TSTP Solution File: SEU588^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU588^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 03:28:23 EDT 2024

% Result   : Theorem 2.55s 0.87s
% Output   : CNFRefutation 2.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  262
% Syntax   : Number of formulae    :  293 (   3 unt; 157 typ;   0 def)
%            Number of atoms       : 1119 ( 176 equ;   0 cnn)
%            Maximal formula atoms :  327 (   8 avg)
%            Number of connectives : 3632 ( 274   ~; 271   |; 215   &;2162   @)
%                                         ( 162 <=>; 548  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  396 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  240 ( 240   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  160 ( 157 usr; 111 con; 0-4 aty)
%            Number of variables   :  930 (  59   ^ 808   !;  63   ?; 930   :)

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

thf(decl_23,type,
    exu: ( $i > $o ) > $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_33,type,
    omega: $i ).

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_40,type,
    descr: ( $i > $o ) > $i ).

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_47,type,
    prop2set: $o > $i ).

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_57,type,
    nonempty: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_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,
    epred1_0: $o ).

thf(decl_143,type,
    esk1_2: $i > $i > $i ).

thf(decl_144,type,
    esk2_2: $i > $i > $i ).

thf(decl_145,type,
    esk3_2: $i > $i > $i ).

thf(decl_146,type,
    esk4_1: $i > $i ).

thf(decl_147,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_148,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_149,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_150,type,
    esk8_1: $i > $i ).

thf(decl_151,type,
    esk9_1: ( $i > $o ) > $i ).

thf(decl_152,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_153,type,
    esk11_2: $i > $i > $i ).

thf(decl_154,type,
    esk12_2: $i > $i > $i ).

thf(decl_155,type,
    esk13_1: $i > $i ).

thf(decl_156,type,
    esk14_1: $i > $i ).

thf(decl_157,type,
    esk15_1: $i > $i ).

thf(decl_158,type,
    esk16_2: $i > $i > $i ).

thf(decl_159,type,
    esk17_3: $i > $i > $o > $i ).

thf(decl_160,type,
    esk18_1: ( $i > $o ) > $i ).

thf(decl_161,type,
    esk19_1: $i > $i ).

thf(decl_162,type,
    esk20_2: $i > ( $i > $o ) > $i ).

thf(decl_163,type,
    esk21_2: $i > ( $i > $o ) > $i ).

thf(decl_164,type,
    esk22_2: $i > ( $i > $o ) > $i ).

thf(decl_165,type,
    esk23_2: $i > ( $i > $o ) > $i ).

thf(decl_166,type,
    esk24_2: $i > ( $i > $o ) > $i ).

thf(decl_167,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_168,type,
    esk26_2: ( $i > $o ) > $i > $i ).

thf(decl_169,type,
    esk27_1: ( $i > $o ) > $i ).

thf(decl_170,type,
    esk28_1: ( $i > $o ) > $i ).

thf(decl_171,type,
    esk29_2: ( $i > $o ) > $i > $i ).

thf(decl_172,type,
    esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_173,type,
    esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_174,type,
    esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_175,type,
    esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_176,type,
    esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_177,type,
    esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_178,type,
    esk36_2: $i > $i > $i ).

thf(decl_179,type,
    esk37_2: $i > $i > $i ).

thf(decl_180,type,
    esk38_0: $i ).

thf(decl_181,type,
    esk39_0: $i ).

thf(setoftrueEq,axiom,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [X2: $i] : $true )
        = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).

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

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

thf(exuI1,axiom,
    ( exuI1
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).

thf(exuE2,axiom,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).

thf(emptyE1,axiom,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [X2: $i] : ( X1 @ X2 ) )
            = emptyset )
         => ~ $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).

thf(exuI3,axiom,
    ( exuI3
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] : ( X1 @ X2 )
       => ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
         => ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).

thf(exuI2,axiom,
    ( exuI2
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).

thf(exuE3u,axiom,
    ( exuE3u
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).

thf(exu__Cong,axiom,
    ( exu__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
        <=> ( exu
            @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).

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

thf(descr__Cong,axiom,
    ( descr__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
         => ( ( exu
              @ ^ [X2: $i] : ( X17 @ X2 ) )
           => ( ( descr
                @ ^ [X2: $i] : ( X1 @ X2 ) )
              = ( descr
                @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).

thf(dsetconstr__Cong,axiom,
    ( dsetconstr__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X1: $i > $o,X17: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( X2 = X3 )
                     => ( ( X1 @ X2 )
                      <=> ( X17 @ X3 ) ) ) ) )
           => ( ( dsetconstr @ X4
                @ ^ [X2: $i] : ( X1 @ X2 ) )
              = ( dsetconstr @ X5
                @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).

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

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

thf(exuE3e,axiom,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).

thf(exuE1,axiom,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).

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

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

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

thf(descrp,axiom,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ( X1
          @ ( descr
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).

thf(replAx,axiom,
    ( replAx
  <=> ! [X6: $i > $i > $o,X4: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( exu
              @ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
       => ? [X5: $i] :
          ! [X2: $i] :
            ( ( in @ X2 @ X5 )
          <=> ? [X3: $i] :
                ( ( in @ X3 @ X4 )
                & ( X6 @ X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).

thf(binunionRsub,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
                                                                                                                                                                                                                 => ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).

thf(binunionLsub,axiom,
    ( binunionLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).

thf(notequalI1,axiom,
    ( notequalI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ( subset @ X4 @ X5 )
       => ( X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).

thf(setadjoinE,axiom,
    ( setadjoinE
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ! [X12: $o] :
            ( ( ( X3 = X2 )
             => X12 )
           => ( ( ( in @ X3 @ X4 )
               => X12 )
             => X12 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).

thf(notequalI2,axiom,
    ( notequalI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( X4 != X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).

thf(subsetRefl,axiom,
    ( subsetRefl
  <=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).

thf(subsetTrans,axiom,
    ( subsetTrans
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X7 )
         => ( subset @ X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).

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

thf(setadjoinSub,axiom,
    ( setadjoinSub
  <=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).

thf(setadjoinSub2,axiom,
    ( setadjoinSub2
  <=> ! [X4: $i,X2: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).

thf(subset2powerset,axiom,
    ( subset2powerset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( in @ X4 @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).

thf(setextsub,axiom,
    ( setextsub
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X4 )
         => ( X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).

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

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
  <=> ! [X4: $i] :
        ( ( subset @ X4 @ emptyset )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).

thf(powersetI1,axiom,
    ( powersetI1
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).

thf(emptyinPowerset,axiom,
    ( emptyinPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).

thf(powersetE1,axiom,
    ( powersetE1
  <=> ! [X4: $i,X5: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).

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

thf(emptyInPowerset,axiom,
    ( emptyInPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).

thf(powersetsubset,axiom,
    ( powersetsubset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).

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

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

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

thf(upairset2IR,axiom,
    ( upairset2IR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).

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

thf(setunionE,axiom,
    ( setunionE
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
       => ! [X13: $o] :
            ( ! [X5: $i] :
                ( ( in @ X2 @ X5 )
               => ( ( in @ X5 @ X4 )
                 => X13 ) )
           => X13 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).

thf(binunionEcases,axiom,
    ( binunionEcases
  <=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
        ( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
       => ( ( ( in @ X2 @ X4 )
           => X19 )
         => ( ( ( in @ X2 @ X5 )
             => X19 )
           => X19 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).

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

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

thf(nonemptyImpWitness,axiom,
    ( nonemptyImpWitness
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).

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

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

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

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

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

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

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

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

thf(quantDeMorgan1,axiom,
    ( quantDeMorgan1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).

thf(quantDeMorgan2,axiom,
    ( quantDeMorgan2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) )
       => ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).

thf(quantDeMorgan3,axiom,
    ( quantDeMorgan3
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).

thf(quantDeMorgan4,axiom,
    ( quantDeMorgan4
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).

thf(prop2setI,axiom,
    ( prop2setI
  <=> ! [X15: $o] :
        ( X15
       => ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).

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

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

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

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

thf(emptyset__Cong,axiom,
    ( emptyset__Cong
  <=> ( emptyset = emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).

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

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

thf(setunion__Cong,axiom,
    ( setunion__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( setunion @ X4 )
          = ( setunion @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).

thf(omega__Cong,axiom,
    ( omega__Cong
  <=> ( omega = omega ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).

thf(subsetI1,axiom,
    ( subsetI1
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).

thf(eqimpsubset2,axiom,
    ( eqimpsubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).

thf(eqimpsubset1,axiom,
    ( eqimpsubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).

thf(emptysetsubset,axiom,
    ( emptysetsubset
  <=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).

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

thf(subsetE2,axiom,
    ( subsetE2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).

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

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

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
  <=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).

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

thf(nonemptyI1,axiom,
    ( nonemptyI1
  <=> ! [X4: $i] :
        ( ? [X2: $i] : ( in @ X2 @ X4 )
       => ( nonempty @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).

thf(emptyI,axiom,
    ( emptyI
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).

