TSTP Solution File: SEU598^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU598^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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 03:28:27 EDT 2024

% Result   : Theorem 0.77s 0.61s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  284
% Syntax   : Number of formulae    :  317 (   5 unt; 169 typ;   0 def)
%            Number of atoms       : 1207 ( 193 equ;   0 cnn)
%            Maximal formula atoms :  349 (   8 avg)
%            Number of connectives : 3885 ( 287   ~; 283   |; 229   &;2326   @)
%                                         ( 172 <=>; 588  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  430 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  244 ( 244   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  172 ( 169 usr; 121 con; 0-4 aty)
%            Number of variables   : 1004 (  59   ^ 880   !;  65   ?;1004   :)

% 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,
    binunionRsub: $o ).

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

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

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

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

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

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

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

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

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

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

thf(decl_153,type,
    epred1_0: $o ).

thf(decl_154,type,
    esk1_2: $i > $i > $i ).

thf(decl_155,type,
    esk2_2: $i > $i > $i ).

thf(decl_156,type,
    esk3_2: $i > $i > $i ).

thf(decl_157,type,
    esk4_1: $i > $i ).

thf(decl_158,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_159,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_160,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_161,type,
    esk8_1: $i > $i ).

thf(decl_162,type,
    esk9_1: ( $i > $o ) > $i ).

thf(decl_163,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_164,type,
    esk11_2: $i > $i > $i ).

thf(decl_165,type,
    esk12_2: $i > $i > $i ).

thf(decl_166,type,
    esk13_1: $i > $i ).

thf(decl_167,type,
    esk14_1: $i > $i ).

thf(decl_168,type,
    esk15_1: $i > $i ).

thf(decl_169,type,
    esk16_2: $i > $i > $i ).

thf(decl_170,type,
    esk17_3: $i > $i > $o > $i ).

thf(decl_171,type,
    esk18_1: ( $i > $o ) > $i ).

thf(decl_172,type,
    esk19_1: $i > $i ).

thf(decl_173,type,
    esk20_2: $i > ( $i > $o ) > $i ).

thf(decl_174,type,
    esk21_2: $i > ( $i > $o ) > $i ).

thf(decl_175,type,
    esk22_2: $i > ( $i > $o ) > $i ).

thf(decl_176,type,
    esk23_2: $i > ( $i > $o ) > $i ).

thf(decl_177,type,
    esk24_2: $i > ( $i > $o ) > $i ).

thf(decl_178,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_179,type,
    esk26_2: ( $i > $o ) > $i > $i ).

thf(decl_180,type,
    esk27_1: ( $i > $o ) > $i ).

thf(decl_181,type,
    esk28_1: ( $i > $o ) > $i ).

thf(decl_182,type,
    esk29_2: ( $i > $o ) > $i > $i ).

thf(decl_183,type,
    esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_184,type,
    esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_185,type,
    esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_186,type,
    esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_187,type,
    esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_188,type,
    esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_189,type,
    esk36_2: $i > $i > $i ).

thf(decl_190,type,
    esk37_2: $i > $i > $i ).

thf(decl_191,type,
    esk38_2: $i > $i > $i ).

thf(decl_192,type,
    esk39_0: $i ).

thf(decl_193,type,
    esk40_0: $i ).

thf(sepInPowerset,axiom,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).

thf(sepSubset,axiom,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).

thf(exuE2,axiom,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).

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/sandbox2/benchmark/theBenchmark.p',exuE3u) ).

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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).

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/sandbox2/benchmark/theBenchmark.p',exuI1) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuI2) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).

thf(setoftrueEq,axiom,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [X2: $i] : $true )
        = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setbeta) ).

thf(exuE3e,axiom,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',replAx) ).

thf(binintersectSubset4,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( uniqinunit
                                                                                         => ( notinsingleton
                                                                                           => ( eqinunit
                                                                                             => ( singletonsswitch
                                                                                               => ( upairsetE
                                                                                                 => ( upairsetIL
                                                                                                   => ( upairsetIR
                                                                                                     => ( emptyE1
                                                                                                       => ( vacuousDall
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( emptyset__Cong
                                                                                                                                         => ( setadjoin__Cong
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( emptysetsubset
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( setadjoinSub
                                                                                                                                                                                 => ( setadjoinSub2
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( subsetemptysetimpeq
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( upairset2IR
                                                                                                                                                                                                         => ( binunionIR
                                                                                                                                                                                                           => ( binunionEcases
                                                                                                                                                                                                             => ( binunionE
                                                                                                                                                                                                               => ( binunionLsub
                                                                                                                                                                                                                 => ( binunionRsub
                                                                                                                                                                                                                   => ( binintersectI
                                                                                                                                                                                                                     => ( binintersectSubset5
                                                                                                                                                                                                                       => ( binintersectEL
                                                                                                                                                                                                                         => ( binintersectLsub
                                                                                                                                                                                                                           => ( binintersectSubset2
                                                                                                                                                                                                                             => ( binintersectSubset3
                                                                                                                                                                                                                               => ( binintersectER
                                                                                                                                                                                                                                 => ( disjointsetsI1
                                                                                                                                                                                                                                   => ( binintersectRsub
                                                                                                                                                                                                                                     => ! [X4: $i,X5: $i] :
                                                                                                                                                                                                                                          ( ( subset @ X5 @ X4 )
                                                                                                                                                                                                                                         => ( ( binintersect @ X4 @ X5 )
                                                                                                                                                                                                                                            = X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).

thf(binintersectRsub,axiom,
    ( binintersectRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).

thf(powersetI1,axiom,
    ( powersetI1
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).

thf(emptyInPowerset,axiom,
    ( emptyInPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).

thf(powersetE1,axiom,
    ( powersetE1
  <=> ! [X4: $i,X5: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).

thf(inPowerset,axiom,
    ( inPowerset
  <=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).

thf(powersetsubset,axiom,
    ( powersetsubset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionIL) ).

thf(upairset2IR,axiom,
    ( upairset2IR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).

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/sandbox2/benchmark/theBenchmark.p',setunionE) ).

thf(binunionIR,axiom,
    ( binunionIR
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X5 )
       => ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).

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/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).

thf(subPowSU,axiom,
    ( subPowSU
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).

thf(binunionE,axiom,
    ( binunionE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
       => ( ( in @ X2 @ X4 )
          | ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).

thf(binunionLsub,axiom,
    ( binunionLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).

thf(binunionRsub,axiom,
    ( binunionRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).

thf(binintersectI,axiom,
    ( binintersectI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).

thf(nonemptyImpWitness,axiom,
    ( nonemptyImpWitness
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).

thf(binintersectSubset5,axiom,
    ( binintersectSubset5
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X7 @ X4 )
       => ( ( subset @ X7 @ X5 )
         => ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(binintersectEL,axiom,
    ( binintersectEL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).

thf(binintersectLsub,axiom,
    ( binintersectLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).

thf(binintersectSubset2,axiom,
    ( binintersectSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( binintersect @ X4 @ X5 )
          = X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).

thf(notinsingleton,axiom,
    ( notinsingleton
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 != X3 )
       => ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).

thf(binintersectSubset3,axiom,
    ( binintersectSubset3
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).

thf(binintersectER,axiom,
    ( binintersectER
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).

thf(disjointsetsI1,axiom,
    ( disjointsetsI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( in @ X2 @ X5 ) )
       => ( ( binintersect @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).

thf(eqinunit,axiom,
    ( eqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairsetE) ).

thf(upairsetIL,axiom,
    ( upairsetIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).

thf(upairsetIR,axiom,
    ( upairsetIR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).

thf(vacuousDall,axiom,
    ( vacuousDall
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).

thf(prop2setI,axiom,
    ( prop2setI
  <=> ! [X15: $o] :
        ( X15
       => ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',in__Cong) ).

thf(emptyset__Cong,axiom,
    ( emptyset__Cong
  <=> ( emptyset = emptyset ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(powerset__Cong,axiom,
    ( powerset__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( powerset @ X4 )
          = ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).

thf(setunion__Cong,axiom,
    ( setunion__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( setunion @ X4 )
          = ( setunion @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).

thf(omega__Cong,axiom,
    ( omega__Cong
  <=> ( omega = omega ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetI1) ).

thf(eqimpsubset2,axiom,
    ( eqimpsubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).

thf(eqimpsubset1,axiom,
    ( eqimpsubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

thf(emptysetsubset,axiom,
    ( emptysetsubset
  <=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).

thf(notequalI1,axiom,
    ( notequalI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ( subset @ X4 @ X5 )
       => ( X4 != X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).

thf(notequalI2,axiom,
    ( notequalI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( X4 != X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).

thf(subsetRefl,axiom,
    ( subsetRefl
  <=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).

thf(setadjoinSub,axiom,
    ( setadjoinSub
  <=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).

thf(powersetI,axiom,
    ( powersetI
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X5 )
           => ( in @ X2 @ X4 ) )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).

thf(setadjoinSub2,axiom,
    ( setadjoinSub2
  <=> ! [X4: $i,X2: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).

thf(subset2powerset,axiom,
    ( subset2powerset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( in @ X4 @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).

thf(setextsub,axiom,
    ( setextsub
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X4 )
         => ( X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
  <=> ! [X4: $i] :
        ( ( subset @ X4 @ emptyset )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).

thf(emptyinPowerset,axiom,
    ( emptyinPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).

thf(setadjoinOr,axiom,
    ( setadjoinOr
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ( ( X3 = X2 )
          | ( in @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).

