thf(decl_226,type,
    kpairsurjEq: $o ).

thf(decl_227,type,
    cartprodsndin: $o ).

thf(decl_228,type,
    cartprodpairmemEL: $o ).

thf(decl_229,type,
    cartprodpairmemER: $o ).

thf(decl_230,type,
    cartprodmempaircEq: $o ).

thf(decl_231,type,
    cartprodfstpairEq: $o ).

thf(decl_232,type,
    cartprodsndpairEq: $o ).

thf(decl_233,type,
    cartprodpairsurjEq: $o ).

thf(decl_234,type,
    breln: $i > $i > $i > $o ).

thf(decl_235,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(decl_236,type,
    dpsetconstrI: $o ).

thf(decl_237,type,
    dpsetconstrSub: $o ).

thf(decl_238,type,
    setOfPairsIsBReln: $o ).

thf(decl_239,type,
    dpsetconstrERa: $o ).

thf(decl_240,type,
    dpsetconstrEL1: $o ).

thf(decl_241,type,
    dpsetconstrEL2: $o ).

thf(decl_242,type,
    dpsetconstrER: $o ).

thf(decl_243,type,
    func: $i > $i > $i > $o ).

thf(decl_245,type,
    esk1_2: $i > ( $i > $o ) > $i ).

thf(decl_246,type,
    esk2_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_247,type,
    esk3_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_248,type,
    esk4_2: $i > ( $i > $o ) > $i ).

thf(decl_249,type,
    esk5_2: $i > ( $i > $o ) > $i ).

thf(decl_250,type,
    esk6_2: $i > ( $i > $o ) > $i ).

thf(decl_251,type,
    esk7_0: $i ).

thf(decl_252,type,
    esk8_0: $i ).

thf(decl_253,type,
    esk9_0: $i ).

thf(decl_254,type,
    esk10_1: $i > $i ).

thf(decl_255,type,
    esk11_0: $i ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [X4: $i,X1: $i > $o] :
          ( singleton
          @ ( dsetconstr @ X4
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [X4: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ X4 )
          & ( X4
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).

thf(setOfPairsIsBReln,axiom,
    ( setOfPairsIsBReln
  <=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
        ( breln @ X4 @ X5
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).

thf(breln,axiom,
    ( breln
    = ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).

thf(ex1I2,axiom,
    ( ex1I2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( ex1 @ X4
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).

thf(ex1I,axiom,
    ( ex1I
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).

thf(ex1E1,axiom,
    ( ex1E1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).

thf(func,axiom,
    ( func
    = ( ^ [X4: $i,X5: $i,X29: $i] :
          ( ( breln @ X4 @ X5 @ X29 )
          & ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( ex1 @ X5
                @ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).