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

thf(notinemptyset,axiom,
    ( notinemptyset
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ~ $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).

thf(emptysetE,axiom,
    ( emptysetE
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ! [X11: $o] : X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).

thf(prop2setE,axiom,
    ( prop2setE
  <=> ! [X10: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X10 ) )
       => X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).

thf(wellorderingAx,axiom,
    ( wellorderingAx
  <=> ! [X4: $i] :
      ? [X5: $i] :
        ( ! [X7: $i] :
            ( ( in @ X7 @ X5 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X7 )
               => ( in @ X2 @ X4 ) ) )
        & ! [X2: $i,X3: $i] :
            ( ( ( in @ X2 @ X4 )
              & ( in @ X3 @ X4 ) )
           => ( ! [X7: $i] :
                  ( ( in @ X7 @ X5 )
                 => ( ( in @ X2 @ X7 )
                  <=> ( in @ X3 @ X7 ) ) )
             => ( X2 = X3 ) ) )
        & ! [X7: $i,X8: $i] :
            ( ( ( in @ X7 @ X5 )
              & ( in @ X8 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X8 ) )
              | ! [X2: $i] :
                  ( ( in @ X2 @ X8 )
                 => ( in @ X2 @ X7 ) ) ) )
        & ! [X7: $i] :
            ( ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X4 ) )
              & ? [X2: $i] : ( in @ X2 @ X7 ) )
           => ? [X8: $i,X2: $i] :
                ( ( in @ X8 @ X5 )
                & ( in @ X2 @ X7 )
                & ~ ? [X3: $i] :
                      ( ( in @ X3 @ X8 )
                      & ( in @ X3 @ X7 ) )
                & ! [X9: $i] :
                    ( ( in @ X9 @ X5 )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X9 )
                         => ( in @ X3 @ X8 ) )
                      | ( in @ X2 @ X9 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).

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

thf(omegaIndAx,axiom,
    ( omegaIndAx
  <=> ! [X4: $i] :
        ( ( ( in @ emptyset @ X4 )
          & ! [X2: $i] :
              ( ( ( in @ X2 @ omega )
                & ( in @ X2 @ X4 ) )
             => ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ omega )
           => ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).

thf(omegaSAx,axiom,
    ( omegaSAx
  <=> ! [X2: $i] :
        ( ( in @ X2 @ omega )
       => ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).

thf(omega0Ax,axiom,
    ( omega0Ax
  <=> ( in @ emptyset @ omega ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).

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

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

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

thf(emptysetAx,axiom,
    ( emptysetAx
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).

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

thf(c_0_104,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_105,plain,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ ( powerset @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[sepInPowerset]) ).

thf(c_0_106,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_107,plain,
    ( exuI1
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
       => ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI1]) ).

thf(c_0_108,plain,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE2]) ).

thf(c_0_109,plain,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) )
            = emptyset )
         => ~ $true ) ) ),
    inference(fof_simplification,[status(thm)],[emptyE1]) ).

thf(c_0_110,plain,
    ( exuI3
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] : ( X1 @ X2 )
       => ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
         => ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI3]) ).

thf(c_0_111,plain,
    ( exuI2
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) )
       => ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI2]) ).

thf(c_0_112,plain,
    ( exuE3u
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3u]) ).

thf(c_0_113,plain,
    ( exu__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        <=> ( exu
            @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu__Cong]) ).

thf(c_0_114,plain,
    ( exuEu
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuEu]) ).

thf(c_0_115,plain,
    ( descr__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) )
         => ( ( exu
              @ ^ [Z0: $i] : ( X17 @ Z0 ) )
           => ( ( descr
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
              = ( descr
                @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descr__Cong]) ).

thf(c_0_116,plain,
    ( dsetconstr__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X1: $i > $o,X17: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( X2 = X3 )
                     => ( ( X1 @ X2 )
                      <=> ( X17 @ X3 ) ) ) ) )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
              = ( dsetconstr @ X5
                @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).

thf(c_0_117,plain,
    ( nonemptyI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( nonempty
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[nonemptyI]) ).

thf(c_0_118,plain,
    ( setbeta
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
        <=> ( X1 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setbeta]) ).

thf(c_0_119,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_120,plain,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE1]) ).

thf(c_0_121,plain,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
       => ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrER]) ).

thf(c_0_122,plain,
    ( dsetconstrEL
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).

thf(c_0_123,plain,
    ( dsetconstrI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrI]) ).

thf(c_0_124,plain,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ( X1
          @ ( descr
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descrp]) ).

thf(c_0_125,plain,
    ( replAx
  <=> ! [X6: $i > $i > $o,X4: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( exu
              @ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
       => ? [X5: $i] :
          ! [X2: $i] :
            ( ( in @ X2 @ X5 )
          <=> ? [X3: $i] :
                ( ( in @ X3 @ X4 )
                & ( X6 @ X3 @ X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[replAx]) ).