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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).

thf(setadjoinIR,axiom,
    ( setadjoinIR
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ X4 )
       => ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
  <=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).

thf(setadjoinIL,axiom,
    ( setadjoinIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).

thf(nonemptyI1,axiom,
    ( nonemptyI1
  <=> ! [X4: $i] :
        ( ? [X2: $i] : ( in @ X2 @ X4 )
       => ( nonempty @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).

thf(emptyI,axiom,
    ( emptyI
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setext) ).

thf(notinemptyset,axiom,
    ( notinemptyset
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ~ $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).

thf(emptysetE,axiom,
    ( emptysetE
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ! [X11: $o] : X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).

thf(prop2setE,axiom,
    ( prop2setE
  <=> ! [X10: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X10 ) )
       => X10 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).

thf(omegaSAx,axiom,
    ( omegaSAx
  <=> ! [X2: $i] :
        ( ( in @ X2 @ omega )
       => ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).

thf(omega0Ax,axiom,
    ( omega0Ax
  <=> ( in @ emptyset @ omega ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).

thf(emptysetAx,axiom,
    ( emptysetAx
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextAx) ).

thf(c_0_114,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_115,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_127,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_128,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_129,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_130,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_131,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_132,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_133,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_134,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_135,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_136,plain,
    ( epred1_0
  <=> ! [X352: $i] :
      ? [X353: $i] :
        ( ! [X354: $i] :
            ( ( in @ X354 @ X353 )
           => ! [X355: $i] :
                ( ( in @ X355 @ X354 )
               => ( in @ X355 @ X352 ) ) )
        & ! [X356: $i,X357: $i] :
            ( ( ( in @ X356 @ X352 )
              & ( in @ X357 @ X352 ) )
           => ( ! [X358: $i] :
                  ( ( in @ X358 @ X353 )
                 => ( ( in @ X356 @ X358 )
                  <=> ( in @ X357 @ X358 ) ) )
             => ( X356 = X357 ) ) )
        & ! [X359: $i,X360: $i] :
            ( ( ( in @ X359 @ X353 )
              & ( in @ X360 @ X353 ) )
           => ( ! [X361: $i] :
                  ( ( in @ X361 @ X359 )
                 => ( in @ X361 @ X360 ) )
              | ! [X362: $i] :
                  ( ( in @ X362 @ X360 )
                 => ( in @ X362 @ X359 ) ) ) )
        & ! [X363: $i] :
            ( ( ! [X364: $i] :
                  ( ( in @ X364 @ X363 )
                 => ( in @ X364 @ X352 ) )
              & ? [X365: $i] : ( in @ X365 @ X363 ) )
           => ? [X366: $i,X367: $i] :
                ( ( in @ X366 @ X353 )
                & ( in @ X367 @ X363 )
                & ~ ? [X368: $i] :
                      ( ( in @ X368 @ X366 )
                      & ( in @ X368 @ X363 ) )
                & ! [X369: $i] :
                    ( ( in @ X369 @ X353 )
                   => ( ! [X370: $i] :
                          ( ( in @ X370 @ X369 )
                         => ( in @ X370 @ X366 ) )
                      | ( in @ X367 @ X369 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_137,negated_conjecture,
    ~ ( ! [X325: $i,X326: $i] :
          ( ! [X327: $i] :
              ( ( in @ X327 @ X325 )
            <=> ( in @ X327 @ X326 ) )
         => ( X325 = X326 ) )
     => ( ! [X328: $i] :
            ~ ( in @ X328 @ emptyset )
       => ( ! [X329: $i,X330: $i,X331: $i] :
              ( ( in @ X331 @ ( setadjoin @ X329 @ X330 ) )
            <=> ( ( X331 = X329 )
                | ( in @ X331 @ X330 ) ) )
         => ( ! [X332: $i,X333: $i] :
                ( ( in @ X333 @ ( powerset @ X332 ) )
              <=> ! [X334: $i] :
                    ( ( in @ X334 @ X333 )
                   => ( in @ X334 @ X332 ) ) )
           => ( ! [X335: $i,X336: $i] :
                  ( ( in @ X336 @ ( setunion @ X335 ) )
                <=> ? [X337: $i] :
                      ( ( in @ X336 @ X337 )
                      & ( in @ X337 @ X335 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X338: $i] :
                      ( ( in @ X338 @ omega )
                     => ( in @ ( setadjoin @ X338 @ X338 ) @ omega ) )
                 => ( ! [X339: $i] :
                        ( ( ( in @ emptyset @ X339 )
                          & ! [X340: $i] :
                              ( ( ( in @ X340 @ omega )
                                & ( in @ X340 @ X339 ) )
                             => ( in @ ( setadjoin @ X340 @ X340 ) @ X339 ) ) )
                       => ! [X341: $i] :
                            ( ( in @ X341 @ omega )
                           => ( in @ X341 @ X339 ) ) )
                   => ( ! [X342: $i > $i > $o,X343: $i] :
                          ( ! [X344: $i] :
                              ( ( in @ X344 @ X343 )
                             => ( exu @ ( X342 @ X344 ) ) )
                         => ? [X345: $i] :
                            ! [X346: $i] :
                              ( ( in @ X346 @ X345 )
                            <=> ? [X347: $i] :
                                  ( ( in @ X347 @ X343 )
                                  & ( X342 @ X347 @ X346 ) ) ) )
                     => ( ! [X348: $i] :
                            ( ? [X349: $i] : ( in @ X349 @ X348 )
                           => ? [X350: $i] :
                                ( ( in @ X350 @ X348 )
                                & ~ ? [X351: $i] :
                                      ( ( in @ X351 @ X350 )
                                      & ( in @ X351 @ X348 ) ) ) )
                       => ( epred1_0
                         => ( ! [X371: $i > $o] :
                                ( ( exu @ X371 )
                               => ( X371
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X371 @ Z0 ) ) ) )
                           => ( ! [X372: $i,X373: $i > $o,X374: $i] :
                                  ( ( in @ X374 @ X372 )
                                 => ( ( X373 @ X374 )
                                   => ( in @ X374 @ ( dsetconstr @ X372 @ X373 ) ) ) )
                             => ( ! [X375: $i,X376: $i > $o,X377: $i] :
                                    ( ( in @ X377 @ ( dsetconstr @ X375 @ X376 ) )
                                   => ( in @ X377 @ X375 ) )
                               => ( ! [X378: $i,X379: $i > $o,X380: $i] :
                                      ( ( in @ X380 @ ( dsetconstr @ X378 @ X379 ) )
                                     => ( X379 @ X380 ) )
                                 => ( ! [X381: $i > $o] :
                                        ( ( exu @ X381 )
                                       => ? [X382: $i] :
                                            ( ( X381 @ X382 )
                                            & ! [X383: $i] :
                                                ( ( X381 @ X383 )
                                               => ( X382 = X383 ) ) ) )
                                   => ( ! [X384: $o,X385: $i] :
                                          ( ( in @ X385 @ ( prop2set @ X384 ) )
                                         => X384 )
                                     => ( ! [X386: $i] :
                                            ( ( in @ X386 @ emptyset )
                                           => ! [X387: $o] : X387 )
                                       => ( ! [X388: $i] :
                                              ( ( in @ X388 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X389: $i] :
                                                ~ ( in @ X389 @ emptyset )
                                           => ( ! [X390: $i > $o] :
                                                  ( ( exu @ X390 )
                                                 => ? [X391: $i] : ( X390 @ X391 ) )
                                             => ( ! [X392: $i,X393: $i] :
                                                    ( ! [X394: $i] :
                                                        ( ( in @ X394 @ X392 )
                                                       => ( in @ X394 @ X393 ) )
                                                   => ( ! [X395: $i] :
                                                          ( ( in @ X395 @ X393 )
                                                         => ( in @ X395 @ X392 ) )
                                                     => ( X392 = X393 ) ) )
                                               => ( ! [X396: $i] :
                                                      ( ! [X397: $i] :
                                                          ~ ( in @ X397 @ X396 )
                                                     => ( X396 = emptyset ) )
                                                 => ( ! [X398: $i] :
                                                        ( ! [X399: $i] :
                                                            ~ ( in @ X399 @ X398 )
                                                       => ( X398 = emptyset ) )
                                                   => ( ! [X400: $i,X401: $i > $o,X402: $i] :
                                                          ( ( in @ X402 @ X400 )
                                                         => ( ( in @ X402 @ ( dsetconstr @ X400 @ X401 ) )
                                                          <=> ( X401 @ X402 ) ) )
                                                     => ( ! [X403: $i] :
                                                            ( ( nonempty @ X403 )
                                                           => ? [X404: $i] : ( in @ X404 @ X403 ) )
                                                       => ( ! [X405: $i,X406: $i > $o,X407: $i] :
                                                              ( ( in @ X407 @ X405 )
                                                             => ( ( X406 @ X407 )
                                                               => ( nonempty @ ( dsetconstr @ X405 @ X406 ) ) ) )
                                                         => ( ! [X408: $i] :
                                                                ( ? [X409: $i] : ( in @ X409 @ X408 )
                                                               => ( nonempty @ X408 ) )
                                                           => ( ! [X410: $i,X411: $i] : ( in @ X410 @ ( setadjoin @ X410 @ X411 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X412: $i,X413: $i,X414: $i] :
                                                                      ( ( in @ X414 @ X413 )
                                                                     => ( in @ X414 @ ( setadjoin @ X412 @ X413 ) ) )
                                                                 => ( ! [X415: $i,X416: $i,X417: $i] :
                                                                        ( ( in @ X417 @ ( setadjoin @ X415 @ X416 ) )
                                                                       => ! [X418: $o] :
                                                                            ( ( ( X417 = X415 )
                                                                             => X418 )
                                                                           => ( ( ( in @ X417 @ X416 )
                                                                               => X418 )
                                                                             => X418 ) ) )
                                                                   => ( ! [X419: $i,X420: $i,X421: $i] :
                                                                          ( ( in @ X421 @ ( setadjoin @ X419 @ X420 ) )
                                                                         => ( ( X421 = X419 )
                                                                            | ( in @ X421 @ X420 ) ) )
                                                                     => ( ! [X422: $i] :
                                                                            ( ( dsetconstr @ X422
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X422 )
                                                                       => ( ! [X423: $i,X424: $i] :
                                                                              ( ! [X425: $i] :
                                                                                  ( ( in @ X425 @ X424 )
                                                                                 => ( in @ X425 @ X423 ) )
                                                                             => ( in @ X424 @ ( powerset @ X423 ) ) )
                                                                         => ( ! [X426: $i] : ( in @ emptyset @ ( powerset @ X426 ) )
                                                                           => ( ! [X427: $i] : ( in @ emptyset @ ( powerset @ X427 ) )
                                                                             => ( ! [X428: $i,X429: $i,X430: $i] :
                                                                                    ( ( in @ X429 @ ( powerset @ X428 ) )
                                                                                   => ( ( in @ X430 @ X429 )
                                                                                     => ( in @ X430 @ X428 ) ) )
                                                                               => ( ! [X431: $i,X432: $i,X433: $i] :
                                                                                      ( ( in @ X432 @ X433 )
                                                                                     => ( ( in @ X433 @ X431 )
                                                                                       => ( in @ X432 @ ( setunion @ X431 ) ) ) )
                                                                                 => ( ! [X434: $i,X435: $i] :
                                                                                        ( ( in @ X435 @ ( setunion @ X434 ) )
                                                                                       => ! [X436: $o] :
                                                                                            ( ! [X437: $i] :
                                                                                                ( ( in @ X435 @ X437 )
                                                                                               => ( ( in @ X437 @ X434 )
                                                                                                 => X436 ) )
                                                                                           => X436 ) )
                                                                                   => ( ! [X438: $i,X439: $i] :
                                                                                          ( ( in @ X439 @ X438 )
                                                                                         => ( in @ X439 @ ( powerset @ ( setunion @ X438 ) ) ) )
                                                                                     => ( ! [X440: $i > $o] :
                                                                                            ( ( exu @ X440 )
                                                                                           => ? [X441: $i] :
                                                                                              ! [X442: $i] :
                                                                                                ( ( X440 @ X442 )
                                                                                              <=> ( X442 = X441 ) ) )
                                                                                       => ( ! [X443: $i] :
                                                                                              ( ( nonempty @ X443 )
                                                                                             => ? [X444: $i] :
                                                                                                  ( ( in @ X444 @ X443 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X445: $i,X446: $i] :
                                                                                                ( ( in @ X445 @ ( setadjoin @ X446 @ emptyset ) )
                                                                                               => ( X445 = X446 ) )
                                                                                           => ( ! [X447: $i,X448: $i] :
                                                                                                  ( ( X447 != X448 )
                                                                                                 => ~ ( in @ X448 @ ( setadjoin @ X447 @ emptyset ) ) )
                                                                                             => ( ! [X449: $i,X450: $i] :
                                                                                                    ( ( X449 = X450 )
                                                                                                   => ( in @ X449 @ ( setadjoin @ X450 @ emptyset ) ) )
                                                                                               => ( ! [X451: $i,X452: $i] :
                                                                                                      ( ( in @ X451 @ ( setadjoin @ X452 @ emptyset ) )
                                                                                                     => ( in @ X452 @ ( setadjoin @ X451 @ emptyset ) ) )
                                                                                                 => ( ! [X453: $i,X454: $i,X455: $i] :
                                                                                                        ( ( in @ X455 @ ( setadjoin @ X453 @ ( setadjoin @ X454 @ emptyset ) ) )
                                                                                                       => ( ( X455 = X453 )
                                                                                                          | ( X455 = X454 ) ) )
                                                                                                   => ( ! [X456: $i,X457: $i] : ( in @ X456 @ ( setadjoin @ X456 @ ( setadjoin @ X457 @ emptyset ) ) )
                                                                                                     => ( ! [X458: $i,X459: $i] : ( in @ X459 @ ( setadjoin @ X458 @ ( setadjoin @ X459 @ emptyset ) ) )
                                                                                                       => ( ! [X460: $i,X461: $i > $o] :
                                                                                                              ( ? [X462: $i] :
                                                                                                                  ( ( in @ X462 @ X460 )
                                                                                                                  & ( X461 @ X462 ) )
                                                                                                             => ( ( ( dsetconstr @ X460 @ X461 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X463: $i > $o,X464: $i] :
                                                                                                                ( ( in @ X464 @ emptyset )
                                                                                                               => ( X463 @ X464 ) )
                                                                                                           => ( ! [X465: $i,X466: $i > $o] :
                                                                                                                  ( ~ ! [X467: $i] :
                                                                                                                        ( ( in @ X467 @ X465 )
                                                                                                                       => ( X466 @ X467 ) )
                                                                                                                 => ? [X468: $i] :
                                                                                                                      ( ( in @ X468 @ X465 )
                                                                                                                      & ~ ( X466 @ X468 ) ) )
                                                                                                             => ( ! [X469: $i,X470: $i > $o] :
                                                                                                                    ( ! [X471: $i] :
                                                                                                                        ( ( in @ X471 @ X469 )
                                                                                                                       => ~ ( X470 @ X471 ) )
                                                                                                                   => ~ ? [X472: $i] :
                                                                                                                          ( ( in @ X472 @ X469 )
                                                                                                                          & ( X470 @ X472 ) ) )
                                                                                                               => ( ! [X473: $i,X474: $i > $o] :
