TSTP Solution File: SEU647^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU647^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 03:28:49 EDT 2024

% Result   : Theorem 0.18s 0.50s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  199
% Syntax   : Number of formulae    :  215 (  15 unt; 187 typ;   0 def)
%            Number of atoms       :  612 (  40 equ;   0 cnn)
%            Maximal formula atoms :  188 (  21 avg)
%            Number of connectives : 1311 (  17   ~;  14   |; 196   &; 727   @)
%                                         (  10 <=>; 347  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  205 (  24 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  189 ( 187 usr; 169 con; 0-3 aty)
%            Number of variables   :  132 (   9   ^  99   !;  24   ?; 132   :)

% 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_29,type,
    powerset: $i > $i ).

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

thf(decl_31,type,
    setunion: $i > $i ).

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_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_135,type,
    binunion: $i > $i > $i ).

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_174,type,
    iskpair: $i > $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_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_212,type,
    kfst: $i > $i ).

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

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

thf(decl_215,type,
    esk1_2: $i > $i > $i ).

thf(decl_216,type,
    esk2_2: $i > $i > $i ).

thf(decl_217,type,
    esk3_2: $i > $i > $i ).

thf(decl_218,type,
    esk4_2: $i > $i > $i ).

thf(decl_219,type,
    esk5_3: $i > $i > $i > $i ).

thf(decl_220,type,
    esk6_3: $i > $i > $i > $i ).

thf(decl_221,type,
    esk7_3: $i > $i > $i > $i ).

thf(decl_222,type,
    esk8_3: $i > $i > $i > $i ).

thf(decl_223,type,
    esk9_0: $i ).

thf(decl_224,type,
    esk10_0: $i ).

thf(decl_225,type,
    esk11_0: $i ).

thf(decl_226,type,
    esk12_0: $i ).

thf(iskpair,axiom,
    ( iskpair
    = ( ^ [X4: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ X4 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ X4 ) )
              & ( X4
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).

thf(kfstsingleton,axiom,
    ( kfstsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).

thf(kpairp,axiom,
    ( kpairp
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).

thf(cartprodmempair,axiom,
    ( cartprodmempair
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( iskpair @ X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).

thf(kpairiskpair,axiom,
    ( kpairiskpair
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).

thf(setukpairinjL2,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
                                                                                                                                                                                                                                                                                                                                       => ! [X2: $i,X3: $i,X14: $i,X18: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                           => ( X2 = X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).

thf(cartprodfstin,axiom,
    ( cartprodfstin
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( in @ ( kfst @ X18 ) @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).

thf(kfstpairEq,axiom,
    ( kfstpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( kfst @ ( kpair @ X2 @ X3 ) )
        = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).

thf(cartprodmempair1,axiom,
    ( cartprodmempair1
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ? [X3: $i] :
                ( ( in @ X3 @ X5 )
                & ( X18
                  = ( kpair @ X2 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(cartprodpairin,axiom,
    ( cartprodpairin
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).

thf(ubforcartprodlem3,axiom,
    ( ubforcartprodlem3
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).

thf(kpair,axiom,
    ( kpair
    = ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).

thf(c_0_12,plain,
    ( iskpair
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ Z0 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ Z0 ) )
              & ( Z0
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iskpair]) ).

thf(c_0_13,plain,
    ( kfstsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[kfstsingleton]) ).

thf(c_0_14,axiom,
    ( kpairp
    = ( ! [X2: $i,X3: $i] :
        ? [X54: $i] :
          ( ( in @ X54 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
          & ? [X55: $i] :
              ( ( in @ X55 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
              & ( ( kpair @ X2 @ X3 )
                = ( setadjoin @ ( setadjoin @ X54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X54 @ ( setadjoin @ X55 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[kpairp,c_0_12]) ).

thf(c_0_15,plain,
    ( kfstsingleton
    = ( ! [X18: $i] :
          ( ? [X58: $i] :
              ( ( in @ X58 @ ( setunion @ X18 ) )
              & ? [X59: $i] :
                  ( ( in @ X59 @ ( setunion @ X18 ) )
                  & ( X18
                    = ( setadjoin @ ( setadjoin @ X58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X58 @ ( setadjoin @ X59 @ emptyset ) ) @ emptyset ) ) ) ) )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ X18 )
              @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_13,c_0_12]) ).

thf(c_0_16,axiom,
    ( cartprodmempair
    = ( ! [X4: $i,X5: $i,X18: $i] :
          ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
         => ? [X56: $i] :
              ( ( in @ X56 @ ( setunion @ X18 ) )
              & ? [X57: $i] :
                  ( ( in @ X57 @ ( setunion @ X18 ) )
                  & ( X18
                    = ( setadjoin @ ( setadjoin @ X56 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X56 @ ( setadjoin @ X57 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[cartprodmempair,c_0_12]) ).