thf(c_0_126,plain,
    ( epred1_0
  <=> ! [X327: $i] :
      ? [X328: $i] :
        ( ! [X329: $i] :
            ( ( in @ X329 @ X328 )
           => ! [X330: $i] :
                ( ( in @ X330 @ X329 )
               => ( in @ X330 @ X327 ) ) )
        & ! [X331: $i,X332: $i] :
            ( ( ( in @ X331 @ X327 )
              & ( in @ X332 @ X327 ) )
           => ( ! [X333: $i] :
                  ( ( in @ X333 @ X328 )
                 => ( ( in @ X331 @ X333 )
                  <=> ( in @ X332 @ X333 ) ) )
             => ( X331 = X332 ) ) )
        & ! [X334: $i,X335: $i] :
            ( ( ( in @ X334 @ X328 )
              & ( in @ X335 @ X328 ) )
           => ( ! [X336: $i] :
                  ( ( in @ X336 @ X334 )
                 => ( in @ X336 @ X335 ) )
              | ! [X337: $i] :
                  ( ( in @ X337 @ X335 )
                 => ( in @ X337 @ X334 ) ) ) )
        & ! [X338: $i] :
            ( ( ! [X339: $i] :
                  ( ( in @ X339 @ X338 )
                 => ( in @ X339 @ X327 ) )
              & ? [X340: $i] : ( in @ X340 @ X338 ) )
           => ? [X341: $i,X342: $i] :
                ( ( in @ X341 @ X328 )
                & ( in @ X342 @ X338 )
                & ~ ? [X343: $i] :
                      ( ( in @ X343 @ X341 )
                      & ( in @ X343 @ X338 ) )
                & ! [X344: $i] :
                    ( ( in @ X344 @ X328 )
                   => ( ! [X345: $i] :
                          ( ( in @ X345 @ X344 )
                         => ( in @ X345 @ X341 ) )
                      | ( in @ X342 @ X344 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_127,negated_conjecture,
    ~ ( ! [X300: $i,X301: $i] :
          ( ! [X302: $i] :
              ( ( in @ X302 @ X300 )
            <=> ( in @ X302 @ X301 ) )
         => ( X300 = X301 ) )
     => ( ! [X303: $i] :
            ~ ( in @ X303 @ emptyset )
       => ( ! [X304: $i,X305: $i,X306: $i] :
              ( ( in @ X306 @ ( setadjoin @ X304 @ X305 ) )
            <=> ( ( X306 = X304 )
                | ( in @ X306 @ X305 ) ) )
         => ( ! [X307: $i,X308: $i] :
                ( ( in @ X308 @ ( powerset @ X307 ) )
              <=> ! [X309: $i] :
                    ( ( in @ X309 @ X308 )
                   => ( in @ X309 @ X307 ) ) )
           => ( ! [X310: $i,X311: $i] :
                  ( ( in @ X311 @ ( setunion @ X310 ) )
                <=> ? [X312: $i] :
                      ( ( in @ X311 @ X312 )
                      & ( in @ X312 @ X310 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X313: $i] :
                      ( ( in @ X313 @ omega )
                     => ( in @ ( setadjoin @ X313 @ X313 ) @ omega ) )
                 => ( ! [X314: $i] :
                        ( ( ( in @ emptyset @ X314 )
                          & ! [X315: $i] :
                              ( ( ( in @ X315 @ omega )
                                & ( in @ X315 @ X314 ) )
                             => ( in @ ( setadjoin @ X315 @ X315 ) @ X314 ) ) )
                       => ! [X316: $i] :
                            ( ( in @ X316 @ omega )
                           => ( in @ X316 @ X314 ) ) )
                   => ( ! [X317: $i > $i > $o,X318: $i] :
                          ( ! [X319: $i] :
                              ( ( in @ X319 @ X318 )
                             => ( exu @ ( X317 @ X319 ) ) )
                         => ? [X320: $i] :
                            ! [X321: $i] :
                              ( ( in @ X321 @ X320 )
                            <=> ? [X322: $i] :
                                  ( ( in @ X322 @ X318 )
                                  & ( X317 @ X322 @ X321 ) ) ) )
                     => ( ! [X323: $i] :
                            ( ? [X324: $i] : ( in @ X324 @ X323 )
                           => ? [X325: $i] :
                                ( ( in @ X325 @ X323 )
                                & ~ ? [X326: $i] :
                                      ( ( in @ X326 @ X325 )
                                      & ( in @ X326 @ X323 ) ) ) )
                       => ( epred1_0
                         => ( ! [X346: $i > $o] :
                                ( ( exu @ X346 )
                               => ( X346
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X346 @ Z0 ) ) ) )
                           => ( ! [X347: $i,X348: $i > $o,X349: $i] :
                                  ( ( in @ X349 @ X347 )
                                 => ( ( X348 @ X349 )
                                   => ( in @ X349 @ ( dsetconstr @ X347 @ X348 ) ) ) )
                             => ( ! [X350: $i,X351: $i > $o,X352: $i] :
                                    ( ( in @ X352 @ ( dsetconstr @ X350 @ X351 ) )
                                   => ( in @ X352 @ X350 ) )
                               => ( ! [X353: $i,X354: $i > $o,X355: $i] :
                                      ( ( in @ X355 @ ( dsetconstr @ X353 @ X354 ) )
                                     => ( X354 @ X355 ) )
                                 => ( ! [X356: $i > $o] :
                                        ( ( exu @ X356 )
                                       => ? [X357: $i] :
                                            ( ( X356 @ X357 )
                                            & ! [X358: $i] :
                                                ( ( X356 @ X358 )
                                               => ( X357 = X358 ) ) ) )
                                   => ( ! [X359: $o,X360: $i] :
                                          ( ( in @ X360 @ ( prop2set @ X359 ) )
                                         => X359 )
                                     => ( ! [X361: $i] :
                                            ( ( in @ X361 @ emptyset )
                                           => ! [X362: $o] : X362 )
                                       => ( ! [X363: $i] :
                                              ( ( in @ X363 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X364: $i] :
                                                ~ ( in @ X364 @ emptyset )
                                           => ( ! [X365: $i > $o] :
                                                  ( ( exu @ X365 )
                                                 => ? [X366: $i] : ( X365 @ X366 ) )
                                             => ( ! [X367: $i,X368: $i] :
                                                    ( ! [X369: $i] :
                                                        ( ( in @ X369 @ X367 )
                                                       => ( in @ X369 @ X368 ) )
                                                   => ( ! [X370: $i] :
                                                          ( ( in @ X370 @ X368 )
                                                         => ( in @ X370 @ X367 ) )
                                                     => ( X367 = X368 ) ) )
                                               => ( ! [X371: $i] :
                                                      ( ! [X372: $i] :
                                                          ~ ( in @ X372 @ X371 )
                                                     => ( X371 = emptyset ) )
                                                 => ( ! [X373: $i] :
                                                        ( ! [X374: $i] :
                                                            ~ ( in @ X374 @ X373 )
                                                       => ( X373 = emptyset ) )
                                                   => ( ! [X375: $i,X376: $i > $o,X377: $i] :
                                                          ( ( in @ X377 @ X375 )
                                                         => ( ( in @ X377 @ ( dsetconstr @ X375 @ X376 ) )
                                                          <=> ( X376 @ X377 ) ) )
                                                     => ( ! [X378: $i] :
                                                            ( ( nonempty @ X378 )
                                                           => ? [X379: $i] : ( in @ X379 @ X378 ) )
                                                       => ( ! [X380: $i,X381: $i > $o,X382: $i] :
                                                              ( ( in @ X382 @ X380 )
                                                             => ( ( X381 @ X382 )
                                                               => ( nonempty @ ( dsetconstr @ X380 @ X381 ) ) ) )
                                                         => ( ! [X383: $i] :
                                                                ( ? [X384: $i] : ( in @ X384 @ X383 )
                                                               => ( nonempty @ X383 ) )
                                                           => ( ! [X385: $i,X386: $i] : ( in @ X385 @ ( setadjoin @ X385 @ X386 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X387: $i,X388: $i,X389: $i] :
                                                                      ( ( in @ X389 @ X388 )
                                                                     => ( in @ X389 @ ( setadjoin @ X387 @ X388 ) ) )
                                                                 => ( ! [X390: $i,X391: $i,X392: $i] :
                                                                        ( ( in @ X392 @ ( setadjoin @ X390 @ X391 ) )
                                                                       => ! [X393: $o] :
                                                                            ( ( ( X392 = X390 )
                                                                             => X393 )
                                                                           => ( ( ( in @ X392 @ X391 )
                                                                               => X393 )
                                                                             => X393 ) ) )
                                                                   => ( ! [X394: $i,X395: $i,X396: $i] :
                                                                          ( ( in @ X396 @ ( setadjoin @ X394 @ X395 ) )
                                                                         => ( ( X396 = X394 )
                                                                            | ( in @ X396 @ X395 ) ) )
                                                                     => ( ! [X397: $i] :
                                                                            ( ( dsetconstr @ X397
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X397 )
                                                                       => ( ! [X398: $i,X399: $i] :
                                                                              ( ! [X400: $i] :
                                                                                  ( ( in @ X400 @ X399 )
                                                                                 => ( in @ X400 @ X398 ) )
                                                                             => ( in @ X399 @ ( powerset @ X398 ) ) )
                                                                         => ( ! [X401: $i] : ( in @ emptyset @ ( powerset @ X401 ) )
                                                                           => ( ! [X402: $i] : ( in @ emptyset @ ( powerset @ X402 ) )
                                                                             => ( ! [X403: $i,X404: $i,X405: $i] :
                                                                                    ( ( in @ X404 @ ( powerset @ X403 ) )
                                                                                   => ( ( in @ X405 @ X404 )
                                                                                     => ( in @ X405 @ X403 ) ) )
                                                                               => ( ! [X406: $i,X407: $i,X408: $i] :
                                                                                      ( ( in @ X407 @ X408 )
                                                                                     => ( ( in @ X408 @ X406 )
                                                                                       => ( in @ X407 @ ( setunion @ X406 ) ) ) )
                                                                                 => ( ! [X409: $i,X410: $i] :
                                                                                        ( ( in @ X410 @ ( setunion @ X409 ) )
                                                                                       => ! [X411: $o] :
                                                                                            ( ! [X412: $i] :
                                                                                                ( ( in @ X410 @ X412 )
                                                                                               => ( ( in @ X412 @ X409 )
                                                                                                 => X411 ) )
                                                                                           => X411 ) )
                                                                                   => ( ! [X413: $i,X414: $i] :
                                                                                          ( ( in @ X414 @ X413 )
                                                                                         => ( in @ X414 @ ( powerset @ ( setunion @ X413 ) ) ) )
                                                                                     => ( ! [X415: $i > $o] :
                                                                                            ( ( exu @ X415 )
                                                                                           => ? [X416: $i] :
                                                                                              ! [X417: $i] :
                                                                                                ( ( X415 @ X417 )
                                                                                              <=> ( X417 = X416 ) ) )
                                                                                       => ( ! [X418: $i] :
                                                                                              ( ( nonempty @ X418 )
                                                                                             => ? [X419: $i] :
                                                                                                  ( ( in @ X419 @ X418 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X420: $i,X421: $i] :
                                                                                                ( ( in @ X420 @ ( setadjoin @ X421 @ emptyset ) )
                                                                                               => ( X420 = X421 ) )
                                                                                           => ( ! [X422: $i,X423: $i] :
                                                                                                  ( ( X422 != X423 )
                                                                                                 => ~ ( in @ X423 @ ( setadjoin @ X422 @ emptyset ) ) )
                                                                                             => ( ! [X424: $i,X425: $i] :
                                                                                                    ( ( X424 = X425 )
                                                                                                   => ( in @ X424 @ ( setadjoin @ X425 @ emptyset ) ) )
                                                                                               => ( ! [X426: $i,X427: $i] :
                                                                                                      ( ( in @ X426 @ ( setadjoin @ X427 @ emptyset ) )
                                                                                                     => ( in @ X427 @ ( setadjoin @ X426 @ emptyset ) ) )
                                                                                                 => ( ! [X428: $i,X429: $i,X430: $i] :
                                                                                                        ( ( in @ X430 @ ( setadjoin @ X428 @ ( setadjoin @ X429 @ emptyset ) ) )
                                                                                                       => ( ( X430 = X428 )
                                                                                                          | ( X430 = X429 ) ) )
                                                                                                   => ( ! [X431: $i,X432: $i] : ( in @ X431 @ ( setadjoin @ X431 @ ( setadjoin @ X432 @ emptyset ) ) )
                                                                                                     => ( ! [X433: $i,X434: $i] : ( in @ X434 @ ( setadjoin @ X433 @ ( setadjoin @ X434 @ emptyset ) ) )
                                                                                                       => ( ! [X435: $i,X436: $i > $o] :
                                                                                                              ( ? [X437: $i] :
                                                                                                                  ( ( in @ X437 @ X435 )
                                                                                                                  & ( X436 @ X437 ) )
                                                                                                             => ( ( ( dsetconstr @ X435 @ X436 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X438: $i > $o,X439: $i] :
                                                                                                                ( ( in @ X439 @ emptyset )
                                                                                                               => ( X438 @ X439 ) )
                                                                                                           => ( ! [X440: $i,X441: $i > $o] :
                                                                                                                  ( ~ ! [X442: $i] :
                                                                                                                        ( ( in @ X442 @ X440 )
                                                                                                                       => ( X441 @ X442 ) )
                                                                                                                 => ? [X443: $i] :
                                                                                                                      ( ( in @ X443 @ X440 )
                                                                                                                      & ~ ( X441 @ X443 ) ) )
                                                                                                             => ( ! [X444: $i,X445: $i > $o] :
                                                                                                                    ( ! [X446: $i] :
                                                                                                                        ( ( in @ X446 @ X444 )