                                                                                                                      ( ~ ? [X475: $i] :
                                                                                                                            ( ( in @ X475 @ X473 )
                                                                                                                            & ( X474 @ X475 ) )
                                                                                                                     => ! [X476: $i] :
                                                                                                                          ( ( in @ X476 @ X473 )
                                                                                                                         => ~ ( X474 @ X476 ) ) )
                                                                                                                 => ( ! [X477: $i,X478: $i > $o] :
                                                                                                                        ( ? [X479: $i] :
                                                                                                                            ( ( in @ X479 @ X477 )
                                                                                                                            & ~ ( X478 @ X479 ) )
                                                                                                                       => ~ ! [X480: $i] :
                                                                                                                              ( ( in @ X480 @ X477 )
                                                                                                                             => ( X478 @ X480 ) ) )
                                                                                                                   => ( ! [X481: $o] :
                                                                                                                          ( X481
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X481 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X482: $i,X483: $i > $o] :
                                                                                                                              ( ~ ? [X484: $i] :
                                                                                                                                    ( ( in @ X484 @ X482 )
                                                                                                                                    & ( X483 @ X484 ) )
                                                                                                                             => ! [X485: $i] :
                                                                                                                                  ( ( in @ X485 @ X482 )
                                                                                                                                 => ~ ( X483 @ X485 ) ) )
                                                                                                                         => ( ! [X486: $i,X487: $i > $o] :
                                                                                                                                ( ~ ! [X488: $i] :
                                                                                                                                      ( ( in @ X488 @ X486 )
                                                                                                                                     => ( X487 @ X488 ) )
                                                                                                                               => ? [X489: $i] :
                                                                                                                                    ( ( in @ X489 @ X486 )
                                                                                                                                    & ~ ( X487 @ X489 ) ) )
                                                                                                                           => ( ! [X490: $i > $o] :
                                                                                                                                  ( ? [X491: $i] :
                                                                                                                                      ( ( X490 @ X491 )
                                                                                                                                      & ! [X492: $i] :
                                                                                                                                          ( ( X490 @ X492 )
                                                                                                                                         => ( X491 = X492 ) ) )
                                                                                                                                 => ( exu @ X490 ) )
                                                                                                                             => ( ! [X493: $i > $o] :
                                                                                                                                    ( ? [X494: $i] : ( X493 @ X494 )
                                                                                                                                   => ( ! [X495: $i,X496: $i] :
                                                                                                                                          ( ( X493 @ X495 )
                                                                                                                                         => ( ( X493 @ X496 )
                                                                                                                                           => ( X495 = X496 ) ) )
                                                                                                                                     => ( exu @ X493 ) ) )
                                                                                                                               => ( ! [X497: $i > $o] :
                                                                                                                                      ( ? [X498: $i] :
                                                                                                                                        ! [X499: $i] :
                                                                                                                                          ( ( X497 @ X499 )
                                                                                                                                        <=> ( X499 = X498 ) )
                                                                                                                                     => ( exu @ X497 ) )
                                                                                                                                 => ( ! [X500: $i,X501: $i] :
                                                                                                                                        ( ( X500 = X501 )
                                                                                                                                       => ! [X502: $i,X503: $i] :
                                                                                                                                            ( ( X502 = X503 )
                                                                                                                                           => ( ( in @ X502 @ X500 )
                                                                                                                                             => ( in @ X503 @ X501 ) ) ) )
                                                                                                                                   => ( ! [X504: $i,X505: $i] :
                                                                                                                                          ( ( X504 = X505 )
                                                                                                                                         => ! [X506: $i,X507: $i] :
                                                                                                                                              ( ( X506 = X507 )
                                                                                                                                             => ( ( in @ X506 @ X504 )
                                                                                                                                              <=> ( in @ X507 @ X505 ) ) ) )
                                                                                                                                     => ( ! [X508: $i > $o] :
                                                                                                                                            ( ( exu @ X508 )
                                                                                                                                           => ! [X509: $i,X510: $i] :
                                                                                                                                                ( ( X508 @ X509 )
                                                                                                                                               => ( ( X508 @ X510 )
                                                                                                                                                 => ( X509 = X510 ) ) ) )
                                                                                                                                       => ( ! [X511: $i > $o,X512: $i > $o] :
                                                                                                                                              ( ! [X513: $i,X514: $i] :
                                                                                                                                                  ( ( X513 = X514 )
                                                                                                                                                 => ( ( X511 @ X513 )
                                                                                                                                                  <=> ( X512 @ X514 ) ) )
                                                                                                                                             => ( ( exu @ X511 )
                                                                                                                                              <=> ( exu @ X512 ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X515: $i,X516: $i] :
                                                                                                                                                  ( ( X515 = X516 )
                                                                                                                                                 => ! [X517: $i,X518: $i] :
                                                                                                                                                      ( ( X517 = X518 )
                                                                                                                                                     => ( ( setadjoin @ X515 @ X517 )
                                                                                                                                                        = ( setadjoin @ X516 @ X518 ) ) ) )
                                                                                                                                             => ( ! [X519: $i,X520: $i] :
                                                                                                                                                    ( ( X519 = X520 )
                                                                                                                                                   => ( ( powerset @ X519 )
                                                                                                                                                      = ( powerset @ X520 ) ) )
                                                                                                                                               => ( ! [X521: $i,X522: $i] :
                                                                                                                                                      ( ( X521 = X522 )
                                                                                                                                                     => ( ( setunion @ X521 )
                                                                                                                                                        = ( setunion @ X522 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X523: $i > $o] :
                                                                                                                                                          ( ( exu @ X523 )
                                                                                                                                                         => ! [X524: $i,X525: $i] :
                                                                                                                                                              ( ( X523 @ X524 )
                                                                                                                                                             => ( ( X523 @ X525 )
                                                                                                                                                               => ( X524 = X525 ) ) ) )
                                                                                                                                                     => ( ! [X526: $i > $o,X527: $i > $o] :
                                                                                                                                                            ( ! [X528: $i,X529: $i] :
                                                                                                                                                                ( ( X528 = X529 )
                                                                                                                                                               => ( ( X526 @ X528 )
                                                                                                                                                                <=> ( X527 @ X529 ) ) )
                                                                                                                                                           => ( ( exu @ X526 )
                                                                                                                                                             => ( ( exu @ X527 )
                                                                                                                                                               => ( ( descr @ X526 )
                                                                                                                                                                  = ( descr @ X527 ) ) ) ) )
                                                                                                                                                       => ( ! [X530: $i,X531: $i] :
                                                                                                                                                              ( ( X530 = X531 )
                                                                                                                                                             => ! [X532: $i > $o,X533: $i > $o] :
                                                                                                                                                                  ( ! [X534: $i] :
                                                                                                                                                                      ( ( in @ X534 @ X530 )
                                                                                                                                                                     => ! [X535: $i] :
                                                                                                                                                                          ( ( in @ X535 @ X531 )
                                                                                                                                                                         => ( ( X534 = X535 )
                                                                                                                                                                           => ( ( X532 @ X534 )
                                                                                                                                                                            <=> ( X533 @ X535 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X530 @ X532 )
                                                                                                                                                                    = ( dsetconstr @ X531 @ X533 ) ) ) )
                                                                                                                                                         => ( ! [X536: $i,X537: $i] :
                                                                                                                                                                ( ! [X538: $i] :
                                                                                                                                                                    ( ( in @ X538 @ X536 )
                                                                                                                                                                   => ( in @ X538 @ X537 ) )
                                                                                                                                                               => ( subset @ X536 @ X537 ) )
                                                                                                                                                           => ( ! [X539: $i,X540: $i] :
                                                                                                                                                                  ( ( X539 = X540 )
                                                                                                                                                                 => ( subset @ X540 @ X539 ) )
                                                                                                                                                             => ( ! [X541: $i,X542: $i] :
                                                                                                                                                                    ( ( X541 = X542 )
                                                                                                                                                                   => ( subset @ X541 @ X542 ) )
                                                                                                                                                               => ( ! [X543: $i,X544: $i] :
                                                                                                                                                                      ( ! [X545: $i] :
                                                                                                                                                                          ( ( in @ X545 @ X543 )
                                                                                                                                                                         => ( in @ X545 @ X544 ) )
                                                                                                                                                                     => ( subset @ X543 @ X544 ) )
                                                                                                                                                                 => ( ! [X546: $i] : ( subset @ emptyset @ X546 )
                                                                                                                                                                   => ( ! [X547: $i,X548: $i,X549: $i] :
                                                                                                                                                                          ( ( subset @ X547 @ X548 )
                                                                                                                                                                         => ( ( in @ X549 @ X547 )
                                                                                                                                                                           => ( in @ X549 @ X548 ) ) )
                                                                                                                                                                     => ( ! [X550: $i,X551: $i,X552: $i] :