thf(c_0_17,axiom,
    ( kpairiskpair
    = ( ! [X2: $i,X3: $i] :
        ? [X52: $i] :
          ( ( in @ X52 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [X53: $i] :
              ( ( in @ X53 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X52 @ ( setadjoin @ X53 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[kpairiskpair,c_0_12]) ).

thf(c_0_18,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
                                                                                                                                                                                                                                                                                 => ( ! [X60: $i,X61: $i] :
                                                                                                                                                                                                                                                                                      ? [X62: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X62 @ ( setunion @ ( setadjoin @ ( setadjoin @ X60 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X60 @ ( setadjoin @ X61 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                        & ? [X63: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X63 @ ( setunion @ ( setadjoin @ ( setadjoin @ X60 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X60 @ ( setadjoin @ X61 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                            & ( ( setadjoin @ ( setadjoin @ X60 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X60 @ ( setadjoin @ X61 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X62 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X62 @ ( setadjoin @ X63 @ emptyset ) ) @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X64: $i,X65: $i] :
                                                                                                                                                                                                                                                                                        ? [X66: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X66 @ ( setunion @ ( kpair @ X64 @ X65 ) ) )
                                                                                                                                                                                                                                                                                          & ? [X67: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X67 @ ( setunion @ ( kpair @ X64 @ X65 ) ) )
                                                                                                                                                                                                                                                                                              & ( ( kpair @ X64 @ X65 )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X66 @ ( setadjoin @ X67 @ emptyset ) ) @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( singletonsubset
                                                                                                                                                                                                                                                                                       => ( singletoninpowerset
                                                                                                                                                                                                                                                                                         => ( singletoninpowunion
                                                                                                                                                                                                                                                                                           => ( upairset2E
                                                                                                                                                                                                                                                                                             => ( upairsubunion
                                                                                                                                                                                                                                                                                               => ( upairinpowunion
                                                                                                                                                                                                                                                                                                 => ( ubforcartprodlem1
                                                                                                                                                                                                                                                                                                   => ( ubforcartprodlem2
                                                                                                                                                                                                                                                                                                     => ( ! [X68: $i,X69: $i,X70: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X70 @ X68 )
                                                                                                                                                                                                                                                                                                           => ! [X71: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X71 @ X69 )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X70 @ X71 ) @ ( powerset @ ( powerset @ ( binunion @ X68 @ X69 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X72: $i,X73: $i,X74: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X74 @ X72 )
                                                                                                                                                                                                                                                                                                             => ! [X75: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X75 @ X73 )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X74 @ X75 ) @ ( cartprod @ X72 @ X73 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X76: $i,X77: $i,X78: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X78 @ ( cartprod @ X76 @ X77 ) )
                                                                                                                                                                                                                                                                                                               => ? [X79: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X79 @ X76 )
                                                                                                                                                                                                                                                                                                                    & ? [X80: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X80 @ X77 )
                                                                                                                                                                                                                                                                                                                        & ( X78
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X79 @ X80 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X81: $i,X82: $i,X83: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X83 @ ( cartprod @ X81 @ X82 ) )
                                                                                                                                                                                                                                                                                                                 => ? [X84: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X84 @ ( setunion @ X83 ) )
                                                                                                                                                                                                                                                                                                                      & ? [X85: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X85 @ ( setunion @ X83 ) )
                                                                                                                                                                                                                                                                                                                          & ( X83
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X84 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X84 @ ( setadjoin @ X85 @ emptyset ) ) @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( setunionE2
                                                                                                                                                                                                                                                                                                               => ( setunionsingleton1
                                                                                                                                                                                                                                                                                                                 => ( setunionsingleton2
                                                                                                                                                                                                                                                                                                                   => ( setunionsingleton
                                                                                                                                                                                                                                                                                                                     => ( singletonprop
                                                                                                                                                                                                                                                                                                                       => ( ex1E1
                                                                                                                                                                                                                                                                                                                         => ( ex1I
                                                                                                                                                                                                                                                                                                                           => ( ex1I2
                                                                                                                                                                                                                                                                                                                             => ( singletonsuniq
                                                                                                                                                                                                                                                                                                                               => ( setukpairinjL1
                                                                                                                                                                                                                                                                                                                                 => ( ! [X86: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ? [X87: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X87 @ ( setunion @ X86 ) )
                                                                                                                                                                                                                                                                                                                                            & ? [X88: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X88 @ ( setunion @ X86 ) )
                                                                                                                                                                                                                                                                                                                                                & ( X86
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X87 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X87 @ ( setadjoin @ X88 @ emptyset ) ) @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                       => ( singleton
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X86 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X86 ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( theprop
                                                                                                                                                                                                                                                                                                                                     => ( ! [X89: $i,X90: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X89 @ X90 ) )
                                                                                                                                                                                                                                                                                                                                            = X89 )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X91: $i,X92: $i,X93: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X93 @ ( cartprod @ X91 @ X92 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X93 ) @ X91 ) )
                                                                                                                                                                                                                                                                                                                                         => ! [X2: $i,X3: $i,X14: $i,X18: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                             => ( X2 = X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setukpairinjL2]),c_0_14]),cartprodfstin]),c_0_15]),c_0_16]),c_0_17]),kfstpairEq]),cartprodmempair1]),cartprodpairin]),ubforcartprodlem3]) ).