                                                                                                                       => ~ ( X445 @ X446 ) )
                                                                                                                   => ~ ? [X447: $i] :
                                                                                                                          ( ( in @ X447 @ X444 )
                                                                                                                          & ( X445 @ X447 ) ) )
                                                                                                               => ( ! [X448: $i,X449: $i > $o] :
                                                                                                                      ( ~ ? [X450: $i] :
                                                                                                                            ( ( in @ X450 @ X448 )
                                                                                                                            & ( X449 @ X450 ) )
                                                                                                                     => ! [X451: $i] :
                                                                                                                          ( ( in @ X451 @ X448 )
                                                                                                                         => ~ ( X449 @ X451 ) ) )
                                                                                                                 => ( ! [X452: $i,X453: $i > $o] :
                                                                                                                        ( ? [X454: $i] :
                                                                                                                            ( ( in @ X454 @ X452 )
                                                                                                                            & ~ ( X453 @ X454 ) )
                                                                                                                       => ~ ! [X455: $i] :
                                                                                                                              ( ( in @ X455 @ X452 )
                                                                                                                             => ( X453 @ X455 ) ) )
                                                                                                                   => ( ! [X456: $o] :
                                                                                                                          ( X456
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X456 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X457: $i,X458: $i > $o] :
                                                                                                                              ( ~ ? [X459: $i] :
                                                                                                                                    ( ( in @ X459 @ X457 )
                                                                                                                                    & ( X458 @ X459 ) )
                                                                                                                             => ! [X460: $i] :
                                                                                                                                  ( ( in @ X460 @ X457 )
                                                                                                                                 => ~ ( X458 @ X460 ) ) )
                                                                                                                         => ( ! [X461: $i,X462: $i > $o] :
                                                                                                                                ( ~ ! [X463: $i] :
                                                                                                                                      ( ( in @ X463 @ X461 )
                                                                                                                                     => ( X462 @ X463 ) )
                                                                                                                               => ? [X464: $i] :
                                                                                                                                    ( ( in @ X464 @ X461 )
                                                                                                                                    & ~ ( X462 @ X464 ) ) )
                                                                                                                           => ( ! [X465: $i > $o] :
                                                                                                                                  ( ? [X466: $i] :
                                                                                                                                      ( ( X465 @ X466 )
                                                                                                                                      & ! [X467: $i] :
                                                                                                                                          ( ( X465 @ X467 )
                                                                                                                                         => ( X466 = X467 ) ) )
                                                                                                                                 => ( exu @ X465 ) )
                                                                                                                             => ( ! [X468: $i > $o] :
                                                                                                                                    ( ? [X469: $i] : ( X468 @ X469 )
                                                                                                                                   => ( ! [X470: $i,X471: $i] :
                                                                                                                                          ( ( X468 @ X470 )
                                                                                                                                         => ( ( X468 @ X471 )
                                                                                                                                           => ( X470 = X471 ) ) )
                                                                                                                                     => ( exu @ X468 ) ) )
                                                                                                                               => ( ! [X472: $i > $o] :
                                                                                                                                      ( ? [X473: $i] :
                                                                                                                                        ! [X474: $i] :
                                                                                                                                          ( ( X472 @ X474 )
                                                                                                                                        <=> ( X474 = X473 ) )
                                                                                                                                     => ( exu @ X472 ) )
                                                                                                                                 => ( ! [X475: $i,X476: $i] :
                                                                                                                                        ( ( X475 = X476 )
                                                                                                                                       => ! [X477: $i,X478: $i] :
                                                                                                                                            ( ( X477 = X478 )
                                                                                                                                           => ( ( in @ X477 @ X475 )
                                                                                                                                             => ( in @ X478 @ X476 ) ) ) )
                                                                                                                                   => ( ! [X479: $i,X480: $i] :
                                                                                                                                          ( ( X479 = X480 )
                                                                                                                                         => ! [X481: $i,X482: $i] :
                                                                                                                                              ( ( X481 = X482 )
                                                                                                                                             => ( ( in @ X481 @ X479 )
                                                                                                                                              <=> ( in @ X482 @ X480 ) ) ) )
                                                                                                                                     => ( ! [X483: $i > $o] :
                                                                                                                                            ( ( exu @ X483 )
                                                                                                                                           => ! [X484: $i,X485: $i] :
                                                                                                                                                ( ( X483 @ X484 )
                                                                                                                                               => ( ( X483 @ X485 )
                                                                                                                                                 => ( X484 = X485 ) ) ) )
                                                                                                                                       => ( ! [X486: $i > $o,X487: $i > $o] :
                                                                                                                                              ( ! [X488: $i,X489: $i] :
                                                                                                                                                  ( ( X488 = X489 )
                                                                                                                                                 => ( ( X486 @ X488 )
                                                                                                                                                  <=> ( X487 @ X489 ) ) )
                                                                                                                                             => ( ( exu @ X486 )
                                                                                                                                              <=> ( exu @ X487 ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X490: $i,X491: $i] :
                                                                                                                                                  ( ( X490 = X491 )
                                                                                                                                                 => ! [X492: $i,X493: $i] :
                                                                                                                                                      ( ( X492 = X493 )
                                                                                                                                                     => ( ( setadjoin @ X490 @ X492 )
                                                                                                                                                        = ( setadjoin @ X491 @ X493 ) ) ) )
                                                                                                                                             => ( ! [X494: $i,X495: $i] :
                                                                                                                                                    ( ( X494 = X495 )
                                                                                                                                                   => ( ( powerset @ X494 )
                                                                                                                                                      = ( powerset @ X495 ) ) )
                                                                                                                                               => ( ! [X496: $i,X497: $i] :
                                                                                                                                                      ( ( X496 = X497 )
                                                                                                                                                     => ( ( setunion @ X496 )
                                                                                                                                                        = ( setunion @ X497 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X498: $i > $o] :
                                                                                                                                                          ( ( exu @ X498 )
                                                                                                                                                         => ! [X499: $i,X500: $i] :
                                                                                                                                                              ( ( X498 @ X499 )
                                                                                                                                                             => ( ( X498 @ X500 )
                                                                                                                                                               => ( X499 = X500 ) ) ) )
                                                                                                                                                     => ( ! [X501: $i > $o,X502: $i > $o] :
                                                                                                                                                            ( ! [X503: $i,X504: $i] :
                                                                                                                                                                ( ( X503 = X504 )
                                                                                                                                                               => ( ( X501 @ X503 )
                                                                                                                                                                <=> ( X502 @ X504 ) ) )
                                                                                                                                                           => ( ( exu @ X501 )
                                                                                                                                                             => ( ( exu @ X502 )
                                                                                                                                                               => ( ( descr @ X501 )
                                                                                                                                                                  = ( descr @ X502 ) ) ) ) )
                                                                                                                                                       => ( ! [X505: $i,X506: $i] :
                                                                                                                                                              ( ( X505 = X506 )
                                                                                                                                                             => ! [X507: $i > $o,X508: $i > $o] :
                                                                                                                                                                  ( ! [X509: $i] :
                                                                                                                                                                      ( ( in @ X509 @ X505 )
                                                                                                                                                                     => ! [X510: $i] :
                                                                                                                                                                          ( ( in @ X510 @ X506 )
                                                                                                                                                                         => ( ( X509 = X510 )
                                                                                                                                                                           => ( ( X507 @ X509 )
                                                                                                                                                                            <=> ( X508 @ X510 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X505 @ X507 )
                                                                                                                                                                    = ( dsetconstr @ X506 @ X508 ) ) ) )
                                                                                                                                                         => ( ! [X511: $i,X512: $i] :
                                                                                                                                                                ( ! [X513: $i] :
                                                                                                                                                                    ( ( in @ X513 @ X511 )