thf(funcImageSingleton,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( uniqinunit
                                                                                         => ( notinsingleton
                                                                                           => ( eqinunit
                                                                                             => ( singletonsswitch
                                                                                               => ( upairsetE
                                                                                                 => ( upairsetIL
                                                                                                   => ( upairsetIR
                                                                                                     => ( emptyE1
                                                                                                       => ( vacuousDall
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( emptyset__Cong
                                                                                                                                         => ( setadjoin__Cong
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( emptysetsubset
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( setadjoinSub
                                                                                                                                                                                 => ( setadjoinSub2
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( subsetemptysetimpeq
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( upairset2IR
                                                                                                                                                                                                         => ( binunionIR
                                                                                                                                                                                                           => ( binunionEcases
                                                                                                                                                                                                             => ( binunionE
                                                                                                                                                                                                               => ( binunionLsub
                                                                                                                                                                                                                 => ( binunionRsub
                                                                                                                                                                                                                   => ( binintersectI
                                                                                                                                                                                                                     => ( binintersectSubset5
                                                                                                                                                                                                                       => ( binintersectEL
                                                                                                                                                                                                                         => ( binintersectLsub
                                                                                                                                                                                                                           => ( binintersectSubset2
                                                                                                                                                                                                                             => ( binintersectSubset3
                                                                                                                                                                                                                               => ( binintersectER
                                                                                                                                                                                                                                 => ( disjointsetsI1
                                                                                                                                                                                                                                   => ( binintersectRsub
                                                                                                                                                                                                                                     => ( binintersectSubset4
                                                                                                                                                                                                                                       => ( binintersectSubset1
                                                                                                                                                                                                                                         => ( bs114d
                                                                                                                                                                                                                                           => ( setminusI
                                                                                                                                                                                                                                             => ( setminusEL
                                                                                                                                                                                                                                               => ( setminusER
                                                                                                                                                                                                                                                 => ( setminusSubset2
                                                                                                                                                                                                                                                   => ( setminusERneg
                                                                                                                                                                                                                                                     => ( setminusELneg
                                                                                                                                                                                                                                                       => ( setminusILneg
                                                                                                                                                                                                                                                         => ( setminusIRneg
                                                                                                                                                                                                                                                           => ( setminusLsub
                                                                                                                                                                                                                                                             => ( setminusSubset1
                                                                                                                                                                                                                                                               => ( symdiffE
                                                                                                                                                                                                                                                                 => ( symdiffI1
                                                                                                                                                                                                                                                                   => ( symdiffI2
                                                                                                                                                                                                                                                                     => ( symdiffIneg1
                                                                                                                                                                                                                                                                       => ( symdiffIneg2
                                                                                                                                                                                                                                                                         => ( secondinupair
                                                                                                                                                                                                                                                                           => ( setukpairIL
                                                                                                                                                                                                                                                                             => ( setukpairIR
                                                                                                                                                                                                                                                                               => ( kpairiskpair
                                                                                                                                                                                                                                                                                 => ( kpairp
                                                                                                                                                                                                                                                                                   => ( singletonsubset
                                                                                                                                                                                                                                                                                     => ( singletoninpowerset
                                                                                                                                                                                                                                                                                       => ( singletoninpowunion
                                                                                                                                                                                                                                                                                         => ( upairset2E
                                                                                                                                                                                                                                                                                           => ( upairsubunion
                                                                                                                                                                                                                                                                                             => ( upairinpowunion
                                                                                                                                                                                                                                                                                               => ( ubforcartprodlem1
                                                                                                                                                                                                                                                                                                 => ( ubforcartprodlem2
                                                                                                                                                                                                                                                                                                   => ( ubforcartprodlem3
                                                                                                                                                                                                                                                                                                     => ( cartprodpairin
                                                                                                                                                                                                                                                                                                       => ( cartprodmempair1
                                                                                                                                                                                                                                                                                                         => ( cartprodmempair
                                                                                                                                                                                                                                                                                                           => ( setunionE2
                                                                                                                                                                                                                                                                                                             => ( setunionsingleton1
                                                                                                                                                                                                                                                                                                               => ( setunionsingleton2
                                                                                                                                                                                                                                                                                                                 => ( setunionsingleton
                                                                                                                                                                                                                                                                                                                   => ( singletonprop
                                                                                                                                                                                                                                                                                                                     => ( ex1E1
                                                                                                                                                                                                                                                                                                                       => ( ex1I
                                                                                                                                                                                                                                                                                                                         => ( ex1I2
                                                                                                                                                                                                                                                                                                                           => ( singletonsuniq
                                                                                                                                                                                                                                                                                                                             => ( setukpairinjL1
                                                                                                                                                                                                                                                                                                                               => ( kfstsingleton
                                                                                                                                                                                                                                                                                                                                 => ( theprop
                                                                                                                                                                                                                                                                                                                                   => ( kfstpairEq
                                                                                                                                                                                                                                                                                                                                     => ( cartprodfstin
                                                                                                                                                                                                                                                                                                                                       => ( setukpairinjL2
                                                                                                                                                                                                                                                                                                                                         => ( setukpairinjL
                                                                                                                                                                                                                                                                                                                                           => ( setukpairinjR11
                                                                                                                                                                                                                                                                                                                                             => ( setukpairinjR12
                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR1
                                                                                                                                                                                                                                                                                                                                                 => ( upairequniteq
                                                                                                                                                                                                                                                                                                                                                   => ( setukpairinjR2
                                                                                                                                                                                                                                                                                                                                                     => ( setukpairinjR
                                                                                                                                                                                                                                                                                                                                                       => ( ksndsingleton
                                                                                                                                                                                                                                                                                                                                                         => ( ksndpairEq
                                                                                                                                                                                                                                                                                                                                                           => ( kpairsurjEq
                                                                                                                                                                                                                                                                                                                                                             => ( cartprodsndin
                                                                                                                                                                                                                                                                                                                                                               => ( cartprodpairmemEL
                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemER
                                                                                                                                                                                                                                                                                                                                                                   => ( cartprodmempaircEq
                                                                                                                                                                                                                                                                                                                                                                     => ( cartprodfstpairEq
                                                                                                                                                                                                                                                                                                                                                                       => ( cartprodsndpairEq
                                                                                                                                                                                                                                                                                                                                                                         => ( cartprodpairsurjEq
                                                                                                                                                                                                                                                                                                                                                                           => ( dpsetconstrI
                                                                                                                                                                                                                                                                                                                                                                             => ( dpsetconstrSub
                                                                                                                                                                                                                                                                                                                                                                               => ( setOfPairsIsBReln
                                                                                                                                                                                                                                                                                                                                                                                 => ( dpsetconstrERa
                                                                                                                                                                                                                                                                                                                                                                                   => ( dpsetconstrEL1
                                                                                                                                                                                                                                                                                                                                                                                     => ( dpsetconstrEL2
                                                                                                                                                                                                                                                                                                                                                                                       => ( dpsetconstrER
                                                                                                                                                                                                                                                                                                                                                                                         => ! [X4: $i,X5: $i,X30: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X4 @ X5 @ X30 )
                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ X5
                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).

thf(c_0_9,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X50: $i] :
          ( ( in @ X50
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X50 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1]) ).

thf(c_0_10,plain,
    ( singleton
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ Z0 )
          & ( Z0
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singleton]) ).

thf(c_0_11,plain,
    ( setOfPairsIsBReln
  <=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
        ( breln @ X4 @ X5
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).

thf(c_0_12,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_13,plain,
    ( ex1I2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( ex1 @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1I2]) ).

thf(c_0_14,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X50: $i] :
          ( ( in @ X50
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X50 @ emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_15,plain,
    ( ex1I
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1I]) ).