thf(c_0_19,plain,
    ! [X94: $i,X95: $i] :
      ( ( kpair @ X94 @ X95 )
      = ( setadjoin @ ( setadjoin @ X94 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X94 @ ( setadjoin @ X95 @ emptyset ) ) @ emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).

thf(c_0_20,negated_conjecture,
    ! [X96: $i,X97: $i,X100: $i,X101: $i,X104: $i,X105: $i,X106: $i,X107: $i,X108: $i,X109: $i,X110: $i,X111: $i,X112: $i,X113: $i,X114: $i,X117: $i,X118: $i,X119: $i,X122: $i,X123: $i,X124: $i,X125: $i,X126: $i,X127: $i,X128: $i,X129: $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
      & ( in @ ( esk1_2 @ X96 @ X97 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X97 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ ( esk2_2 @ X96 @ X97 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X97 @ emptyset ) ) @ emptyset ) ) ) )
      & ( ( setadjoin @ ( setadjoin @ X96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X96 @ ( setadjoin @ X97 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ ( esk1_2 @ X96 @ X97 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X96 @ X97 ) @ ( setadjoin @ ( esk2_2 @ X96 @ X97 ) @ emptyset ) ) @ emptyset ) ) )
      & ( in @ ( esk3_2 @ X100 @ X101 ) @ ( setunion @ ( kpair @ X100 @ X101 ) ) )
      & ( in @ ( esk4_2 @ X100 @ X101 ) @ ( setunion @ ( kpair @ X100 @ X101 ) ) )
      & ( ( kpair @ X100 @ X101 )
        = ( setadjoin @ ( setadjoin @ ( esk3_2 @ X100 @ X101 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk3_2 @ X100 @ X101 ) @ ( setadjoin @ ( esk4_2 @ X100 @ X101 ) @ emptyset ) ) @ emptyset ) ) )
      & singletonsubset
      & singletoninpowerset
      & singletoninpowunion
      & upairset2E
      & upairsubunion
      & upairinpowunion
      & ubforcartprodlem1
      & ubforcartprodlem2
      & ( ~ ( in @ X106 @ X104 )
        | ~ ( in @ X107 @ X105 )
        | ( in @ ( kpair @ X106 @ X107 ) @ ( powerset @ ( powerset @ ( binunion @ X104 @ X105 ) ) ) ) )
      & ( ~ ( in @ X110 @ X108 )
        | ~ ( in @ X111 @ X109 )
        | ( in @ ( kpair @ X110 @ X111 ) @ ( cartprod @ X108 @ X109 ) ) )
      & ( ( in @ ( esk5_3 @ X112 @ X113 @ X114 ) @ X112 )
        | ~ ( in @ X114 @ ( cartprod @ X112 @ X113 ) ) )
      & ( ( in @ ( esk6_3 @ X112 @ X113 @ X114 ) @ X113 )
        | ~ ( in @ X114 @ ( cartprod @ X112 @ X113 ) ) )
      & ( ( X114
          = ( kpair @ ( esk5_3 @ X112 @ X113 @ X114 ) @ ( esk6_3 @ X112 @ X113 @ X114 ) ) )
        | ~ ( in @ X114 @ ( cartprod @ X112 @ X113 ) ) )
      & ( ( in @ ( esk7_3 @ X117 @ X118 @ X119 ) @ ( setunion @ X119 ) )
        | ~ ( in @ X119 @ ( cartprod @ X117 @ X118 ) ) )
      & ( ( in @ ( esk8_3 @ X117 @ X118 @ X119 ) @ ( setunion @ X119 ) )
        | ~ ( in @ X119 @ ( cartprod @ X117 @ X118 ) ) )
      & ( ( X119
          = ( setadjoin @ ( setadjoin @ ( esk7_3 @ X117 @ X118 @ X119 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk7_3 @ X117 @ X118 @ X119 ) @ ( setadjoin @ ( esk8_3 @ X117 @ X118 @ X119 ) @ emptyset ) ) @ emptyset ) ) )
        | ~ ( in @ X119 @ ( cartprod @ X117 @ X118 ) ) )
      & setunionE2
      & setunionsingleton1
      & setunionsingleton2
      & setunionsingleton
      & singletonprop
      & ex1E1
      & ex1I
      & ex1I2
      & singletonsuniq
      & setukpairinjL1
      & ( ~ ( in @ X123 @ ( setunion @ X122 ) )
        | ~ ( in @ X124 @ ( setunion @ X122 ) )
        | ( X122
         != ( setadjoin @ ( setadjoin @ X123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X123 @ ( setadjoin @ X124 @ emptyset ) ) @ emptyset ) ) )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X122 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X122 ) ) ) )
      & theprop
      & ( ( kfst @ ( kpair @ X125 @ X126 ) )
        = X125 )
      & ( ~ ( in @ X129 @ ( cartprod @ X127 @ X128 ) )
        | ( in @ ( kfst @ X129 ) @ X127 ) )
      & ( ( setadjoin @ ( setadjoin @ esk9_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk9_0 @ ( setadjoin @ esk10_0 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ esk11_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk11_0 @ ( setadjoin @ esk12_0 @ emptyset ) ) @ emptyset ) ) )
      & ( esk9_0 != esk11_0 ) ),
    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_18])])])])])]) ).