                                                                                                                                                                   => ( in @ X513 @ X512 ) )
                                                                                                                                                               => ( subset @ X511 @ X512 ) )
                                                                                                                                                           => ( ! [X514: $i,X515: $i] :
                                                                                                                                                                  ( ( X514 = X515 )
                                                                                                                                                                 => ( subset @ X515 @ X514 ) )
                                                                                                                                                             => ( ! [X516: $i,X517: $i] :
                                                                                                                                                                    ( ( X516 = X517 )
                                                                                                                                                                   => ( subset @ X516 @ X517 ) )
                                                                                                                                                               => ( ! [X518: $i,X519: $i] :
                                                                                                                                                                      ( ! [X520: $i] :
                                                                                                                                                                          ( ( in @ X520 @ X518 )
                                                                                                                                                                         => ( in @ X520 @ X519 ) )
                                                                                                                                                                     => ( subset @ X518 @ X519 ) )
                                                                                                                                                                 => ( ! [X521: $i] : ( subset @ emptyset @ X521 )
                                                                                                                                                                   => ( ! [X522: $i,X523: $i,X524: $i] :
                                                                                                                                                                          ( ( subset @ X522 @ X523 )
                                                                                                                                                                         => ( ( in @ X524 @ X522 )
                                                                                                                                                                           => ( in @ X524 @ X523 ) ) )
                                                                                                                                                                     => ( ! [X525: $i,X526: $i,X527: $i] :
                                                                                                                                                                            ( ( subset @ X525 @ X526 )
                                                                                                                                                                           => ( ~ ( in @ X527 @ X526 )
                                                                                                                                                                             => ~ ( in @ X527 @ X525 ) ) )
                                                                                                                                                                       => ( ! [X528: $i,X529: $i,X530: $i] :
                                                                                                                                                                              ( ( in @ X530 @ X528 )
                                                                                                                                                                             => ( ~ ( in @ X530 @ X529 )
                                                                                                                                                                               => ~ ( subset @ X528 @ X529 ) ) )
                                                                                                                                                                         => ( ! [X531: $i,X532: $i] :
                                                                                                                                                                                ( ~ ( subset @ X531 @ X532 )
                                                                                                                                                                               => ( X531 != X532 ) )
                                                                                                                                                                           => ( ! [X533: $i,X534: $i,X535: $i] :
                                                                                                                                                                                  ( ( in @ X535 @ X533 )
                                                                                                                                                                                 => ( ~ ( in @ X535 @ X534 )
                                                                                                                                                                                   => ( X533 != X534 ) ) )
                                                                                                                                                                             => ( ! [X536: $i] : ( subset @ X536 @ X536 )
                                                                                                                                                                               => ( ! [X537: $i,X538: $i,X539: $i] :
                                                                                                                                                                                      ( ( subset @ X537 @ X538 )
                                                                                                                                                                                     => ( ( subset @ X538 @ X539 )
                                                                                                                                                                                       => ( subset @ X537 @ X539 ) ) )
                                                                                                                                                                                 => ( ! [X540: $i,X541: $i] : ( subset @ X541 @ ( setadjoin @ X540 @ X541 ) )
                                                                                                                                                                                   => ( ! [X542: $i,X543: $i,X544: $i] :
                                                                                                                                                                                          ( ( subset @ X542 @ X544 )
                                                                                                                                                                                         => ( subset @ X542 @ ( setadjoin @ X543 @ X544 ) ) )
                                                                                                                                                                                     => ( ! [X545: $i,X546: $i] :
                                                                                                                                                                                            ( ( subset @ X545 @ X546 )
                                                                                                                                                                                           => ( in @ X545 @ ( powerset @ X546 ) ) )
                                                                                                                                                                                       => ( ! [X547: $i,X548: $i] :
                                                                                                                                                                                              ( ( subset @ X547 @ X548 )
                                                                                                                                                                                             => ( ( subset @ X548 @ X547 )
                                                                                                                                                                                               => ( X547 = X548 ) ) )
                                                                                                                                                                                         => ( ! [X549: $i] :
                                                                                                                                                                                                ( ( subset @ X549 @ emptyset )
                                                                                                                                                                                               => ( X549 = emptyset ) )
                                                                                                                                                                                           => ( ! [X550: $i,X551: $i] :
                                                                                                                                                                                                  ( ( subset @ X551 @ X550 )
                                                                                                                                                                                                 => ( in @ X551 @ ( powerset @ X550 ) ) )
                                                                                                                                                                                             => ( ! [X552: $i,X553: $i] :
                                                                                                                                                                                                    ( ( in @ X553 @ ( powerset @ X552 ) )
                                                                                                                                                                                                   => ( subset @ X553 @ X552 ) )
                                                                                                                                                                                               => ( ! [X554: $i] : ( in @ X554 @ ( powerset @ X554 ) )
                                                                                                                                                                                                 => ( ! [X555: $i,X556: $i] :
                                                                                                                                                                                                        ( ( subset @ X555 @ X556 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X555 ) @ ( powerset @ X556 ) ) )
                                                                                                                                                                                                   => ( ! [X557: $i,X558: $i > $o] : ( in @ ( dsetconstr @ X557 @ X558 ) @ ( powerset @ X557 ) )
                                                                                                                                                                                                     => ( ! [X559: $i,X560: $i > $o] : ( subset @ ( dsetconstr @ X559 @ X560 ) @ X559 )
                                                                                                                                                                                                       => ( ! [X561: $i,X562: $i,X563: $i] :
                                                                                                                                                                                                              ( ( in @ X563 @ X561 )
                                                                                                                                                                                                             => ( in @ X563 @ ( binunion @ X561 @ X562 ) ) )
                                                                                                                                                                                                         => ( ! [X564: $i,X565: $i] : ( in @ X565 @ ( setadjoin @ X564 @ ( setadjoin @ X565 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X566: $i,X567: $i,X568: $i] :
                                                                                                                                                                                                                  ( ( in @ X568 @ X567 )
                                                                                                                                                                                                                 => ( in @ X568 @ ( binunion @ X566 @ X567 ) ) )
                                                                                                                                                                                                             => ( ! [X569: $i,X570: $i,X571: $i,X572: $o] :
                                                                                                                                                                                                                    ( ( in @ X571 @ ( binunion @ X569 @ X570 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X571 @ X569 )
                                                                                                                                                                                                                       => X572 )
                                                                                                                                                                                                                     => ( ( ( in @ X571 @ X570 )
                                                                                                                                                                                                                         => X572 )
                                                                                                                                                                                                                       => X572 ) ) )
                                                                                                                                                                                                               => ( ! [X573: $i,X574: $i,X575: $i] :
                                                                                                                                                                                                                      ( ( in @ X575 @ ( binunion @ X573 @ X574 ) )
                                                                                                                                                                                                                     => ( ( in @ X575 @ X573 )
                                                                                                                                                                                                                        | ( in @ X575 @ X574 ) ) )
                                                                                                                                                                                                                 => ( ! [X576: $i,X577: $i] : ( subset @ X576 @ ( binunion @ X576 @ X577 ) )
                                                                                                                                                                                                                   => ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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(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(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(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(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(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(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(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(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(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(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)],[binunionRsub]),binunionLsub]),notequalI1]),setadjoinE]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinOr]),setadjoinSub]),setadjoinSub2]),c_0_104]),subset2powerset]),setextsub]),powersetI]),subsetemptysetimpeq]),powersetI1]),emptyinPowerset]),powersetE1]),inPowerset]),emptyInPowerset]),powersetsubset]),c_0_105]),powersetE]),c_0_106]),setunionI]),binunionIL]),upairset2IR]),binunionIR]),setunionE]),binunionEcases]),binunionE]),subPowSU]),c_0_107]),c_0_108]),nonemptyImpWitness]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_109]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_110]),c_0_111]),inCongP]),in__Cong]),c_0_112]),c_0_113]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_114]),c_0_115]),c_0_116]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_117]),nonemptyE1]),c_0_118]),noeltsimpempty]),emptyI]),setext]),c_0_119]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_120]),c_0_121]),c_0_122]),c_0_123]),c_0_124]),wellorderingAx]),foundationAx]),c_0_125]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_126]) ).