                                                                                                                                                                            ( ( subset @ X550 @ X551 )
                                                                                                                                                                           => ( ~ ( in @ X552 @ X551 )
                                                                                                                                                                             => ~ ( in @ X552 @ X550 ) ) )
                                                                                                                                                                       => ( ! [X553: $i,X554: $i,X555: $i] :
                                                                                                                                                                              ( ( in @ X555 @ X553 )
                                                                                                                                                                             => ( ~ ( in @ X555 @ X554 )
                                                                                                                                                                               => ~ ( subset @ X553 @ X554 ) ) )
                                                                                                                                                                         => ( ! [X556: $i,X557: $i] :
                                                                                                                                                                                ( ~ ( subset @ X556 @ X557 )
                                                                                                                                                                               => ( X556 != X557 ) )
                                                                                                                                                                           => ( ! [X558: $i,X559: $i,X560: $i] :
                                                                                                                                                                                  ( ( in @ X560 @ X558 )
                                                                                                                                                                                 => ( ~ ( in @ X560 @ X559 )
                                                                                                                                                                                   => ( X558 != X559 ) ) )
                                                                                                                                                                             => ( ! [X561: $i] : ( subset @ X561 @ X561 )
                                                                                                                                                                               => ( ! [X562: $i,X563: $i,X564: $i] :
                                                                                                                                                                                      ( ( subset @ X562 @ X563 )
                                                                                                                                                                                     => ( ( subset @ X563 @ X564 )
                                                                                                                                                                                       => ( subset @ X562 @ X564 ) ) )
                                                                                                                                                                                 => ( ! [X565: $i,X566: $i] : ( subset @ X566 @ ( setadjoin @ X565 @ X566 ) )
                                                                                                                                                                                   => ( ! [X567: $i,X568: $i,X569: $i] :
                                                                                                                                                                                          ( ( subset @ X567 @ X569 )
                                                                                                                                                                                         => ( subset @ X567 @ ( setadjoin @ X568 @ X569 ) ) )
                                                                                                                                                                                     => ( ! [X570: $i,X571: $i] :
                                                                                                                                                                                            ( ( subset @ X570 @ X571 )
                                                                                                                                                                                           => ( in @ X570 @ ( powerset @ X571 ) ) )
                                                                                                                                                                                       => ( ! [X572: $i,X573: $i] :
                                                                                                                                                                                              ( ( subset @ X572 @ X573 )
                                                                                                                                                                                             => ( ( subset @ X573 @ X572 )
                                                                                                                                                                                               => ( X572 = X573 ) ) )
                                                                                                                                                                                         => ( ! [X574: $i] :
                                                                                                                                                                                                ( ( subset @ X574 @ emptyset )
                                                                                                                                                                                               => ( X574 = emptyset ) )
                                                                                                                                                                                           => ( ! [X575: $i,X576: $i] :
                                                                                                                                                                                                  ( ( subset @ X576 @ X575 )
                                                                                                                                                                                                 => ( in @ X576 @ ( powerset @ X575 ) ) )
                                                                                                                                                                                             => ( ! [X577: $i,X578: $i] :
                                                                                                                                                                                                    ( ( in @ X578 @ ( powerset @ X577 ) )
                                                                                                                                                                                                   => ( subset @ X578 @ X577 ) )
                                                                                                                                                                                               => ( ! [X579: $i] : ( in @ X579 @ ( powerset @ X579 ) )
                                                                                                                                                                                                 => ( ! [X580: $i,X581: $i] :
                                                                                                                                                                                                        ( ( subset @ X580 @ X581 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X580 ) @ ( powerset @ X581 ) ) )
                                                                                                                                                                                                   => ( ! [X582: $i,X583: $i > $o] : ( in @ ( dsetconstr @ X582 @ X583 ) @ ( powerset @ X582 ) )
                                                                                                                                                                                                     => ( ! [X584: $i,X585: $i > $o] : ( subset @ ( dsetconstr @ X584 @ X585 ) @ X584 )
                                                                                                                                                                                                       => ( ! [X586: $i,X587: $i,X588: $i] :
                                                                                                                                                                                                              ( ( in @ X588 @ X586 )
                                                                                                                                                                                                             => ( in @ X588 @ ( binunion @ X586 @ X587 ) ) )
                                                                                                                                                                                                         => ( ! [X589: $i,X590: $i] : ( in @ X590 @ ( setadjoin @ X589 @ ( setadjoin @ X590 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X591: $i,X592: $i,X593: $i] :
                                                                                                                                                                                                                  ( ( in @ X593 @ X592 )
                                                                                                                                                                                                                 => ( in @ X593 @ ( binunion @ X591 @ X592 ) ) )
                                                                                                                                                                                                             => ( ! [X594: $i,X595: $i,X596: $i,X597: $o] :
                                                                                                                                                                                                                    ( ( in @ X596 @ ( binunion @ X594 @ X595 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X596 @ X594 )
                                                                                                                                                                                                                       => X597 )
                                                                                                                                                                                                                     => ( ( ( in @ X596 @ X595 )
                                                                                                                                                                                                                         => X597 )
                                                                                                                                                                                                                       => X597 ) ) )
                                                                                                                                                                                                               => ( ! [X598: $i,X599: $i,X600: $i] :
                                                                                                                                                                                                                      ( ( in @ X600 @ ( binunion @ X598 @ X599 ) )
                                                                                                                                                                                                                     => ( ( in @ X600 @ X598 )
                                                                                                                                                                                                                        | ( in @ X600 @ X599 ) ) )
                                                                                                                                                                                                                 => ( ! [X601: $i,X602: $i] : ( subset @ X601 @ ( binunion @ X601 @ X602 ) )
                                                                                                                                                                                                                   => ( ! [X603: $i,X604: $i] : ( subset @ X604 @ ( binunion @ X603 @ X604 ) )
                                                                                                                                                                                                                     => ( ! [X605: $i,X606: $i,X607: $i] :
                                                                                                                                                                                                                            ( ( in @ X607 @ X605 )
                                                                                                                                                                                                                           => ( ( in @ X607 @ X606 )
                                                                                                                                                                                                                             => ( in @ X607 @ ( binintersect @ X605 @ X606 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X608: $i,X609: $i,X610: $i] :
                                                                                                                                                                                                                              ( ( subset @ X610 @ X608 )
                                                                                                                                                                                                                             => ( ( subset @ X610 @ X609 )
                                                                                                                                                                                                                               => ( subset @ X610 @ ( binintersect @ X608 @ X609 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X611: $i,X612: $i,X613: $i] :
                                                                                                                                                                                                                                ( ( in @ X613 @ ( binintersect @ X611 @ X612 ) )
                                                                                                                                                                                                                               => ( in @ X613 @ X611 ) )
                                                                                                                                                                                                                           => ( ! [X614: $i,X615: $i] : ( subset @ ( binintersect @ X614 @ X615 ) @ X614 )
                                                                                                                                                                                                                             => ( ! [X616: $i,X617: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X616 @ X617 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X616 @ X617 )
                                                                                                                                                                                                                                      = X616 ) )
                                                                                                                                                                                                                               => ( ! [X618: $i,X619: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X618 @ X619 )
                                                                                                                                                                                                                                        = X619 )
                                                                                                                                                                                                                                     => ( subset @ X619 @ X618 ) )
                                                                                                                                                                                                                                 => ( ! [X620: $i,X621: $i,X622: $i] :
                                                                                                                                                                                                                                        ( ( in @ X622 @ ( binintersect @ X620 @ X621 ) )
                                                                                                                                                                                                                                       => ( in @ X622 @ X621 ) )
                                                                                                                                                                                                                                   => ( ! [X623: $i,X624: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X625: $i] :
                                                                                                                                                                                                                                                ( ( in @ X625 @ X623 )
                                                                                                                                                                                                                                                & ( in @ X625 @ X624 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X623 @ X624 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X626: $i,X627: $i] : ( subset @ ( binintersect @ X626 @ X627 ) @ X627 )
                                                                                                                                                                                                                                       => ! [X4: $i,X5: $i] :
                                                                                                                                                                                                                                            ( ( subset @ X5 @ X4 )
                                                                                                                                                                                                                                           => ( ( binintersect @ X4 @ X5 )
                                                                                                                                                                                                                                              = 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(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)],[binintersectSubset4]),binintersectRsub]),powersetI1]),emptyInPowerset]),powersetE1]),inPowerset]),powersetsubset]),powersetE]),c_0_114]),c_0_115]),setunionI]),binunionIL]),upairset2IR]),setunionE]),binunionIR]),binunionEcases]),subPowSU]),binunionE]),binunionLsub]),c_0_116]),binunionRsub]),binintersectI]),nonemptyImpWitness]),binintersectSubset5]),uniqinunit]),binintersectEL]),binintersectLsub]),binintersectSubset2]),notinsingleton]),binintersectSubset3]),binintersectER]),disjointsetsI1]),eqinunit]),c_0_117]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_118]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_119]),c_0_120]),c_0_121]),inCongP]),in__Cong]),c_0_122]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_123]),c_0_124]),c_0_125]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),powersetI]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),emptyinPowerset]),c_0_126]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_127]),nonemptyE1]),c_0_128]),noeltsimpempty]),emptyI]),setext]),c_0_129]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_130]),c_0_131]),c_0_132]),c_0_133]),c_0_134]),wellorderingAx]),foundationAx]),c_0_135]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_136]) ).