thf(c_0_16,plain,
    ( ex1E1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1E1]) ).

thf(c_0_17,plain,
    ( func
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] :
          ( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
          & ! [X2: $i] :
              ( ( in @ X2 @ Z0 )
             => ? [X54: $i] :
                  ( ( in @ X54
                    @ ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
                  & ( ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
                    = ( setadjoin @ X54 @ emptyset ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[func]) ).

thf(c_0_18,plain,
    ( setOfPairsIsBReln
    = ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
          @ ( cartprod @ X4 @ X5 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_19,plain,
    ( ex1I2
    = ( ! [X4: $i,X1: $i > $o] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) )
         => ( ? [X2: $i] :
                ( ( in @ X2 @ X4 )
                & ( X1 @ X2 ) )
           => ? [X53: $i] :
                ( ( in @ X53
                  @ ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                  = ( setadjoin @ X53 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_20,plain,
    ( ex1I
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X3 )
                   => ( X3 = X2 ) ) )
             => ? [X52: $i] :
                  ( ( in @ X52
                    @ ( dsetconstr @ X4
                      @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
                  & ( ( dsetconstr @ X4
                      @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                    = ( setadjoin @ X52 @ emptyset ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_15,c_0_14]) ).

thf(c_0_21,plain,
    ( ex1E1
    = ( ! [X4: $i,X1: $i > $o] :
          ( ? [X51: $i] :
              ( ( in @ X51
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( setadjoin @ X51 @ emptyset ) ) )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_16,c_0_14]) ).

thf(c_0_22,plain,
    ( func
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] :
          ( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
          & ! [X2: $i] :
              ( ( in @ X2 @ Z0 )
             => ? [X54: $i] :
                  ( ( in @ X54
                    @ ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
                  & ( ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
                    = ( setadjoin @ X54 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_12]),c_0_14]) ).