thf(c_0_128,negated_conjecture,
    ! [X578: $i,X579: $i,X581: $i,X582: $i,X583: $i,X584: $i,X585: $i,X586: $i,X587: $i,X588: $i,X589: $i,X591: $i,X592: $i,X594: $i,X595: $i,X596: $i,X597: $i,X598: $i,X600: $i,X601: $i > $i > $o,X602: $i,X605: $i,X607: $i,X608: $i,X609: $i,X610: $i,X612: $i,X613: $i > $o,X614: $i,X615: $i > $o,X616: $i,X617: $i,X618: $i > $o,X619: $i,X620: $i,X621: $i > $o,X622: $i,X623: $i > $o,X625: $i,X626: $o,X627: $i,X628: $i,X629: $o,X630: $i,X631: $i,X632: $i > $o,X634: $i,X635: $i,X638: $i,X640: $i,X642: $i,X643: $i > $o,X644: $i,X645: $i,X647: $i,X648: $i > $o,X649: $i,X650: $i,X651: $i,X652: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i,X660: $o,X661: $i,X662: $i,X663: $i,X664: $i,X665: $i,X666: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $i,X674: $i,X675: $i,X676: $i,X677: $i,X678: $o,X680: $i,X681: $i,X682: $i > $o,X684: $i,X685: $i,X686: $i,X688: $i,X689: $i,X690: $i,X691: $i,X692: $i,X693: $i,X694: $i,X695: $i,X696: $i,X697: $i,X698: $i,X699: $i,X700: $i,X701: $i,X702: $i,X703: $i,X704: $i > $o,X705: $i,X706: $i > $o,X707: $i,X708: $i,X709: $i > $o,X710: $i,X712: $i,X713: $i > $o,X715: $i,X716: $i,X717: $i > $o,X719: $i,X720: $i,X721: $i > $o,X722: $i,X724: $o,X725: $i,X726: $i > $o,X728: $i,X729: $i,X730: $i > $o,X731: $i,X733: $i > $o,X734: $i,X736: $i > $o,X737: $i,X740: $i > $o,X741: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i > $o,X752: $i,X753: $i,X754: $i > $o,X755: $i > $o,X758: $i,X759: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i > $o,X767: $i,X768: $i,X769: $i > $o,X770: $i > $o,X773: $i,X774: $i,X775: $i > $o,X776: $i > $o,X779: $i,X780: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i,X787: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X814: $i,X815: $i,X816: $i,X817: $i,X818: $i,X819: $i,X820: $i,X821: $i,X822: $i,X823: $i,X824: $i,X825: $i,X826: $i > $o,X827: $i,X828: $i > $o,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X838: $i,X839: $i,X840: $o,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X578 @ X579 ) @ X578 )
        | ~ ( in @ ( esk1_2 @ X578 @ X579 ) @ X579 )
        | ( X578 = X579 ) )
      & ( ( in @ ( esk1_2 @ X578 @ X579 ) @ X578 )
        | ( in @ ( esk1_2 @ X578 @ X579 ) @ X579 )
        | ( X578 = X579 ) )
      & ~ ( in @ X581 @ emptyset )
      & ( ~ ( in @ X584 @ ( setadjoin @ X582 @ X583 ) )
        | ( X584 = X582 )
        | ( in @ X584 @ X583 ) )
      & ( ( X584 != X582 )
        | ( in @ X584 @ ( setadjoin @ X582 @ X583 ) ) )
      & ( ~ ( in @ X584 @ X583 )
        | ( in @ X584 @ ( setadjoin @ X582 @ X583 ) ) )
      & ( ~ ( in @ X586 @ ( powerset @ X585 ) )
        | ~ ( in @ X587 @ X586 )
        | ( in @ X587 @ X585 ) )
      & ( ( in @ ( esk2_2 @ X588 @ X589 ) @ X589 )
        | ( in @ X589 @ ( powerset @ X588 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X588 @ X589 ) @ X588 )
        | ( in @ X589 @ ( powerset @ X588 ) ) )
      & ( ( in @ X592 @ ( esk3_2 @ X591 @ X592 ) )
        | ~ ( in @ X592 @ ( setunion @ X591 ) ) )
      & ( ( in @ ( esk3_2 @ X591 @ X592 ) @ X591 )
        | ~ ( in @ X592 @ ( setunion @ X591 ) ) )
      & ( ~ ( in @ X595 @ X596 )
        | ~ ( in @ X596 @ X594 )
        | ( in @ X595 @ ( setunion @ X594 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X597 @ omega )
        | ( in @ ( setadjoin @ X597 @ X597 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X598 ) @ omega )
        | ~ ( in @ emptyset @ X598 )
        | ~ ( in @ X600 @ omega )
        | ( in @ X600 @ X598 ) )
      & ( ( in @ ( esk4_1 @ X598 ) @ X598 )
        | ~ ( in @ emptyset @ X598 )
        | ~ ( in @ X600 @ omega )
        | ( in @ X600 @ X598 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X598 ) @ ( esk4_1 @ X598 ) ) @ X598 )
        | ~ ( in @ emptyset @ X598 )
        | ~ ( in @ X600 @ omega )
        | ( in @ X600 @ X598 ) )
      & ( ( in @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X602 )
        | ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
        | ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
      & ( ( X601 @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X605 )
        | ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
        | ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
      & ( ~ ( in @ X608 @ X602 )
        | ~ ( X601 @ X608 @ X607 )
        | ( in @ X607 @ ( esk6_2 @ X601 @ X602 ) )
        | ( in @ ( esk5_2 @ X601 @ X602 ) @ X602 ) )
      & ( ( in @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X602 )
        | ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
        | ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
      & ( ( X601 @ ( esk7_3 @ X601 @ X602 @ X605 ) @ X605 )
        | ~ ( in @ X605 @ ( esk6_2 @ X601 @ X602 ) )
        | ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
      & ( ~ ( in @ X608 @ X602 )
        | ~ ( X601 @ X608 @ X607 )
        | ( in @ X607 @ ( esk6_2 @ X601 @ X602 ) )
        | ~ ( exu @ ( X601 @ ( esk5_2 @ X601 @ X602 ) ) ) )
      & ( ( in @ ( esk8_1 @ X609 ) @ X609 )
        | ~ ( in @ X610 @ X609 ) )
      & ( ~ ( in @ X612 @ ( esk8_1 @ X609 ) )
        | ~ ( in @ X612 @ X609 )
        | ~ ( in @ X610 @ X609 ) )
      & epred1_0
      & ( ~ ( exu @ X613 )
        | ( X613 @ ( descr @ X613 ) ) )
      & ( ~ ( in @ X616 @ X614 )
        | ~ ( X615 @ X616 )
        | ( in @ X616 @ ( dsetconstr @ X614 @ X615 ) ) )
      & ( ~ ( in @ X619 @ ( dsetconstr @ X617 @ X618 ) )
        | ( in @ X619 @ X617 ) )
      & ( ~ ( in @ X622 @ ( dsetconstr @ X620 @ X621 ) )
        | ( X621 @ X622 ) )
      & ( ( X623 @ ( esk9_1 @ X623 ) )
        | ~ ( exu @ X623 ) )
      & ( ~ ( X623 @ X625 )
        | ( ( esk9_1 @ X623 )
          = X625 )
        | ~ ( exu @ X623 ) )
      & ( ~ ( in @ X627 @ ( prop2set @ X626 ) )
        | X626 )
      & ( ~ ( in @ X628 @ emptyset )
        | X629 )
      & ( ~ ( in @ X630 @ emptyset )
        | ~ $true )
      & ~ ( in @ X631 @ emptyset )
      & ( ~ ( exu @ X632 )
        | ( X632 @ ( esk10_1 @ X632 ) ) )
      & ( ( in @ ( esk12_2 @ X634 @ X635 ) @ X635 )
        | ( X634 = X635 )
        | ( in @ ( esk11_2 @ X634 @ X635 ) @ X634 ) )
      & ( ~ ( in @ ( esk12_2 @ X634 @ X635 ) @ X634 )
        | ( X634 = X635 )
        | ( in @ ( esk11_2 @ X634 @ X635 ) @ X634 ) )
      & ( ( in @ ( esk12_2 @ X634 @ X635 ) @ X635 )
        | ( X634 = X635 )
        | ~ ( in @ ( esk11_2 @ X634 @ X635 ) @ X635 ) )
      & ( ~ ( in @ ( esk12_2 @ X634 @ X635 ) @ X634 )
        | ( X634 = X635 )
        | ~ ( in @ ( esk11_2 @ X634 @ X635 ) @ X635 ) )
      & ( ( in @ ( esk13_1 @ X638 ) @ X638 )
        | ( X638 = emptyset ) )
      & ( ( in @ ( esk14_1 @ X640 ) @ X640 )
        | ( X640 = emptyset ) )
      & ( ~ ( in @ X644 @ ( dsetconstr @ X642 @ X643 ) )
        | ( X643 @ X644 )
        | ~ ( in @ X644 @ X642 ) )
      & ( ~ ( X643 @ X644 )
        | ( in @ X644 @ ( dsetconstr @ X642 @ X643 ) )
        | ~ ( in @ X644 @ X642 ) )
      & ( ~ ( nonempty @ X645 )
        | ( in @ ( esk15_1 @ X645 ) @ X645 ) )
      & ( ~ ( in @ X649 @ X647 )
        | ~ ( X648 @ X649 )
        | ( nonempty @ ( dsetconstr @ X647 @ X648 ) ) )
      & ( ~ ( in @ X651 @ X650 )
        | ( nonempty @ X650 ) )
      & ( in @ X652 @ ( setadjoin @ X652 @ X653 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X656 @ X655 )
        | ( in @ X656 @ ( setadjoin @ X654 @ X655 ) ) )
      & ( ( in @ X659 @ X658 )
        | X660
        | ( X659 = X657 )
        | ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
      & ( ~ X660
        | X660
        | ( X659 = X657 )
        | ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
      & ( ( in @ X659 @ X658 )
        | X660
        | ~ X660
        | ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
      & ( ~ X660
        | X660
        | ~ X660
        | ~ ( in @ X659 @ ( setadjoin @ X657 @ X658 ) ) )
      & ( ~ ( in @ X663 @ ( setadjoin @ X661 @ X662 ) )
        | ( X663 = X661 )
        | ( in @ X663 @ X662 ) )
      & ( ( dsetconstr @ X664
          @ ^ [Z0: $i] : $true )
        = X664 )
      & ( ( in @ ( esk16_2 @ X665 @ X666 ) @ X666 )
        | ( in @ X666 @ ( powerset @ X665 ) ) )
      & ( ~ ( in @ ( esk16_2 @ X665 @ X666 ) @ X665 )
        | ( in @ X666 @ ( powerset @ X665 ) ) )
      & ( in @ emptyset @ ( powerset @ X668 ) )
      & ( in @ emptyset @ ( powerset @ X669 ) )
      & ( ~ ( in @ X671 @ ( powerset @ X670 ) )
        | ~ ( in @ X672 @ X671 )
        | ( in @ X672 @ X670 ) )
      & ( ~ ( in @ X674 @ X675 )
        | ~ ( in @ X675 @ X673 )
        | ( in @ X674 @ ( setunion @ X673 ) ) )
      & ( ( in @ X677 @ ( esk17_3 @ X676 @ X677 @ X678 ) )
        | X678
        | ~ ( in @ X677 @ ( setunion @ X676 ) ) )
      & ( ( in @ ( esk17_3 @ X676 @ X677 @ X678 ) @ X676 )
        | X678
        | ~ ( in @ X677 @ ( setunion @ X676 ) ) )
      & ( ~ X678
        | X678
        | ~ ( in @ X677 @ ( setunion @ X676 ) ) )
      & ( ~ ( in @ X681 @ X680 )
        | ( in @ X681 @ ( powerset @ ( setunion @ X680 ) ) ) )
      & ( ~ ( X682 @ X684 )
        | ( X684
          = ( esk18_1 @ X682 ) )
        | ~ ( exu @ X682 ) )
      & ( ( X685
         != ( esk18_1 @ X682 ) )
        | ( X682 @ X685 )
        | ~ ( exu @ X682 ) )
      & ( ( in @ ( esk19_1 @ X686 ) @ X686 )
        | ~ ( nonempty @ X686 ) )
      & ( $true
        | ~ ( nonempty @ X686 ) )
      & ( ~ ( in @ X688 @ ( setadjoin @ X689 @ emptyset ) )
        | ( X688 = X689 ) )
      & ( ( X690 = X691 )
        | ~ ( in @ X691 @ ( setadjoin @ X690 @ emptyset ) ) )
      & ( ( X692 != X693 )