thf(c_0_138,negated_conjecture,
    ! [X628: $i,X629: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X641: $i,X642: $i,X644: $i,X645: $i,X646: $i,X647: $i,X648: $i,X650: $i,X651: $i > $i > $o,X652: $i,X655: $i,X657: $i,X658: $i,X659: $i,X660: $i,X662: $i,X663: $i > $o,X664: $i,X665: $i > $o,X666: $i,X667: $i,X668: $i > $o,X669: $i,X670: $i,X671: $i > $o,X672: $i,X673: $i > $o,X675: $i,X676: $o,X677: $i,X678: $i,X679: $o,X680: $i,X681: $i,X682: $i > $o,X684: $i,X685: $i,X688: $i,X690: $i,X692: $i,X693: $i > $o,X694: $i,X695: $i,X697: $i,X698: $i > $o,X699: $i,X700: $i,X701: $i,X702: $i,X703: $i,X704: $i,X705: $i,X706: $i,X707: $i,X708: $i,X709: $i,X710: $o,X711: $i,X712: $i,X713: $i,X714: $i,X715: $i,X716: $i,X718: $i,X719: $i,X720: $i,X721: $i,X722: $i,X723: $i,X724: $i,X725: $i,X726: $i,X727: $i,X728: $o,X730: $i,X731: $i,X732: $i > $o,X734: $i,X735: $i,X736: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i,X752: $i,X753: $i,X754: $i > $o,X755: $i,X756: $i > $o,X757: $i,X758: $i,X759: $i > $o,X760: $i,X762: $i,X763: $i > $o,X765: $i,X766: $i,X767: $i > $o,X769: $i,X770: $i,X771: $i > $o,X772: $i,X774: $o,X775: $i,X776: $i > $o,X778: $i,X779: $i,X780: $i > $o,X781: $i,X783: $i > $o,X784: $i,X786: $i > $o,X787: $i,X790: $i > $o,X791: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i > $o,X802: $i,X803: $i,X804: $i > $o,X805: $i > $o,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X814: $i,X815: $i,X816: $i > $o,X817: $i,X818: $i,X819: $i > $o,X820: $i > $o,X823: $i,X824: $i,X825: $i > $o,X826: $i > $o,X829: $i,X830: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X839: $i,X840: $i,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $i,X859: $i,X860: $i,X861: $i,X862: $i,X863: $i,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i > $o,X877: $i,X878: $i > $o,X879: $i,X880: $i,X881: $i,X882: $i,X883: $i,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X890: $o,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X901: $i,X902: $i,X903: $i,X904: $i,X905: $i,X906: $i,X907: $i,X908: $i,X909: $i,X910: $i,X911: $i,X912: $i,X913: $i,X914: $i,X915: $i,X916: $i,X917: $i,X919: $i,X920: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X628 @ X629 ) @ X628 )
        | ~ ( in @ ( esk1_2 @ X628 @ X629 ) @ X629 )
        | ( X628 = X629 ) )
      & ( ( in @ ( esk1_2 @ X628 @ X629 ) @ X628 )
        | ( in @ ( esk1_2 @ X628 @ X629 ) @ X629 )
        | ( X628 = X629 ) )
      & ~ ( in @ X631 @ emptyset )
      & ( ~ ( in @ X634 @ ( setadjoin @ X632 @ X633 ) )
        | ( X634 = X632 )
        | ( in @ X634 @ X633 ) )
      & ( ( X634 != X632 )
        | ( in @ X634 @ ( setadjoin @ X632 @ X633 ) ) )
      & ( ~ ( in @ X634 @ X633 )
        | ( in @ X634 @ ( setadjoin @ X632 @ X633 ) ) )
      & ( ~ ( in @ X636 @ ( powerset @ X635 ) )
        | ~ ( in @ X637 @ X636 )
        | ( in @ X637 @ X635 ) )
      & ( ( in @ ( esk2_2 @ X638 @ X639 ) @ X639 )
        | ( in @ X639 @ ( powerset @ X638 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X638 @ X639 ) @ X638 )
        | ( in @ X639 @ ( powerset @ X638 ) ) )
      & ( ( in @ X642 @ ( esk3_2 @ X641 @ X642 ) )
        | ~ ( in @ X642 @ ( setunion @ X641 ) ) )
      & ( ( in @ ( esk3_2 @ X641 @ X642 ) @ X641 )
        | ~ ( in @ X642 @ ( setunion @ X641 ) ) )
      & ( ~ ( in @ X645 @ X646 )
        | ~ ( in @ X646 @ X644 )
        | ( in @ X645 @ ( setunion @ X644 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X647 @ omega )
        | ( in @ ( setadjoin @ X647 @ X647 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X648 ) @ omega )
        | ~ ( in @ emptyset @ X648 )
        | ~ ( in @ X650 @ omega )
        | ( in @ X650 @ X648 ) )
      & ( ( in @ ( esk4_1 @ X648 ) @ X648 )
        | ~ ( in @ emptyset @ X648 )
        | ~ ( in @ X650 @ omega )
        | ( in @ X650 @ X648 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X648 ) @ ( esk4_1 @ X648 ) ) @ X648 )
        | ~ ( in @ emptyset @ X648 )
        | ~ ( in @ X650 @ omega )
        | ( in @ X650 @ X648 ) )
      & ( ( in @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X652 )
        | ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
        | ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
      & ( ( X651 @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X655 )
        | ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
        | ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
      & ( ~ ( in @ X658 @ X652 )
        | ~ ( X651 @ X658 @ X657 )
        | ( in @ X657 @ ( esk6_2 @ X651 @ X652 ) )
        | ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
      & ( ( in @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X652 )
        | ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
        | ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
      & ( ( X651 @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X655 )
        | ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
        | ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
      & ( ~ ( in @ X658 @ X652 )
        | ~ ( X651 @ X658 @ X657 )
        | ( in @ X657 @ ( esk6_2 @ X651 @ X652 ) )
        | ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
      & ( ( in @ ( esk8_1 @ X659 ) @ X659 )
        | ~ ( in @ X660 @ X659 ) )
      & ( ~ ( in @ X662 @ ( esk8_1 @ X659 ) )
        | ~ ( in @ X662 @ X659 )
        | ~ ( in @ X660 @ X659 ) )
      & epred1_0
      & ( ~ ( exu @ X663 )
        | ( X663 @ ( descr @ X663 ) ) )
      & ( ~ ( in @ X666 @ X664 )
        | ~ ( X665 @ X666 )
        | ( in @ X666 @ ( dsetconstr @ X664 @ X665 ) ) )
      & ( ~ ( in @ X669 @ ( dsetconstr @ X667 @ X668 ) )
        | ( in @ X669 @ X667 ) )
      & ( ~ ( in @ X672 @ ( dsetconstr @ X670 @ X671 ) )
        | ( X671 @ X672 ) )
      & ( ( X673 @ ( esk9_1 @ X673 ) )
        | ~ ( exu @ X673 ) )
      & ( ~ ( X673 @ X675 )
        | ( ( esk9_1 @ X673 )
          = X675 )
        | ~ ( exu @ X673 ) )
      & ( ~ ( in @ X677 @ ( prop2set @ X676 ) )
        | X676 )
      & ( ~ ( in @ X678 @ emptyset )
        | X679 )
      & ( ~ ( in @ X680 @ emptyset )
        | ~ $true )
      & ~ ( in @ X681 @ emptyset )
      & ( ~ ( exu @ X682 )
        | ( X682 @ ( esk10_1 @ X682 ) ) )
      & ( ( in @ ( esk12_2 @ X684 @ X685 ) @ X685 )
        | ( X684 = X685 )
        | ( in @ ( esk11_2 @ X684 @ X685 ) @ X684 ) )
      & ( ~ ( in @ ( esk12_2 @ X684 @ X685 ) @ X684 )
        | ( X684 = X685 )
        | ( in @ ( esk11_2 @ X684 @ X685 ) @ X684 ) )
      & ( ( in @ ( esk12_2 @ X684 @ X685 ) @ X685 )
        | ( X684 = X685 )
        | ~ ( in @ ( esk11_2 @ X684 @ X685 ) @ X685 ) )
      & ( ~ ( in @ ( esk12_2 @ X684 @ X685 ) @ X684 )
        | ( X684 = X685 )
        | ~ ( in @ ( esk11_2 @ X684 @ X685 ) @ X685 ) )
      & ( ( in @ ( esk13_1 @ X688 ) @ X688 )
        | ( X688 = emptyset ) )