thf(c_0_21,plain,
    ! [X134: $i,X135: $i] :
      ( ( kpair @ X134 @ X135 )
      = ( setadjoin @ ( setadjoin @ X134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X134 @ ( setadjoin @ X135 @ emptyset ) ) @ emptyset ) ) ),
    inference(variable_rename,[status(thm)],[c_0_19]) ).

thf(c_0_22,negated_conjecture,
    ( ( setadjoin @ ( setadjoin @ esk9_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk9_0 @ ( setadjoin @ esk10_0 @ emptyset ) ) @ emptyset ) )
    = ( setadjoin @ ( setadjoin @ esk11_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk11_0 @ ( setadjoin @ esk12_0 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_23,plain,
    ! [X2: $i,X3: $i] :
      ( ( kpair @ X2 @ X3 )
      = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_24,negated_conjecture,
    ! [X3: $i,X2: $i] :
      ( ( kfst @ ( kpair @ X2 @ X3 ) )
      = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_25,negated_conjecture,
    ( ( kpair @ esk9_0 @ esk10_0 )
    = ( kpair @ esk11_0 @ esk12_0 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).

thf(c_0_26,negated_conjecture,
    esk9_0 != esk11_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_27,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_24]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SEU647^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 16:08:37 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.18/0.45  Running higher-order theorem proving
% 0.18/0.45  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
% 0.18/0.50  # Version: 3.1.0-ho
% 0.18/0.50  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.18/0.50  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting ehoh_best5 with 300s (1) cores
% 0.18/0.50  # Starting almost_fo_3_lam with 300s (1) cores
% 0.18/0.50  # Starting new_bool_5 with 300s (1) cores
% 0.18/0.50  # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.50  # Starting ho_unfolding_8 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_5 with 300s (1) cores
% 0.18/0.50  # new_ho_5 with pid 24795 completed with status 0
% 0.18/0.50  # Result found by new_ho_5
% 0.18/0.50  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.18/0.50  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting ehoh_best5 with 300s (1) cores
% 0.18/0.50  # Starting almost_fo_3_lam with 300s (1) cores
% 0.18/0.50  # Starting new_bool_5 with 300s (1) cores
% 0.18/0.50  # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.50  # Starting ho_unfolding_8 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_5 with 300s (1) cores
% 0.18/0.50  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.18/0.50  # Search class: HHUSM-FFMM32-MHFMMFNN
% 0.18/0.50  # partial match(4): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.50  # new_ho_10 with pid 24796 completed with status 0
% 0.18/0.50  # Result found by new_ho_10
% 0.18/0.50  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.18/0.50  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting ehoh_best5 with 300s (1) cores
% 0.18/0.50  # Starting almost_fo_3_lam with 300s (1) cores
% 0.18/0.50  # Starting new_bool_5 with 300s (1) cores
% 0.18/0.50  # Starting pre_casc_3 with 300s (1) cores
% 0.18/0.50  # Starting ho_unfolding_8 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.18/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.50  # Starting new_ho_5 with 300s (1) cores
% 0.18/0.50  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.18/0.50  # Search class: HHUSM-FFMM32-MHFMMFNN
% 0.18/0.50  # partial match(4): HHUSS-FFSF32-SHFMMFNN
% 0.18/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.50  # Preprocessing time       : 0.003 s
% 0.18/0.50  # Presaturation interreduction done
% 0.18/0.50  
% 0.18/0.50  # Proof found!
% 0.18/0.50  # SZS status Theorem