thf(c_0_23,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( setext
                                               => ( emptyI
                                                 => ( noeltsimpempty
                                                   => ( setbeta
                                                     => ( nonemptyE1
                                                       => ( nonemptyI
                                                         => ( nonemptyI1
                                                           => ( setadjoinIL
                                                             => ( emptyinunitempty
                                                               => ( setadjoinIR
                                                                 => ( setadjoinE
                                                                   => ( setadjoinOr
                                                                     => ( setoftrueEq
                                                                       => ( powersetI
                                                                         => ( emptyinPowerset
                                                                           => ( emptyInPowerset
                                                                             => ( powersetE
                                                                               => ( setunionI
                                                                                 => ( setunionE
                                                                                   => ( subPowSU
                                                                                     => ( exuE2
                                                                                       => ( nonemptyImpWitness
                                                                                         => ( uniqinunit
                                                                                           => ( notinsingleton
                                                                                             => ( eqinunit
                                                                                               => ( singletonsswitch
                                                                                                 => ( upairsetE
                                                                                                   => ( upairsetIL
                                                                                                     => ( upairsetIR
                                                                                                       => ( emptyE1
                                                                                                         => ( vacuousDall
                                                                                                           => ( quantDeMorgan1
                                                                                                             => ( quantDeMorgan2
                                                                                                               => ( quantDeMorgan3
                                                                                                                 => ( quantDeMorgan4
                                                                                                                   => ( prop2setI
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( notdexE
                                                                                                                         => ( notdallE
                                                                                                                           => ( exuI1
                                                                                                                             => ( exuI3
                                                                                                                               => ( exuI2
                                                                                                                                 => ( inCongP
                                                                                                                                   => ( in__Cong
                                                                                                                                     => ( exuE3u
                                                                                                                                       => ( exu__Cong
                                                                                                                                         => ( emptyset__Cong
                                                                                                                                           => ( setadjoin__Cong
                                                                                                                                             => ( powerset__Cong
                                                                                                                                               => ( setunion__Cong
                                                                                                                                                 => ( omega__Cong
                                                                                                                                                   => ( exuEu
                                                                                                                                                     => ( descr__Cong
                                                                                                                                                       => ( dsetconstr__Cong
                                                                                                                                                         => ( subsetI1
                                                                                                                                                           => ( eqimpsubset2
                                                                                                                                                             => ( eqimpsubset1
                                                                                                                                                               => ( subsetI2
                                                                                                                                                                 => ( emptysetsubset
                                                                                                                                                                   => ( subsetE
                                                                                                                                                                     => ( subsetE2
                                                                                                                                                                       => ( notsubsetI
                                                                                                                                                                         => ( notequalI1
                                                                                                                                                                           => ( notequalI2
                                                                                                                                                                             => ( subsetRefl
                                                                                                                                                                               => ( subsetTrans
                                                                                                                                                                                 => ( setadjoinSub
                                                                                                                                                                                   => ( setadjoinSub2
                                                                                                                                                                                     => ( subset2powerset
                                                                                                                                                                                       => ( setextsub
                                                                                                                                                                                         => ( subsetemptysetimpeq
                                                                                                                                                                                           => ( powersetI1
                                                                                                                                                                                             => ( powersetE1
                                                                                                                                                                                               => ( inPowerset
                                                                                                                                                                                                 => ( powersetsubset
                                                                                                                                                                                                   => ( sepInPowerset
                                                                                                                                                                                                     => ( sepSubset
                                                                                                                                                                                                       => ( binunionIL
                                                                                                                                                                                                         => ( upairset2IR
                                                                                                                                                                                                           => ( binunionIR
                                                                                                                                                                                                             => ( binunionEcases
                                                                                                                                                                                                               => ( binunionE
                                                                                                                                                                                                                 => ( binunionLsub
                                                                                                                                                                                                                   => ( binunionRsub
                                                                                                                                                                                                                     => ( binintersectI
                                                                                                                                                                                                                       => ( binintersectSubset5
                                                                                                                                                                                                                         => ( binintersectEL
                                                                                                                                                                                                                           => ( binintersectLsub
                                                                                                                                                                                                                             => ( binintersectSubset2
                                                                                                                                                                                                                               => ( binintersectSubset3
                                                                                                                                                                                                                                 => ( binintersectER
                                                                                                                                                                                                                                   => ( disjointsetsI1
                                                                                                                                                                                                                                     => ( binintersectRsub
                                                                                                                                                                                                                                       => ( binintersectSubset4
                                                                                                                                                                                                                                         => ( binintersectSubset1
                                                                                                                                                                                                                                           => ( bs114d
                                                                                                                                                                                                                                             => ( setminusI
                                                                                                                                                                                                                                               => ( setminusEL
                                                                                                                                                                                                                                                 => ( setminusER
                                                                                                                                                                                                                                                   => ( setminusSubset2
                                                                                                                                                                                                                                                     => ( setminusERneg
                                                                                                                                                                                                                                                       => ( setminusELneg
                                                                                                                                                                                                                                                         => ( setminusILneg
                                                                                                                                                                                                                                                           => ( setminusIRneg
                                                                                                                                                                                                                                                             => ( setminusLsub
                                                                                                                                                                                                                                                               => ( setminusSubset1
                                                                                                                                                                                                                                                                 => ( symdiffE
                                                                                                                                                                                                                                                                   => ( symdiffI1
                                                                                                                                                                                                                                                                     => ( symdiffI2
                                                                                                                                                                                                                                                                       => ( symdiffIneg1
                                                                                                                                                                                                                                                                         => ( symdiffIneg2
                                                                                                                                                                                                                                                                           => ( secondinupair
                                                                                                                                                                                                                                                                             => ( setukpairIL
                                                                                                                                                                                                                                                                               => ( setukpairIR
                                                                                                                                                                                                                                                                                 => ( kpairiskpair
                                                                                                                                                                                                                                                                                   => ( kpairp
                                                                                                                                                                                                                                                                                     => ( singletonsubset
                                                                                                                                                                                                                                                                                       => ( singletoninpowerset
                                                                                                                                                                                                                                                                                         => ( singletoninpowunion
                                                                                                                                                                                                                                                                                           => ( upairset2E
                                                                                                                                                                                                                                                                                             => ( upairsubunion
                                                                                                                                                                                                                                                                                               => ( upairinpowunion