        | ( in @ X692 @ ( setadjoin @ X693 @ emptyset ) ) )
      & ( ~ ( in @ X694 @ ( setadjoin @ X695 @ emptyset ) )
        | ( in @ X695 @ ( setadjoin @ X694 @ emptyset ) ) )
      & ( ~ ( in @ X698 @ ( setadjoin @ X696 @ ( setadjoin @ X697 @ emptyset ) ) )
        | ( X698 = X696 )
        | ( X698 = X697 ) )
      & ( in @ X699 @ ( setadjoin @ X699 @ ( setadjoin @ X700 @ emptyset ) ) )
      & ( in @ X702 @ ( setadjoin @ X701 @ ( setadjoin @ X702 @ emptyset ) ) )
      & ( ~ ( in @ X705 @ X703 )
        | ~ ( X704 @ X705 )
        | ( ( dsetconstr @ X703 @ X704 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X707 @ emptyset )
        | ( X706 @ X707 ) )
      & ( ( in @ ( esk20_2 @ X708 @ X709 ) @ X708 )
        | ~ ( in @ X710 @ X708 )
        | ( X709 @ X710 ) )
      & ( ~ ( X709 @ ( esk20_2 @ X708 @ X709 ) )
        | ~ ( in @ X710 @ X708 )
        | ( X709 @ X710 ) )
      & ( ( in @ ( esk21_2 @ X712 @ X713 ) @ X712 )
        | ~ ( in @ X715 @ X712 )
        | ~ ( X713 @ X715 ) )
      & ( ( X713 @ ( esk21_2 @ X712 @ X713 ) )
        | ~ ( in @ X715 @ X712 )
        | ~ ( X713 @ X715 ) )
      & ( ( in @ ( esk22_2 @ X716 @ X717 ) @ X716 )
        | ~ ( in @ X719 @ X716 )
        | ~ ( X717 @ X719 ) )
      & ( ( X717 @ ( esk22_2 @ X716 @ X717 ) )
        | ~ ( in @ X719 @ X716 )
        | ~ ( X717 @ X719 ) )
      & ( ( in @ ( esk23_2 @ X720 @ X721 ) @ X720 )
        | ~ ( in @ X722 @ X720 )
        | ( X721 @ X722 ) )
      & ( ~ ( X721 @ ( esk23_2 @ X720 @ X721 ) )
        | ~ ( in @ X722 @ X720 )
        | ( X721 @ X722 ) )
      & ( ~ X724
        | ( in @ emptyset @ ( prop2set @ X724 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk24_2 @ X725 @ X726 ) @ X725 )
        | ~ ( in @ X728 @ X725 )
        | ~ ( X726 @ X728 ) )
      & ( ( X726 @ ( esk24_2 @ X725 @ X726 ) )
        | ~ ( in @ X728 @ X725 )
        | ~ ( X726 @ X728 ) )
      & ( ( in @ ( esk25_2 @ X729 @ X730 ) @ X729 )
        | ~ ( in @ X731 @ X729 )
        | ( X730 @ X731 ) )
      & ( ~ ( X730 @ ( esk25_2 @ X729 @ X730 ) )
        | ~ ( in @ X731 @ X729 )
        | ( X730 @ X731 ) )
      & ( ( X733 @ ( esk26_2 @ X733 @ X734 ) )
        | ~ ( X733 @ X734 )
        | ( exu @ X733 ) )
      & ( ( X734
         != ( esk26_2 @ X733 @ X734 ) )
        | ~ ( X733 @ X734 )
        | ( exu @ X733 ) )
      & ( ( X736 @ ( esk27_1 @ X736 ) )
        | ( exu @ X736 )
        | ~ ( X736 @ X737 ) )
      & ( ( X736 @ ( esk28_1 @ X736 ) )
        | ( exu @ X736 )
        | ~ ( X736 @ X737 ) )
      & ( ( ( esk27_1 @ X736 )
         != ( esk28_1 @ X736 ) )
        | ( exu @ X736 )
        | ~ ( X736 @ X737 ) )
      & ( ~ ( X740 @ ( esk29_2 @ X740 @ X741 ) )
        | ( ( esk29_2 @ X740 @ X741 )
         != X741 )
        | ( exu @ X740 ) )
      & ( ( X740 @ ( esk29_2 @ X740 @ X741 ) )
        | ( ( esk29_2 @ X740 @ X741 )
          = X741 )
        | ( exu @ X740 ) )
      & ( ( X743 != X744 )
        | ( X745 != X746 )
        | ~ ( in @ X745 @ X743 )
        | ( in @ X746 @ X744 ) )
      & ( ~ ( in @ X749 @ X747 )
        | ( in @ X750 @ X748 )
        | ( X749 != X750 )
        | ( X747 != X748 ) )
      & ( ~ ( in @ X750 @ X748 )
        | ( in @ X749 @ X747 )
        | ( X749 != X750 )
        | ( X747 != X748 ) )
      & ( ~ ( exu @ X751 )
        | ~ ( X751 @ X752 )
        | ~ ( X751 @ X753 )
        | ( X752 = X753 ) )
      & ( ~ ( exu @ X754 )
        | ( exu @ X755 )
        | ( ( esk30_2 @ X754 @ X755 )
          = ( esk31_2 @ X754 @ X755 ) ) )
      & ( ~ ( exu @ X755 )
        | ( exu @ X754 )
        | ( ( esk30_2 @ X754 @ X755 )
          = ( esk31_2 @ X754 @ X755 ) ) )
      & ( ~ ( exu @ X754 )
        | ( exu @ X755 )
        | ~ ( X754 @ ( esk30_2 @ X754 @ X755 ) )
        | ~ ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
      & ( ~ ( exu @ X755 )
        | ( exu @ X754 )
        | ~ ( X754 @ ( esk30_2 @ X754 @ X755 ) )
        | ~ ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
      & ( ~ ( exu @ X754 )
        | ( exu @ X755 )
        | ( X754 @ ( esk30_2 @ X754 @ X755 ) )
        | ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
      & ( ~ ( exu @ X755 )
        | ( exu @ X754 )
        | ( X754 @ ( esk30_2 @ X754 @ X755 ) )
        | ( X755 @ ( esk31_2 @ X754 @ X755 ) ) )
      & ( emptyset = emptyset )
      & ( ( X758 != X759 )
        | ( X760 != X761 )
        | ( ( setadjoin @ X758 @ X760 )
          = ( setadjoin @ X759 @ X761 ) ) )
      & ( ( X762 != X763 )
        | ( ( powerset @ X762 )
          = ( powerset @ X763 ) ) )
      & ( ( X764 != X765 )
        | ( ( setunion @ X764 )
          = ( setunion @ X765 ) ) )
      & ( omega = omega )
      & ( ~ ( exu @ X766 )
        | ~ ( X766 @ X767 )
        | ~ ( X766 @ X768 )
        | ( X767 = X768 ) )
      & ( ( ( esk32_2 @ X769 @ X770 )
          = ( esk33_2 @ X769 @ X770 ) )
        | ~ ( exu @ X769 )
        | ~ ( exu @ X770 )
        | ( ( descr @ X769 )
          = ( descr @ X770 ) ) )
      & ( ~ ( X769 @ ( esk32_2 @ X769 @ X770 ) )
        | ~ ( X770 @ ( esk33_2 @ X769 @ X770 ) )
        | ~ ( exu @ X769 )
        | ~ ( exu @ X770 )
        | ( ( descr @ X769 )
          = ( descr @ X770 ) ) )
      & ( ( X769 @ ( esk32_2 @ X769 @ X770 ) )
        | ( X770 @ ( esk33_2 @ X769 @ X770 ) )
        | ~ ( exu @ X769 )
        | ~ ( exu @ X770 )
        | ( ( descr @ X769 )
          = ( descr @ X770 ) ) )
      & ( ( in @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) @ X773 )
        | ( ( dsetconstr @ X773 @ X775 )
          = ( dsetconstr @ X774 @ X776 ) )
        | ( X773 != X774 ) )
      & ( ( in @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) @ X774 )
        | ( ( dsetconstr @ X773 @ X775 )
          = ( dsetconstr @ X774 @ X776 ) )
        | ( X773 != X774 ) )
      & ( ( ( esk34_4 @ X773 @ X774 @ X775 @ X776 )
          = ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
        | ( ( dsetconstr @ X773 @ X775 )
          = ( dsetconstr @ X774 @ X776 ) )
        | ( X773 != X774 ) )
      & ( ~ ( X775 @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) )
        | ~ ( X776 @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
        | ( ( dsetconstr @ X773 @ X775 )
          = ( dsetconstr @ X774 @ X776 ) )
        | ( X773 != X774 ) )
      & ( ( X775 @ ( esk34_4 @ X773 @ X774 @ X775 @ X776 ) )
        | ( X776 @ ( esk35_4 @ X773 @ X774 @ X775 @ X776 ) )
        | ( ( dsetconstr @ X773 @ X775 )
          = ( dsetconstr @ X774 @ X776 ) )
        | ( X773 != X774 ) )
      & ( ( in @ ( esk36_2 @ X779 @ X780 ) @ X779 )
        | ( subset @ X779 @ X780 ) )
      & ( ~ ( in @ ( esk36_2 @ X779 @ X780 ) @ X780 )
        | ( subset @ X779 @ X780 ) )
      & ( ( X782 != X783 )
        | ( subset @ X783 @ X782 ) )
      & ( ( X784 != X785 )
        | ( subset @ X784 @ X785 ) )
      & ( ( in @ ( esk37_2 @ X786 @ X787 ) @ X786 )
        | ( subset @ X786 @ X787 ) )
      & ( ~ ( in @ ( esk37_2 @ X786 @ X787 ) @ X787 )
        | ( subset @ X786 @ X787 ) )
      & ( subset @ emptyset @ X789 )
      & ( ~ ( subset @ X790 @ X791 )
        | ~ ( in @ X792 @ X790 )
        | ( in @ X792 @ X791 ) )
      & ( ~ ( subset @ X793 @ X794 )
        | ( in @ X795 @ X794 )
        | ~ ( in @ X795 @ X793 ) )
      & ( ~ ( in @ X798 @ X796 )
        | ( in @ X798 @ X797 )
        | ~ ( subset @ X796 @ X797 ) )
      & ( ( subset @ X799 @ X800 )
        | ( X799 != X800 ) )
      & ( ~ ( in @ X803 @ X801 )
        | ( in @ X803 @ X802 )
        | ( X801 != X802 ) )
      & ( subset @ X804 @ X804 )
      & ( ~ ( subset @ X805 @ X806 )
        | ~ ( subset @ X806 @ X807 )
        | ( subset @ X805 @ X807 ) )
      & ( subset @ X809 @ ( setadjoin @ X808 @ X809 ) )
      & ( ~ ( subset @ X810 @ X812 )
        | ( subset @ X810 @ ( setadjoin @ X811 @ X812 ) ) )
      & ( ~ ( subset @ X813 @ X814 )
        | ( in @ X813 @ ( powerset @ X814 ) ) )
      & ( ~ ( subset @ X815 @ X816 )
        | ~ ( subset @ X816 @ X815 )
        | ( X815 = X816 ) )
      & ( ~ ( subset @ X817 @ emptyset )
        | ( X817 = emptyset ) )
      & ( ~ ( subset @ X819 @ X818 )
        | ( in @ X819 @ ( powerset @ X818 ) ) )
      & ( ~ ( in @ X821 @ ( powerset @ X820 ) )
        | ( subset @ X821 @ X820 ) )
      & ( in @ X822 @ ( powerset @ X822 ) )
      & ( ~ ( subset @ X823 @ X824 )
        | ( subset @ ( powerset @ X823 ) @ ( powerset @ X824 ) ) )
      & ( in @ ( dsetconstr @ X825 @ X826 ) @ ( powerset @ X825 ) )
      & ( subset @ ( dsetconstr @ X827 @ X828 ) @ X827 )
      & ( ~ ( in @ X831 @ X829 )
        | ( in @ X831 @ ( binunion @ X829 @ X830 ) ) )
      & ( in @ X833 @ ( setadjoin @ X832 @ ( setadjoin @ X833 @ emptyset ) ) )
      & ( ~ ( in @ X836 @ X835 )
        | ( in @ X836 @ ( binunion @ X834 @ X835 ) ) )
      & ( ( in @ X839 @ X838 )
        | X840
        | ( in @ X839 @ X837 )
        | ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
      & ( ~ X840
        | X840
        | ( in @ X839 @ X837 )
        | ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
      & ( ( in @ X839 @ X838 )
        | X840
        | ~ X840
        | ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
      & ( ~ X840
        | X840
        | ~ X840
        | ~ ( in @ X839 @ ( binunion @ X837 @ X838 ) ) )
      & ( ~ ( in @ X843 @ ( binunion @ X841 @ X842 ) )
        | ( in @ X843 @ X841 )
        | ( in @ X843 @ X842 ) )
      & ( subset @ X844 @ ( binunion @ X844 @ X845 ) )
      & ~ ( subset @ esk39_0 @ ( binunion @ esk38_0 @ esk39_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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])])])])]) ).