% 0.18/0.50  # SZS output start CNFRefutation
% See solution above
% 0.18/0.50  # Parsed axioms                        : 363
% 0.18/0.50  # Removed by relevancy pruning/SinE    : 351
% 0.18/0.50  # Initial clauses                      : 176
% 0.18/0.50  # Removed in clause preprocessing      : 0
% 0.18/0.50  # Initial clauses in saturation        : 176
% 0.18/0.50  # Processed clauses                    : 336
% 0.18/0.50  # ...of these trivial                  : 0
% 0.18/0.50  # ...subsumed                          : 0
% 0.18/0.50  # ...remaining for further processing  : 336
% 0.18/0.50  # Other redundant clauses eliminated   : 1
% 0.18/0.50  # Clauses deleted for lack of memory   : 0
% 0.18/0.50  # Backward-subsumed                    : 0
% 0.18/0.50  # Backward-rewritten                   : 1
% 0.18/0.50  # Generated clauses                    : 2
% 0.18/0.50  # ...of the previous two non-redundant : 2
% 0.18/0.50  # ...aggressively subsumed             : 0
% 0.18/0.50  # Contextual simplify-reflections      : 0
% 0.18/0.50  # Paramodulations                      : 1
% 0.18/0.50  # Factorizations                       : 0
% 0.18/0.50  # NegExts                              : 0
% 0.18/0.50  # Equation resolutions                 : 1
% 0.18/0.50  # Disequality decompositions           : 0
% 0.18/0.50  # Total rewrite steps                  : 10
% 0.18/0.50  # ...of those cached                   : 2
% 0.18/0.50  # Propositional unsat checks           : 0
% 0.18/0.50  #    Propositional check models        : 0
% 0.18/0.50  #    Propositional check unsatisfiable : 0
% 0.18/0.50  #    Propositional clauses             : 0
% 0.18/0.50  #    Propositional clauses after purity: 0
% 0.18/0.50  #    Propositional unsat core size     : 0
% 0.18/0.50  #    Propositional preprocessing time  : 0.000
% 0.18/0.50  #    Propositional encoding time       : 0.000
% 0.18/0.50  #    Propositional solver time         : 0.000
% 0.18/0.50  #    Success case prop preproc time    : 0.000
% 0.18/0.50  #    Success case prop encoding time   : 0.000
% 0.18/0.50  #    Success case prop solver time     : 0.000
% 0.18/0.50  # Current number of processed clauses  : 158
% 0.18/0.50  #    Positive orientable unit clauses  : 156
% 0.18/0.50  #    Positive unorientable unit clauses: 0
% 0.18/0.50  #    Negative unit clauses             : 1
% 0.18/0.50  #    Non-unit-clauses                  : 1
% 0.18/0.50  # Current number of unprocessed clauses: 18
% 0.18/0.50  # ...number of literals in the above   : 32
% 0.18/0.50  # Current number of archived formulas  : 0
% 0.18/0.50  # Current number of archived clauses   : 177
% 0.18/0.50  # Clause-clause subsumption calls (NU) : 69
% 0.18/0.50  # Rec. Clause-clause subsumption calls : 52
% 0.18/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.18/0.50  # Unit Clause-clause subsumption calls : 0
% 0.18/0.50  # Rewrite failures with RHS unbound    : 0
% 0.18/0.50  # BW rewrite match attempts            : 2
% 0.18/0.50  # BW rewrite match successes           : 2
% 0.18/0.50  # Condensation attempts                : 336
% 0.18/0.50  # Condensation successes               : 0
% 0.18/0.50  # Termbank termtop insertions          : 11011
% 0.18/0.50  # Search garbage collected termcells   : 4132
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.020 s
% 0.18/0.50  # System time              : 0.006 s
% 0.18/0.50  # Total time               : 0.026 s
% 0.18/0.50  # Maximum resident set size: 3196 pages
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.031 s
% 0.18/0.50  # System time              : 0.009 s
% 0.18/0.50  # Total time               : 0.040 s
% 0.18/0.50  # Maximum resident set size: 2096 pages
% 0.18/0.50  % E---3.1 exiting
% 0.18/0.50  % E exiting
%------------------------------------------------------------------------------