                                                                                                                                                                                                                                                                                                 => ( ubforcartprodlem1
                                                                                                                                                                                                                                                                                                   => ( ubforcartprodlem2
                                                                                                                                                                                                                                                                                                     => ( ubforcartprodlem3
                                                                                                                                                                                                                                                                                                       => ( cartprodpairin
                                                                                                                                                                                                                                                                                                         => ( cartprodmempair1
                                                                                                                                                                                                                                                                                                           => ( cartprodmempair
                                                                                                                                                                                                                                                                                                             => ( setunionE2
                                                                                                                                                                                                                                                                                                               => ( setunionsingleton1
                                                                                                                                                                                                                                                                                                                 => ( setunionsingleton2
                                                                                                                                                                                                                                                                                                                   => ( setunionsingleton
                                                                                                                                                                                                                                                                                                                     => ( singletonprop
                                                                                                                                                                                                                                                                                                                       => ( ! [X55: $i,X56: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ? [X57: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X57 @ ( dsetconstr @ X55 @ X56 ) )
                                                                                                                                                                                                                                                                                                                                  & ( ( dsetconstr @ X55 @ X56 )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X57 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                             => ? [X58: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X58 @ X55 )
                                                                                                                                                                                                                                                                                                                                  & ( X56 @ X58 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X59: $i,X60: $i > $o,X61: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X61 @ X59 )
                                                                                                                                                                                                                                                                                                                               => ( ( X60 @ X61 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X62: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X62 @ X59 )
                                                                                                                                                                                                                                                                                                                                       => ( ( X60 @ X62 )
                                                                                                                                                                                                                                                                                                                                         => ( X62 = X61 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ? [X63: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X63 @ ( dsetconstr @ X59 @ X60 ) )
                                                                                                                                                                                                                                                                                                                                        & ( ( dsetconstr @ X59 @ X60 )
                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X63 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X64: $i,X65: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [X66: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X66 @ X64 )
                                                                                                                                                                                                                                                                                                                                     => ! [X67: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X67 @ X64 )
                                                                                                                                                                                                                                                                                                                                         => ( ( X65 @ X66 )
                                                                                                                                                                                                                                                                                                                                           => ( ( X65 @ X67 )
                                                                                                                                                                                                                                                                                                                                             => ( X66 = X67 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [X68: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X68 @ X64 )
                                                                                                                                                                                                                                                                                                                                        & ( X65 @ X68 ) )
                                                                                                                                                                                                                                                                                                                                   => ? [X69: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X69 @ ( dsetconstr @ X64 @ X65 ) )
                                                                                                                                                                                                                                                                                                                                        & ( ( dsetconstr @ X64 @ X65 )
                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X69 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( singletonsuniq
                                                                                                                                                                                                                                                                                                                               => ( setukpairinjL1
                                                                                                                                                                                                                                                                                                                                 => ( kfstsingleton
                                                                                                                                                                                                                                                                                                                                   => ( theprop
                                                                                                                                                                                                                                                                                                                                     => ( kfstpairEq
                                                                                                                                                                                                                                                                                                                                       => ( cartprodfstin
                                                                                                                                                                                                                                                                                                                                         => ( setukpairinjL2
                                                                                                                                                                                                                                                                                                                                           => ( setukpairinjL
                                                                                                                                                                                                                                                                                                                                             => ( setukpairinjR11
                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR12
                                                                                                                                                                                                                                                                                                                                                 => ( setukpairinjR1
                                                                                                                                                                                                                                                                                                                                                   => ( upairequniteq
                                                                                                                                                                                                                                                                                                                                                     => ( setukpairinjR2
                                                                                                                                                                                                                                                                                                                                                       => ( setukpairinjR
                                                                                                                                                                                                                                                                                                                                                         => ( ksndsingleton
                                                                                                                                                                                                                                                                                                                                                           => ( ksndpairEq
                                                                                                                                                                                                                                                                                                                                                             => ( kpairsurjEq
                                                                                                                                                                                                                                                                                                                                                               => ( cartprodsndin
                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemEL
                                                                                                                                                                                                                                                                                                                                                                   => ( cartprodpairmemER
                                                                                                                                                                                                                                                                                                                                                                     => ( cartprodmempaircEq
                                                                                                                                                                                                                                                                                                                                                                       => ( cartprodfstpairEq
                                                                                                                                                                                                                                                                                                                                                                         => ( cartprodsndpairEq
                                                                                                                                                                                                                                                                                                                                                                           => ( cartprodpairsurjEq
                                                                                                                                                                                                                                                                                                                                                                             => ( dpsetconstrI
                                                                                                                                                                                                                                                                                                                                                                               => ( dpsetconstrSub
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X70: $i,X71: $i,X72: $i > $i > $o] : ( subset @ ( dpsetconstr @ X70 @ X71 @ X72 ) @ ( cartprod @ X70 @ X71 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( dpsetconstrERa
                                                                                                                                                                                                                                                                                                                                                                                     => ( dpsetconstrEL1
                                                                                                                                                                                                                                                                                                                                                                                       => ( dpsetconstrEL2
                                                                                                                                                                                                                                                                                                                                                                                         => ( dpsetconstrER
                                                                                                                                                                                                                                                                                                                                                                                           => ! [X4: $i,X5: $i,X30: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                ( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
                                                                                                                                                                                                                                                                                                                                                                                                  & ! [X73: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X73 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ? [X74: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X74
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X5
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X73 @ Z0 ) @ X30 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          & ( ( dsetconstr @ X5
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X73 @ Z0 ) @ X30 ) )
                                                                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X74 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ? [X75: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X75
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ X5
                                                                                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                        & ( ( dsetconstr @ X5
                                                                                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
                                                                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X75 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[funcImageSingleton])]),c_0_10]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22])]) ).