thf(c_0_129,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( subset @ X2 @ X3 )
      | ~ ( in @ ( esk37_2 @ X2 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

thf(c_0_130,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( in @ X2 @ ( binunion @ X4 @ X3 ) )
      | ~ ( in @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

thf(c_0_131,negated_conjecture,
    ! [X2: $i,X3: $i,X4: $i] :
      ( ( subset @ X2 @ ( binunion @ X3 @ X4 ) )
      | ~ ( in @ ( esk37_2 @ X2 @ ( binunion @ X3 @ X4 ) ) @ X4 ) ),
    inference(spm,[status(thm)],[c_0_129,c_0_130]) ).

thf(c_0_132,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ ( esk37_2 @ X2 @ X3 ) @ X2 )
      | ( subset @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

thf(c_0_133,negated_conjecture,
    ~ ( subset @ esk39_0 @ ( binunion @ esk38_0 @ esk39_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

thf(c_0_134,negated_conjecture,
    ! [X3: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X3 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

thf(c_0_135,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU588^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sun May 19 16:06:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.46  Running higher-order theorem proving
% 0.19/0.46  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
% 2.55/0.87  # Version: 3.1.0-ho
% 2.55/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87  # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87  # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87  # Starting pre_casc_3 with 300s (1) cores
% 2.55/0.87  # Starting ho_unfolding_8 with 300s (1) cores
% 2.55/0.87  # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.55/0.87  # Starting new_bool_3 with 300s (1) cores
% 2.55/0.87  # Starting new_ho_5 with 300s (1) cores
% 2.55/0.87  # new_ho_5 with pid 32634 completed with status 8
% 2.55/0.87  # pre_casc_3 with pid 32630 completed with status 8
% 2.55/0.87  # new_bool_5 with pid 32629 completed with status 0
% 2.55/0.87  # Result found by new_bool_5
% 2.55/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87  # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87  # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.55/0.87  # Search class: HGHSM-FSLS31-SHFMMSBN
% 2.55/0.87  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.55/0.87  # Starting sh3 with 163s (1) cores
% 2.55/0.87  # sh3 with pid 32641 completed with status 0
% 2.55/0.87  # Result found by sh3
% 2.55/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.55/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.55/0.87  # Starting ehoh_best5 with 300s (1) cores
% 2.55/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 2.55/0.87  # Starting new_bool_5 with 300s (1) cores
% 2.55/0.87  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.55/0.87  # Search class: HGHSM-FSLS31-SHFMMSBN
% 2.55/0.87  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.55/0.87  # Starting sh3 with 163s (1) cores
% 2.55/0.87  # Preprocessing time       : 0.004 s
% 2.55/0.87  # Presaturation interreduction done
% 2.55/0.87  
% 2.55/0.87  # Proof found!
% 2.55/0.87  # SZS status Theorem
% 2.55/0.87  # SZS output start CNFRefutation
% See solution above
% 2.55/0.87  # Parsed axioms                        : 227
% 2.55/0.87  # Removed by relevancy pruning/SinE    : 123
% 2.55/0.87  # Initial clauses                      : 175
% 2.55/0.87  # Removed in clause preprocessing      : 18
% 2.55/0.87  # Initial clauses in saturation        : 157
% 2.55/0.87  # Processed clauses                    : 3099
% 2.55/0.87  # ...of these trivial                  : 80
% 2.55/0.87  # ...subsumed                          : 1821
% 2.55/0.87  # ...remaining for further processing  : 1198
% 2.55/0.87  # Other redundant clauses eliminated   : 23
% 2.55/0.87  # Clauses deleted for lack of memory   : 0
% 2.55/0.87  # Backward-subsumed                    : 242
% 2.55/0.87  # Backward-rewritten                   : 12
% 2.55/0.87  # Generated clauses                    : 21390
% 2.55/0.87  # ...of the previous two non-redundant : 19695
% 2.55/0.87  # ...aggressively subsumed             : 0
% 2.55/0.87  # Contextual simplify-reflections      : 11
% 2.55/0.87  # Paramodulations                      : 21356
% 2.55/0.87  # Factorizations                       : 4
% 2.55/0.87  # NegExts                              : 0
% 2.55/0.87  # Equation resolutions                 : 23
% 2.55/0.87  # Disequality decompositions           : 0
% 2.55/0.87  # Total rewrite steps                  : 2141
% 2.55/0.87  # ...of those cached                   : 1903
% 2.55/0.87  # Propositional unsat checks           : 0
% 2.55/0.87  #    Propositional check models        : 0
% 2.55/0.87  #    Propositional check unsatisfiable : 0
% 2.55/0.87  #    Propositional clauses             : 0
% 2.55/0.87  #    Propositional clauses after purity: 0
% 2.55/0.87  #    Propositional unsat core size     : 0
% 2.55/0.87  #    Propositional preprocessing time  : 0.000
% 2.55/0.87  #    Propositional encoding time       : 0.000
% 2.55/0.87  #    Propositional solver time         : 0.000
% 2.55/0.87  #    Success case prop preproc time    : 0.000
% 2.55/0.87  #    Success case prop encoding time   : 0.000
% 2.55/0.87  #    Success case prop solver time     : 0.000
% 2.55/0.87  # Current number of processed clauses  : 796
% 2.55/0.87  #    Positive orientable unit clauses  : 97
% 2.55/0.87  #    Positive unorientable unit clauses: 0
% 2.55/0.87  #    Negative unit clauses             : 25
% 2.55/0.87  #    Non-unit-clauses                  : 674
% 2.55/0.87  # Current number of unprocessed clauses: 15913
% 2.55/0.87  # ...number of literals in the above   : 49898
% 2.55/0.87  # Current number of archived formulas  : 0
% 2.55/0.87  # Current number of archived clauses   : 391
% 2.55/0.87  # Clause-clause subsumption calls (NU) : 58322
% 2.55/0.87  # Rec. Clause-clause subsumption calls : 51333
% 2.55/0.87  # Non-unit clause-clause subsumptions  : 1159
% 2.55/0.87  # Unit Clause-clause subsumption calls : 1625
% 2.55/0.87  # Rewrite failures with RHS unbound    : 0
% 2.55/0.87  # BW rewrite match attempts            : 22
% 2.55/0.87  # BW rewrite match successes           : 9
% 2.55/0.87  # Condensation attempts                : 0
% 2.55/0.87  # Condensation successes               : 0
% 2.55/0.87  # Termbank termtop insertions          : 320862
% 2.55/0.87  # Search garbage collected termcells   : 9626
% 2.55/0.87  
% 2.55/0.87  # -------------------------------------------------
% 2.55/0.87  # User time                : 0.361 s
% 2.55/0.87  # System time              : 0.018 s
% 2.55/0.87  # Total time               : 0.379 s
% 2.55/0.87  # Maximum resident set size: 4476 pages
% 2.55/0.87  
% 2.55/0.87  # -------------------------------------------------
% 2.55/0.87  # User time                : 0.475 s
% 2.55/0.87  # System time              : 0.061 s
% 2.55/0.87  # Total time               : 0.536 s
% 2.55/0.87  # Maximum resident set size: 2008 pages
% 2.55/0.87  % E---3.1 exiting
% 2.55/0.87  % E exiting
%------------------------------------------------------------------------------