      & ( ( in @ ( esk14_1 @ X690 ) @ X690 )
        | ( X690 = emptyset ) )
      & ( ~ ( in @ X694 @ ( dsetconstr @ X692 @ X693 ) )
        | ( X693 @ X694 )
        | ~ ( in @ X694 @ X692 ) )
      & ( ~ ( X693 @ X694 )
        | ( in @ X694 @ ( dsetconstr @ X692 @ X693 ) )
        | ~ ( in @ X694 @ X692 ) )
      & ( ~ ( nonempty @ X695 )
        | ( in @ ( esk15_1 @ X695 ) @ X695 ) )
      & ( ~ ( in @ X699 @ X697 )
        | ~ ( X698 @ X699 )
        | ( nonempty @ ( dsetconstr @ X697 @ X698 ) ) )
      & ( ~ ( in @ X701 @ X700 )
        | ( nonempty @ X700 ) )
      & ( in @ X702 @ ( setadjoin @ X702 @ X703 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X706 @ X705 )
        | ( in @ X706 @ ( setadjoin @ X704 @ X705 ) ) )
      & ( ( in @ X709 @ X708 )
        | X710
        | ( X709 = X707 )
        | ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
      & ( ~ X710
        | X710
        | ( X709 = X707 )
        | ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
      & ( ( in @ X709 @ X708 )
        | X710
        | ~ X710
        | ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
      & ( ~ X710
        | X710
        | ~ X710
        | ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
      & ( ~ ( in @ X713 @ ( setadjoin @ X711 @ X712 ) )
        | ( X713 = X711 )
        | ( in @ X713 @ X712 ) )
      & ( ( dsetconstr @ X714
          @ ^ [Z0: $i] : $true )
        = X714 )
      & ( ( in @ ( esk16_2 @ X715 @ X716 ) @ X716 )
        | ( in @ X716 @ ( powerset @ X715 ) ) )
      & ( ~ ( in @ ( esk16_2 @ X715 @ X716 ) @ X715 )
        | ( in @ X716 @ ( powerset @ X715 ) ) )
      & ( in @ emptyset @ ( powerset @ X718 ) )
      & ( in @ emptyset @ ( powerset @ X719 ) )
      & ( ~ ( in @ X721 @ ( powerset @ X720 ) )
        | ~ ( in @ X722 @ X721 )
        | ( in @ X722 @ X720 ) )
      & ( ~ ( in @ X724 @ X725 )
        | ~ ( in @ X725 @ X723 )
        | ( in @ X724 @ ( setunion @ X723 ) ) )
      & ( ( in @ X727 @ ( esk17_3 @ X726 @ X727 @ X728 ) )
        | X728
        | ~ ( in @ X727 @ ( setunion @ X726 ) ) )
      & ( ( in @ ( esk17_3 @ X726 @ X727 @ X728 ) @ X726 )
        | X728
        | ~ ( in @ X727 @ ( setunion @ X726 ) ) )
      & ( ~ X728
        | X728
        | ~ ( in @ X727 @ ( setunion @ X726 ) ) )
      & ( ~ ( in @ X731 @ X730 )
        | ( in @ X731 @ ( powerset @ ( setunion @ X730 ) ) ) )
      & ( ~ ( X732 @ X734 )
        | ( X734
          = ( esk18_1 @ X732 ) )
        | ~ ( exu @ X732 ) )
      & ( ( X735
         != ( esk18_1 @ X732 ) )
        | ( X732 @ X735 )
        | ~ ( exu @ X732 ) )
      & ( ( in @ ( esk19_1 @ X736 ) @ X736 )
        | ~ ( nonempty @ X736 ) )
      & ( $true
        | ~ ( nonempty @ X736 ) )
      & ( ~ ( in @ X738 @ ( setadjoin @ X739 @ emptyset ) )
        | ( X738 = X739 ) )
      & ( ( X740 = X741 )
        | ~ ( in @ X741 @ ( setadjoin @ X740 @ emptyset ) ) )
      & ( ( X742 != X743 )
        | ( in @ X742 @ ( setadjoin @ X743 @ emptyset ) ) )
      & ( ~ ( in @ X744 @ ( setadjoin @ X745 @ emptyset ) )
        | ( in @ X745 @ ( setadjoin @ X744 @ emptyset ) ) )
      & ( ~ ( in @ X748 @ ( setadjoin @ X746 @ ( setadjoin @ X747 @ emptyset ) ) )
        | ( X748 = X746 )
        | ( X748 = X747 ) )
      & ( in @ X749 @ ( setadjoin @ X749 @ ( setadjoin @ X750 @ emptyset ) ) )
      & ( in @ X752 @ ( setadjoin @ X751 @ ( setadjoin @ X752 @ emptyset ) ) )
      & ( ~ ( in @ X755 @ X753 )
        | ~ ( X754 @ X755 )
        | ( ( dsetconstr @ X753 @ X754 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X757 @ emptyset )
        | ( X756 @ X757 ) )
      & ( ( in @ ( esk20_2 @ X758 @ X759 ) @ X758 )
        | ~ ( in @ X760 @ X758 )
        | ( X759 @ X760 ) )
      & ( ~ ( X759 @ ( esk20_2 @ X758 @ X759 ) )
        | ~ ( in @ X760 @ X758 )
        | ( X759 @ X760 ) )
      & ( ( in @ ( esk21_2 @ X762 @ X763 ) @ X762 )
        | ~ ( in @ X765 @ X762 )
        | ~ ( X763 @ X765 ) )
      & ( ( X763 @ ( esk21_2 @ X762 @ X763 ) )
        | ~ ( in @ X765 @ X762 )
        | ~ ( X763 @ X765 ) )
      & ( ( in @ ( esk22_2 @ X766 @ X767 ) @ X766 )
        | ~ ( in @ X769 @ X766 )
        | ~ ( X767 @ X769 ) )
      & ( ( X767 @ ( esk22_2 @ X766 @ X767 ) )
        | ~ ( in @ X769 @ X766 )
        | ~ ( X767 @ X769 ) )
      & ( ( in @ ( esk23_2 @ X770 @ X771 ) @ X770 )
        | ~ ( in @ X772 @ X770 )
        | ( X771 @ X772 ) )
      & ( ~ ( X771 @ ( esk23_2 @ X770 @ X771 ) )
        | ~ ( in @ X772 @ X770 )
        | ( X771 @ X772 ) )
      & ( ~ X774
        | ( in @ emptyset @ ( prop2set @ X774 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk24_2 @ X775 @ X776 ) @ X775 )
        | ~ ( in @ X778 @ X775 )
        | ~ ( X776 @ X778 ) )
      & ( ( X776 @ ( esk24_2 @ X775 @ X776 ) )
        | ~ ( in @ X778 @ X775 )
        | ~ ( X776 @ X778 ) )
      & ( ( in @ ( esk25_2 @ X779 @ X780 ) @ X779 )
        | ~ ( in @ X781 @ X779 )
        | ( X780 @ X781 ) )
      & ( ~ ( X780 @ ( esk25_2 @ X779 @ X780 ) )
        | ~ ( in @ X781 @ X779 )
        | ( X780 @ X781 ) )
      & ( ( X783 @ ( esk26_2 @ X783 @ X784 ) )
        | ~ ( X783 @ X784 )
        | ( exu @ X783 ) )
      & ( ( X784
         != ( esk26_2 @ X783 @ X784 ) )
        | ~ ( X783 @ X784 )
        | ( exu @ X783 ) )
      & ( ( X786 @ ( esk27_1 @ X786 ) )
        | ( exu @ X786 )
        | ~ ( X786 @ X787 ) )
      & ( ( X786 @ ( esk28_1 @ X786 ) )
        | ( exu @ X786 )
        | ~ ( X786 @ X787 ) )
      & ( ( ( esk27_1 @ X786 )
         != ( esk28_1 @ X786 ) )
        | ( exu @ X786 )
        | ~ ( X786 @ X787 ) )
      & ( ~ ( X790 @ ( esk29_2 @ X790 @ X791 ) )
        | ( ( esk29_2 @ X790 @ X791 )
         != X791 )
        | ( exu @ X790 ) )
      & ( ( X790 @ ( esk29_2 @ X790 @ X791 ) )
        | ( ( esk29_2 @ X790 @ X791 )
          = X791 )
        | ( exu @ X790 ) )
      & ( ( X793 != X794 )
        | ( X795 != X796 )
        | ~ ( in @ X795 @ X793 )
        | ( in @ X796 @ X794 ) )
      & ( ~ ( in @ X799 @ X797 )
        | ( in @ X800 @ X798 )
        | ( X799 != X800 )
        | ( X797 != X798 ) )
      & ( ~ ( in @ X800 @ X798 )
        | ( in @ X799 @ X797 )
        | ( X799 != X800 )
        | ( X797 != X798 ) )
      & ( ~ ( exu @ X801 )
        | ~ ( X801 @ X802 )
        | ~ ( X801 @ X803 )
        | ( X802 = X803 ) )
      & ( ~ ( exu @ X804 )
        | ( exu @ X805 )
        | ( ( esk30_2 @ X804 @ X805 )
          = ( esk31_2 @ X804 @ X805 ) ) )
      & ( ~ ( exu @ X805 )
        | ( exu @ X804 )
        | ( ( esk30_2 @ X804 @ X805 )
          = ( esk31_2 @ X804 @ X805 ) ) )
      & ( ~ ( exu @ X804 )
        | ( exu @ X805 )
        | ~ ( X804 @ ( esk30_2 @ X804 @ X805 ) )
        | ~ ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
      & ( ~ ( exu @ X805 )
        | ( exu @ X804 )
        | ~ ( X804 @ ( esk30_2 @ X804 @ X805 ) )