thf(c_0_24,negated_conjecture,
    ! [X78: $i,X79: $i > $o,X80: $i,X82: $i,X83: $i > $o,X84: $i,X87: $i,X88: $i > $o,X91: $i,X93: $i,X94: $i,X95: $i > $i > $o,X99: $i,X102: $i] :
      ( setextAx
      & emptysetAx
      & setadjoinAx
      & powersetAx
      & setunionAx
      & omega0Ax
      & omegaSAx
      & omegaIndAx
      & replAx
      & foundationAx
      & wellorderingAx
      & descrp
      & dsetconstrI
      & dsetconstrEL
      & dsetconstrER
      & exuE1
      & prop2setE
      & emptysetE
      & emptysetimpfalse
      & notinemptyset
      & exuE3e
      & setext
      & emptyI
      & noeltsimpempty
      & setbeta
      & nonemptyE1
      & nonemptyI
      & nonemptyI1
      & setadjoinIL
      & emptyinunitempty
      & setadjoinIR
      & setadjoinE
      & setadjoinOr
      & setoftrueEq
      & powersetI
      & emptyinPowerset
      & emptyInPowerset
      & powersetE
      & setunionI
      & setunionE
      & subPowSU
      & exuE2
      & nonemptyImpWitness
      & uniqinunit
      & notinsingleton
      & eqinunit
      & singletonsswitch
      & upairsetE
      & upairsetIL
      & upairsetIR
      & emptyE1
      & vacuousDall
      & quantDeMorgan1
      & quantDeMorgan2
      & quantDeMorgan3
      & quantDeMorgan4
      & prop2setI
      & prop2set2propI
      & notdexE
      & notdallE
      & exuI1
      & exuI3
      & exuI2
      & inCongP
      & in__Cong
      & exuE3u
      & exu__Cong
      & emptyset__Cong
      & setadjoin__Cong
      & powerset__Cong
      & setunion__Cong
      & omega__Cong
      & exuEu
      & descr__Cong
      & dsetconstr__Cong
      & subsetI1
      & eqimpsubset2
      & eqimpsubset1
      & subsetI2
      & emptysetsubset
      & subsetE
      & subsetE2
      & notsubsetI
      & notequalI1
      & notequalI2
      & subsetRefl
      & subsetTrans
      & setadjoinSub
      & setadjoinSub2
      & subset2powerset
      & setextsub
      & subsetemptysetimpeq
      & powersetI1
      & powersetE1
      & inPowerset
      & powersetsubset
      & sepInPowerset
      & sepSubset
      & binunionIL
      & upairset2IR
      & binunionIR
      & binunionEcases
      & binunionE
      & binunionLsub
      & binunionRsub
      & binintersectI
      & binintersectSubset5
      & binintersectEL
      & binintersectLsub
      & binintersectSubset2
      & binintersectSubset3
      & binintersectER
      & disjointsetsI1
      & binintersectRsub
      & binintersectSubset4
      & binintersectSubset1
      & bs114d
      & setminusI
      & setminusEL
      & setminusER
      & setminusSubset2
      & setminusERneg
      & setminusELneg
      & setminusILneg
      & setminusIRneg
      & setminusLsub
      & setminusSubset1
      & symdiffE
      & symdiffI1
      & symdiffI2
      & symdiffIneg1
      & symdiffIneg2
      & secondinupair
      & setukpairIL
      & setukpairIR
      & kpairiskpair
      & kpairp
      & singletonsubset
      & singletoninpowerset
      & singletoninpowunion
      & upairset2E
      & upairsubunion
      & upairinpowunion
      & ubforcartprodlem1
      & ubforcartprodlem2
      & ubforcartprodlem3
      & cartprodpairin
      & cartprodmempair1
      & cartprodmempair
      & setunionE2
      & setunionsingleton1
      & setunionsingleton2
      & setunionsingleton
      & singletonprop
      & ( ( in @ ( esk1_2 @ X78 @ X79 ) @ X78 )
        | ~ ( in @ X80 @ ( dsetconstr @ X78 @ X79 ) )
        | ( ( dsetconstr @ X78 @ X79 )
         != ( setadjoin @ X80 @ emptyset ) ) )
      & ( ( X79 @ ( esk1_2 @ X78 @ X79 ) )
        | ~ ( in @ X80 @ ( dsetconstr @ X78 @ X79 ) )
        | ( ( dsetconstr @ X78 @ X79 )
         != ( setadjoin @ X80 @ emptyset ) ) )
      & ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
        | ( in @ ( esk2_3 @ X82 @ X83 @ X84 ) @ X82 )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( ( dsetconstr @ X82 @ X83 )
          = ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
        | ( in @ ( esk2_3 @ X82 @ X83 @ X84 ) @ X82 )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
        | ( X83 @ ( esk2_3 @ X82 @ X83 @ X84 ) )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( ( dsetconstr @ X82 @ X83 )
          = ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
        | ( X83 @ ( esk2_3 @ X82 @ X83 @ X84 ) )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( in @ ( esk3_3 @ X82 @ X83 @ X84 ) @ ( dsetconstr @ X82 @ X83 ) )
        | ( ( esk2_3 @ X82 @ X83 @ X84 )
         != X84 )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( ( dsetconstr @ X82 @ X83 )
          = ( setadjoin @ ( esk3_3 @ X82 @ X83 @ X84 ) @ emptyset ) )
        | ( ( esk2_3 @ X82 @ X83 @ X84 )
         != X84 )
        | ~ ( X83 @ X84 )
        | ~ ( in @ X84 @ X82 ) )
      & ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( in @ ( esk4_2 @ X87 @ X88 ) @ X87 ) )
      & ( ( ( dsetconstr @ X87 @ X88 )
          = ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( in @ ( esk4_2 @ X87 @ X88 ) @ X87 ) )
      & ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( in @ ( esk5_2 @ X87 @ X88 ) @ X87 ) )
      & ( ( ( dsetconstr @ X87 @ X88 )
          = ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( in @ ( esk5_2 @ X87 @ X88 ) @ X87 ) )
      & ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( X88 @ ( esk4_2 @ X87 @ X88 ) ) )
      & ( ( ( dsetconstr @ X87 @ X88 )
          = ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( X88 @ ( esk4_2 @ X87 @ X88 ) ) )
      & ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( X88 @ ( esk5_2 @ X87 @ X88 ) ) )
      & ( ( ( dsetconstr @ X87 @ X88 )
          = ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( X88 @ ( esk5_2 @ X87 @ X88 ) ) )
      & ( ( in @ ( esk6_2 @ X87 @ X88 ) @ ( dsetconstr @ X87 @ X88 ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( ( esk4_2 @ X87 @ X88 )
         != ( esk5_2 @ X87 @ X88 ) ) )
      & ( ( ( dsetconstr @ X87 @ X88 )
          = ( setadjoin @ ( esk6_2 @ X87 @ X88 ) @ emptyset ) )
        | ~ ( in @ X91 @ X87 )
        | ~ ( X88 @ X91 )
        | ( ( esk4_2 @ X87 @ X88 )
         != ( esk5_2 @ X87 @ X88 ) ) )
      & singletonsuniq
      & setukpairinjL1
      & kfstsingleton
      & theprop
      & kfstpairEq
      & cartprodfstin
      & setukpairinjL2
      & setukpairinjL
      & setukpairinjR11
      & setukpairinjR12
      & setukpairinjR1
      & upairequniteq
      & setukpairinjR2
      & setukpairinjR
      & ksndsingleton
      & ksndpairEq
      & kpairsurjEq
      & cartprodsndin
      & cartprodpairmemEL
      & cartprodpairmemER
      & cartprodmempaircEq
      & cartprodfstpairEq
      & cartprodsndpairEq
      & cartprodpairsurjEq
      & dpsetconstrI
      & dpsetconstrSub
      & ( subset @ ( dpsetconstr @ X93 @ X94 @ X95 ) @ ( cartprod @ X93 @ X94 ) )
      & dpsetconstrERa
      & dpsetconstrEL1
      & dpsetconstrEL2
      & dpsetconstrER
      & ( subset @ esk9_0 @ ( cartprod @ esk7_0 @ esk8_0 ) )
      & ( ( in @ ( esk10_1 @ X99 )
          @ ( dsetconstr @ esk8_0
            @ ^ [Z0: $i] : ( in @ ( kpair @ X99 @ Z0 ) @ esk9_0 ) ) )
        | ~ ( in @ X99 @ esk7_0 ) )
      & ( ( ( dsetconstr @ esk8_0
            @ ^ [Z0: $i] : ( in @ ( kpair @ X99 @ Z0 ) @ esk9_0 ) )
          = ( setadjoin @ ( esk10_1 @ X99 ) @ emptyset ) )
        | ~ ( in @ X99 @ esk7_0 ) )
      & ( in @ esk11_0 @ esk7_0 )
      & ( ~ ( in @ X102
            @ ( dsetconstr @ esk8_0
              @ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) ) )
        | ( ( dsetconstr @ esk8_0
            @ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
         != ( setadjoin @ X102 @ emptyset ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])]) ).