        | ~ ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
      & ( ~ ( exu @ X804 )
        | ( exu @ X805 )
        | ( X804 @ ( esk30_2 @ X804 @ X805 ) )
        | ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
      & ( ~ ( exu @ X805 )
        | ( exu @ X804 )
        | ( X804 @ ( esk30_2 @ X804 @ X805 ) )
        | ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
      & ( emptyset = emptyset )
      & ( ( X808 != X809 )
        | ( X810 != X811 )
        | ( ( setadjoin @ X808 @ X810 )
          = ( setadjoin @ X809 @ X811 ) ) )
      & ( ( X812 != X813 )
        | ( ( powerset @ X812 )
          = ( powerset @ X813 ) ) )
      & ( ( X814 != X815 )
        | ( ( setunion @ X814 )
          = ( setunion @ X815 ) ) )
      & ( omega = omega )
      & ( ~ ( exu @ X816 )
        | ~ ( X816 @ X817 )
        | ~ ( X816 @ X818 )
        | ( X817 = X818 ) )
      & ( ( ( esk32_2 @ X819 @ X820 )
          = ( esk33_2 @ X819 @ X820 ) )
        | ~ ( exu @ X819 )
        | ~ ( exu @ X820 )
        | ( ( descr @ X819 )
          = ( descr @ X820 ) ) )
      & ( ~ ( X819 @ ( esk32_2 @ X819 @ X820 ) )
        | ~ ( X820 @ ( esk33_2 @ X819 @ X820 ) )
        | ~ ( exu @ X819 )
        | ~ ( exu @ X820 )
        | ( ( descr @ X819 )
          = ( descr @ X820 ) ) )
      & ( ( X819 @ ( esk32_2 @ X819 @ X820 ) )
        | ( X820 @ ( esk33_2 @ X819 @ X820 ) )
        | ~ ( exu @ X819 )
        | ~ ( exu @ X820 )
        | ( ( descr @ X819 )
          = ( descr @ X820 ) ) )
      & ( ( in @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) @ X823 )
        | ( ( dsetconstr @ X823 @ X825 )
          = ( dsetconstr @ X824 @ X826 ) )
        | ( X823 != X824 ) )
      & ( ( in @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) @ X824 )
        | ( ( dsetconstr @ X823 @ X825 )
          = ( dsetconstr @ X824 @ X826 ) )
        | ( X823 != X824 ) )
      & ( ( ( esk34_4 @ X823 @ X824 @ X825 @ X826 )
          = ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
        | ( ( dsetconstr @ X823 @ X825 )
          = ( dsetconstr @ X824 @ X826 ) )
        | ( X823 != X824 ) )
      & ( ~ ( X825 @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) )
        | ~ ( X826 @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
        | ( ( dsetconstr @ X823 @ X825 )
          = ( dsetconstr @ X824 @ X826 ) )
        | ( X823 != X824 ) )
      & ( ( X825 @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) )
        | ( X826 @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
        | ( ( dsetconstr @ X823 @ X825 )
          = ( dsetconstr @ X824 @ X826 ) )
        | ( X823 != X824 ) )
      & ( ( in @ ( esk36_2 @ X829 @ X830 ) @ X829 )
        | ( subset @ X829 @ X830 ) )
      & ( ~ ( in @ ( esk36_2 @ X829 @ X830 ) @ X830 )
        | ( subset @ X829 @ X830 ) )
      & ( ( X832 != X833 )
        | ( subset @ X833 @ X832 ) )
      & ( ( X834 != X835 )
        | ( subset @ X834 @ X835 ) )
      & ( ( in @ ( esk37_2 @ X836 @ X837 ) @ X836 )
        | ( subset @ X836 @ X837 ) )
      & ( ~ ( in @ ( esk37_2 @ X836 @ X837 ) @ X837 )
        | ( subset @ X836 @ X837 ) )
      & ( subset @ emptyset @ X839 )
      & ( ~ ( subset @ X840 @ X841 )
        | ~ ( in @ X842 @ X840 )
        | ( in @ X842 @ X841 ) )
      & ( ~ ( subset @ X843 @ X844 )
        | ( in @ X845 @ X844 )
        | ~ ( in @ X845 @ X843 ) )
      & ( ~ ( in @ X848 @ X846 )
        | ( in @ X848 @ X847 )
        | ~ ( subset @ X846 @ X847 ) )
      & ( ( subset @ X849 @ X850 )
        | ( X849 != X850 ) )
      & ( ~ ( in @ X853 @ X851 )
        | ( in @ X853 @ X852 )
        | ( X851 != X852 ) )
      & ( subset @ X854 @ X854 )
      & ( ~ ( subset @ X855 @ X856 )
        | ~ ( subset @ X856 @ X857 )
        | ( subset @ X855 @ X857 ) )
      & ( subset @ X859 @ ( setadjoin @ X858 @ X859 ) )
      & ( ~ ( subset @ X860 @ X862 )
        | ( subset @ X860 @ ( setadjoin @ X861 @ X862 ) ) )
      & ( ~ ( subset @ X863 @ X864 )
        | ( in @ X863 @ ( powerset @ X864 ) ) )
      & ( ~ ( subset @ X865 @ X866 )
        | ~ ( subset @ X866 @ X865 )
        | ( X865 = X866 ) )
      & ( ~ ( subset @ X867 @ emptyset )
        | ( X867 = emptyset ) )
      & ( ~ ( subset @ X869 @ X868 )
        | ( in @ X869 @ ( powerset @ X868 ) ) )
      & ( ~ ( in @ X871 @ ( powerset @ X870 ) )
        | ( subset @ X871 @ X870 ) )
      & ( in @ X872 @ ( powerset @ X872 ) )
      & ( ~ ( subset @ X873 @ X874 )
        | ( subset @ ( powerset @ X873 ) @ ( powerset @ X874 ) ) )
      & ( in @ ( dsetconstr @ X875 @ X876 ) @ ( powerset @ X875 ) )
      & ( subset @ ( dsetconstr @ X877 @ X878 ) @ X877 )
      & ( ~ ( in @ X881 @ X879 )
        | ( in @ X881 @ ( binunion @ X879 @ X880 ) ) )
      & ( in @ X883 @ ( setadjoin @ X882 @ ( setadjoin @ X883 @ emptyset ) ) )
      & ( ~ ( in @ X886 @ X885 )
        | ( in @ X886 @ ( binunion @ X884 @ X885 ) ) )
      & ( ( in @ X889 @ X888 )
        | X890
        | ( in @ X889 @ X887 )
        | ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
      & ( ~ X890
        | X890
        | ( in @ X889 @ X887 )
        | ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
      & ( ( in @ X889 @ X888 )
        | X890
        | ~ X890
        | ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
      & ( ~ X890
        | X890
        | ~ X890
        | ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
      & ( ~ ( in @ X893 @ ( binunion @ X891 @ X892 ) )
        | ( in @ X893 @ X891 )
        | ( in @ X893 @ X892 ) )
      & ( subset @ X894 @ ( binunion @ X894 @ X895 ) )
      & ( subset @ X897 @ ( binunion @ X896 @ X897 ) )
      & ( ~ ( in @ X900 @ X898 )
        | ~ ( in @ X900 @ X899 )
        | ( in @ X900 @ ( binintersect @ X898 @ X899 ) ) )
      & ( ~ ( subset @ X903 @ X901 )
        | ~ ( subset @ X903 @ X902 )
        | ( subset @ X903 @ ( binintersect @ X901 @ X902 ) ) )
      & ( ~ ( in @ X906 @ ( binintersect @ X904 @ X905 ) )
        | ( in @ X906 @ X904 ) )
      & ( subset @ ( binintersect @ X907 @ X908 ) @ X907 )
      & ( ~ ( subset @ X909 @ X910 )
        | ( ( binintersect @ X909 @ X910 )
          = X909 ) )
      & ( ( ( binintersect @ X911 @ X912 )
         != X912 )
        | ( subset @ X912 @ X911 ) )
      & ( ~ ( in @ X915 @ ( binintersect @ X913 @ X914 ) )
        | ( in @ X915 @ X914 ) )
      & ( ( in @ ( esk38_2 @ X916 @ X917 ) @ X916 )
        | ( ( binintersect @ X916 @ X917 )
          = emptyset ) )
      & ( ( in @ ( esk38_2 @ X916 @ X917 ) @ X917 )
        | ( ( binintersect @ X916 @ X917 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X919 @ X920 ) @ X920 )
      & ( subset @ esk40_0 @ esk39_0 )
      & ( ( binintersect @ esk39_0 @ esk40_0 )
       != esk40_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_137])])])])])])]) ).