thf(c_0_25,negated_conjecture,
    ! [X2: $i] :
      ( ( ( dsetconstr @ esk8_0
          @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ esk9_0 ) )
        = ( setadjoin @ ( esk10_1 @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ esk7_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_26,negated_conjecture,
    in @ esk11_0 @ esk7_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_27,negated_conjecture,
    ! [X2: $i] :
      ( ~ ( in @ X2
          @ ( dsetconstr @ esk8_0
            @ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) ) )
      | ( ( dsetconstr @ esk8_0
          @ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
       != ( setadjoin @ X2 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_28,negated_conjecture,
    ( ( dsetconstr @ esk8_0
      @ ^ [Z0: $i] : ( in @ ( kpair @ esk11_0 @ Z0 ) @ esk9_0 ) )
    = ( setadjoin @ ( esk10_1 @ esk11_0 ) @ emptyset ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_29,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ ( esk10_1 @ X2 )
        @ ( dsetconstr @ esk8_0
          @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ esk9_0 ) ) )
      | ~ ( in @ X2 @ esk7_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: $i] :
      ( ( ( setadjoin @ ( esk10_1 @ esk11_0 ) @ emptyset )
       != ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ ( setadjoin @ ( esk10_1 @ esk11_0 ) @ emptyset ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).

thf(c_0_31,negated_conjecture,
    in @ ( esk10_1 @ esk11_0 ) @ ( setadjoin @ ( esk10_1 @ esk11_0 ) @ emptyset ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_26])]) ).

thf(c_0_32,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_30,c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU672^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 15:47:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.57  # Version: 3.1.0-ho
% 0.35/0.57  # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.35/0.57  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.57  # Starting ho_unfolding_5 with 1200s (4) cores
% 0.35/0.57  # Starting pre_casc_3 with 300s (1) cores
% 0.35/0.57  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.35/0.57  # Starting full_lambda_10 with 300s (1) cores
% 0.35/0.57  # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.35/0.57  # full_lambda_10 with pid 22981 completed with status 0
% 0.35/0.57  # Result found by full_lambda_10
% 0.35/0.57  # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.35/0.57  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.57  # Starting ho_unfolding_5 with 1200s (4) cores
% 0.35/0.57  # Starting pre_casc_3 with 300s (1) cores
% 0.35/0.57  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.35/0.57  # Starting full_lambda_10 with 300s (1) cores
% 0.35/0.57  # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.35/0.57  # Search class: HGHSF-FFMM32-DHSMMFBN
% 0.35/0.57  # partial match(4): HGHSM-FMLM32-MHSMMFBN
% 0.35/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.57  # Starting sh10 with 160s (1) cores
% 0.35/0.57  # sh10 with pid 22986 completed with status 0
% 0.35/0.57  # Result found by sh10
% 0.35/0.57  # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.35/0.57  # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.57  # Starting ho_unfolding_5 with 1200s (4) cores
% 0.35/0.57  # Starting pre_casc_3 with 300s (1) cores
% 0.35/0.57  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.35/0.57  # Starting full_lambda_10 with 300s (1) cores
% 0.35/0.57  # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.35/0.57  # Search class: HGHSF-FFMM32-DHSMMFBN
% 0.35/0.57  # partial match(4): HGHSM-FMLM32-MHSMMFBN
% 0.35/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.57  # Starting sh10 with 160s (1) cores
% 0.35/0.57  # Preprocessing time       : 0.011 s
% 0.35/0.57  
% 0.35/0.57  # Proof found!
% 0.35/0.57  # SZS status Theorem
% 0.35/0.57  # SZS output start CNFRefutation
% See solution above
% 0.35/0.58  # Parsed axioms                        : 419
% 0.35/0.58  # Removed by relevancy pruning/SinE    : 409
% 0.35/0.58  # Initial clauses                      : 209
% 0.35/0.58  # Removed in clause preprocessing      : 0
% 0.35/0.58  # Initial clauses in saturation        : 209
% 0.35/0.58  # Processed clauses                    : 214
% 0.35/0.58  # ...of these trivial                  : 0
% 0.35/0.58  # ...subsumed                          : 0
% 0.35/0.58  # ...remaining for further processing  : 214
% 0.35/0.58  # Other redundant clauses eliminated   : 0
% 0.35/0.58  # Clauses deleted for lack of memory   : 0
% 0.35/0.58  # Backward-subsumed                    : 0
% 0.35/0.58  # Backward-rewritten                   : 1
% 0.35/0.58  # Generated clauses                    : 146
% 0.35/0.58  # ...of the previous two non-redundant : 146
% 0.35/0.58  # ...aggressively subsumed             : 0
% 0.35/0.58  # Contextual simplify-reflections      : 0
% 0.35/0.58  # Paramodulations                      : 138
% 0.35/0.58  # Factorizations                       : 0
% 0.35/0.58  # NegExts                              : 1
% 0.35/0.58  # Equation resolutions                 : 0
% 0.35/0.58  # Disequality decompositions           : 0
% 0.35/0.58  # Total rewrite steps                  : 5
% 0.35/0.58  # ...of those cached                   : 3
% 0.35/0.58  # Propositional unsat checks           : 0
% 0.35/0.58  #    Propositional check models        : 0
% 0.35/0.58  #    Propositional check unsatisfiable : 0
% 0.35/0.58  #    Propositional clauses             : 0
% 0.35/0.58  #    Propositional clauses after purity: 0
% 0.35/0.58  #    Propositional unsat core size     : 0
% 0.35/0.58  #    Propositional preprocessing time  : 0.000
% 0.35/0.58  #    Propositional encoding time       : 0.000
% 0.35/0.58  #    Propositional solver time         : 0.000
% 0.35/0.58  #    Success case prop preproc time    : 0.000
% 0.35/0.58  #    Success case prop encoding time   : 0.000
% 0.35/0.58  #    Success case prop solver time     : 0.000
% 0.35/0.58  # Current number of processed clauses  : 213
% 0.35/0.58  #    Positive orientable unit clauses  : 190
% 0.35/0.58  #    Positive unorientable unit clauses: 0
% 0.35/0.58  #    Negative unit clauses             : 0
% 0.35/0.58  #    Non-unit-clauses                  : 23
% 0.35/0.58  # Current number of unprocessed clauses: 129
% 0.35/0.58  # ...number of literals in the above   : 593
% 0.35/0.58  # Current number of archived formulas  : 0
% 0.35/0.58  # Current number of archived clauses   : 1
% 0.35/0.58  # Clause-clause subsumption calls (NU) : 29
% 0.35/0.58  # Rec. Clause-clause subsumption calls : 7
% 0.35/0.58  # Non-unit clause-clause subsumptions  : 0
% 0.35/0.58  # Unit Clause-clause subsumption calls : 6
% 0.35/0.58  # Rewrite failures with RHS unbound    : 0
% 0.35/0.58  # BW rewrite match attempts            : 2
% 0.35/0.58  # BW rewrite match successes           : 1
% 0.35/0.58  # Condensation attempts                : 0
% 0.35/0.58  # Condensation successes               : 0
% 0.35/0.58  # Termbank termtop insertions          : 16996
% 0.35/0.58  # Search garbage collected termcells   : 5565
% 0.35/0.58  
% 0.35/0.58  # -------------------------------------------------
% 0.35/0.58  # User time                : 0.041 s
% 0.35/0.58  # System time              : 0.013 s
% 0.35/0.58  # Total time               : 0.054 s
% 0.35/0.58  # Maximum resident set size: 3416 pages
% 0.35/0.58  
% 0.35/0.58  # -------------------------------------------------
% 0.35/0.58  # User time                : 0.058 s
% 0.35/0.58  # System time              : 0.018 s
% 0.35/0.58  # Total time               : 0.076 s
% 0.35/0.58  # Maximum resident set size: 2212 pages
% 0.35/0.58  % E---3.1 exiting
% 0.35/0.58  % E exiting
%------------------------------------------------------------------------------