thf(c_0_139,negated_conjecture,
    ! [X3: $i,X2: $i] :
      ( ( X2 = X3 )
      | ~ ( subset @ X2 @ X3 )
      | ~ ( subset @ X3 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_140,negated_conjecture,
    ! [X2: $i,X3: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_141,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( ( binintersect @ X2 @ X3 )
        = X3 )
      | ~ ( subset @ X3 @ ( binintersect @ X2 @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_139,c_0_140]) ).

thf(c_0_142,negated_conjecture,
    ! [X2: $i,X3: $i,X4: $i] :
      ( ( subset @ X2 @ ( binintersect @ X3 @ X4 ) )
      | ~ ( subset @ X2 @ X3 )
      | ~ ( subset @ X2 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_143,negated_conjecture,
    ! [X2: $i] : ( subset @ X2 @ X2 ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_144,negated_conjecture,
    ( ( binintersect @ esk39_0 @ esk40_0 )
   != esk40_0 ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_145,negated_conjecture,
    ! [X3: $i,X2: $i] :
      ( ( ( binintersect @ X2 @ X3 )
        = X3 )
      | ~ ( subset @ X3 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143])]) ).

thf(c_0_146,negated_conjecture,
    subset @ esk40_0 @ esk39_0,
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

thf(c_0_147,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU598^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 17:12:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.19/0.46  Running higher-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.77/0.61  # Version: 3.1.0-ho
% 0.77/0.61  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61  # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61  # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61  # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61  # Starting pre_casc_3 with 300s (1) cores
% 0.77/0.61  # Starting ho_unfolding_8 with 300s (1) cores
% 0.77/0.61  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.77/0.61  # Starting new_bool_3 with 300s (1) cores
% 0.77/0.61  # Starting new_ho_5 with 300s (1) cores
% 0.77/0.61  # new_ho_5 with pid 3244 completed with status 8
% 0.77/0.61  # new_bool_5 with pid 3239 completed with status 0
% 0.77/0.61  # Result found by new_bool_5
% 0.77/0.61  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61  # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61  # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61  # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.77/0.61  # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.77/0.61  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.61  # Starting ehoh_best3 with 163s (1) cores
% 0.77/0.61  # ehoh_best3 with pid 3248 completed with status 0
% 0.77/0.61  # Result found by ehoh_best3
% 0.77/0.61  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61  # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61  # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61  # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.77/0.61  # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.77/0.61  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.61  # Starting ehoh_best3 with 163s (1) cores
% 0.77/0.61  # Preprocessing time       : 0.002 s
% 0.77/0.61  # Presaturation interreduction done
% 0.77/0.61  
% 0.77/0.61  # Proof found!
% 0.77/0.61  # SZS status Theorem
% 0.77/0.61  # SZS output start CNFRefutation
% See solution above
% 0.77/0.61  # Parsed axioms                        : 248
% 0.77/0.61  # Removed by relevancy pruning/SinE    : 134
% 0.77/0.61  # Initial clauses                      : 187
% 0.77/0.61  # Removed in clause preprocessing      : 18
% 0.77/0.61  # Initial clauses in saturation        : 169
% 0.77/0.61  # Processed clauses                    : 1215
% 0.77/0.61  # ...of these trivial                  : 53
% 0.77/0.61  # ...subsumed                          : 486
% 0.77/0.61  # ...remaining for further processing  : 676
% 0.77/0.61  # Other redundant clauses eliminated   : 38
% 0.77/0.61  # Clauses deleted for lack of memory   : 0
% 0.77/0.61  # Backward-subsumed                    : 3
% 0.77/0.61  # Backward-rewritten                   : 3
% 0.77/0.61  # Generated clauses                    : 8020
% 0.77/0.61  # ...of the previous two non-redundant : 5761
% 0.77/0.61  # ...aggressively subsumed             : 0
% 0.77/0.61  # Contextual simplify-reflections      : 3
% 0.77/0.61  # Paramodulations                      : 7979
% 0.77/0.61  # Factorizations                       : 2
% 0.77/0.61  # NegExts                              : 0
% 0.77/0.61  # Equation resolutions                 : 38
% 0.77/0.61  # Disequality decompositions           : 0
% 0.77/0.61  # Total rewrite steps                  : 2795
% 0.77/0.61  # ...of those cached                   : 2524
% 0.77/0.61  # Propositional unsat checks           : 0
% 0.77/0.61  #    Propositional check models        : 0
% 0.77/0.61  #    Propositional check unsatisfiable : 0
% 0.77/0.61  #    Propositional clauses             : 0
% 0.77/0.61  #    Propositional clauses after purity: 0
% 0.77/0.61  #    Propositional unsat core size     : 0
% 0.77/0.61  #    Propositional preprocessing time  : 0.000
% 0.77/0.61  #    Propositional encoding time       : 0.000
% 0.77/0.61  #    Propositional solver time         : 0.000
% 0.77/0.61  #    Success case prop preproc time    : 0.000
% 0.77/0.61  #    Success case prop encoding time   : 0.000
% 0.77/0.61  #    Success case prop solver time     : 0.000
% 0.77/0.61  # Current number of processed clauses  : 516
% 0.77/0.61  #    Positive orientable unit clauses  : 150
% 0.77/0.61  #    Positive unorientable unit clauses: 0
% 0.77/0.61  #    Negative unit clauses             : 6
% 0.77/0.61  #    Non-unit-clauses                  : 360
% 0.77/0.61  # Current number of unprocessed clauses: 4785
% 0.77/0.61  # ...number of literals in the above   : 13258
% 0.77/0.61  # Current number of archived formulas  : 0
% 0.77/0.61  # Current number of archived clauses   : 149
% 0.77/0.61  # Clause-clause subsumption calls (NU) : 15812
% 0.77/0.61  # Rec. Clause-clause subsumption calls : 9286
% 0.77/0.61  # Non-unit clause-clause subsumptions  : 452
% 0.77/0.61  # Unit Clause-clause subsumption calls : 2724
% 0.77/0.61  # Rewrite failures with RHS unbound    : 0
% 0.77/0.61  # BW rewrite match attempts            : 389
% 0.77/0.61  # BW rewrite match successes           : 4
% 0.77/0.61  # Condensation attempts                : 0
% 0.77/0.61  # Condensation successes               : 0
% 0.77/0.61  # Termbank termtop insertions          : 114557
% 0.77/0.61  # Search garbage collected termcells   : 10241
% 0.77/0.61  
% 0.77/0.61  # -------------------------------------------------
% 0.77/0.61  # User time                : 0.117 s
% 0.77/0.61  # System time              : 0.005 s
% 0.77/0.61  # Total time               : 0.122 s
% 0.77/0.61  # Maximum resident set size: 4396 pages
% 0.77/0.61  
% 0.77/0.61  # -------------------------------------------------
% 0.77/0.61  # User time                : 0.163 s
% 0.77/0.61  # System time              : 0.046 s
% 0.77/0.61  # Total time               : 0.209 s
% 0.77/0.61  # Maximum resident set size: 2020 pages
% 0.77/0.61  % E---3.1 exiting
% 0.77/0.62  % E exiting
%------------------------------------------------------------------------------