TSTP Solution File: SEU577^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU577^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 03:28:18 EDT 2024

% Result   : Theorem 0.65s 0.55s
% Output   : CNFRefutation 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  259
% Syntax   : Number of formulae    :  307 (  23 unt; 162 typ;   0 def)
%            Number of atoms       : 1169 ( 332 equ;   0 cnn)
%            Maximal formula atoms :  354 (   8 avg)
%            Number of connectives : 4533 ( 412   ~; 460   |; 281   &;2653   @)
%                                         ( 156 <=>; 571  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  417 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  306 ( 306   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  165 ( 162 usr; 100 con; 0-4 aty)
%            Number of variables   :  976 (  63   ^ 809   !; 104   ?; 976   :)

% 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_90,type,
    set2prop: $i > $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,
    epred1_0: $o ).

thf(decl_131,type,
    esk1_2: $i > $i > $i ).

thf(decl_132,type,
    esk2_2: $i > $i > $i ).

thf(decl_133,type,
    esk3_2: $i > $i > $i ).

thf(decl_134,type,
    esk4_1: $i > $i ).

thf(decl_135,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_136,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_137,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_138,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_139,type,
    esk9_1: $i > $i ).

thf(decl_140,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_141,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_142,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_143,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_144,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_145,type,
    esk15_2: $i > $i > $i ).

thf(decl_146,type,
    esk16_2: $i > $i > $i ).

thf(decl_147,type,
    esk17_1: $i > $i ).

thf(decl_148,type,
    esk18_1: $i > $i ).

thf(decl_149,type,
    esk19_1: $i > $i ).

thf(decl_150,type,
    esk20_2: $i > $i > $i ).

thf(decl_151,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_152,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_153,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_154,type,
    esk24_1: $i > $i ).

thf(decl_155,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_156,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_157,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_158,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_159,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_160,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_161,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_162,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_163,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_164,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_165,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_166,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_167,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_168,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_169,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_170,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_171,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_172,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_173,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_174,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_175,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_176,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_177,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_178,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_179,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_180,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_181,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_182,type,
    esk52_2: $i > $i > $i ).

thf(decl_183,type,
    esk53_2: $i > $i > $i ).

thf(decl_184,type,
    esk54_0: $i ).

thf(decl_185,type,
    esk55_0: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(prop2set2propI,axiom,
    ( prop2set2propI
  <=> ! [X16: $o] :
        ( X16
       => ( set2prop @ ( prop2set @ X16 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(notequalI1,axiom,
    ( notequalI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ( subset @ X4 @ X5 )
       => ( X4 != X5 ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',notequalI2) ).

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

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

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

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

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

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

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

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

thf(c_0_96,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_97,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_98,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_99,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_100,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_101,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_102,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_103,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_104,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_105,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_106,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_107,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_108,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_109,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_110,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_111,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X274: $i] :
                  ( ( X6 @ X2 @ X274 )
                  & ! [X275: $i] :
                      ( ( X6 @ X2 @ X275 )
                     => ( X274 = X275 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_96,c_0_97]) ).

thf(c_0_112,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X276: $i] :
              ( ( X1 @ X276 )
              & ! [X277: $i] :
                  ( ( X1 @ X277 )
                 => ( X276 = X277 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_98,c_0_97]) ).

thf(c_0_113,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_114,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_115,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_116,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X278: $i] :
              ( ( X1 @ X278 )
              & ! [X279: $i] :
                  ( ( X1 @ X279 )
                 => ( X278 = X279 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_99,c_0_97]) ).

thf(c_0_117,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X280: $i] :
              ( ( X1 @ X280 )
              & ! [X281: $i] :
                  ( ( X1 @ X281 )
                 => ( X280 = X281 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_100,c_0_97]) ).

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

thf(c_0_119,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_101]) ).

thf(c_0_120,plain,
    ( nonemptyI
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
             != emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_102,c_0_101]) ).

thf(c_0_121,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_101]) ).

thf(c_0_122,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_123,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X282: $i] :
              ( ( X1 @ X282 )
              & ! [X283: $i] :
                  ( ( X1 @ X283 )
                 => ( X282 = X283 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_103,c_0_97]) ).

thf(c_0_124,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_101]) ).

thf(c_0_125,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_126,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X284: $i] :
              ( ( X1 @ X284 )
              & ! [X285: $i] :
                  ( ( X1 @ X285 )
                 => ( X284 = X285 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_104,c_0_97]) ).

thf(c_0_127,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X286: $i] :
                ( ( X1 @ X286 )
                & ! [X287: $i] :
                    ( ( X1 @ X287 )
                   => ( X286 = X287 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_105,c_0_97]) ).

thf(c_0_128,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X288: $i] :
              ( ( X1 @ X288 )
              & ! [X289: $i] :
                  ( ( X1 @ X289 )
                 => ( X288 = X289 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_106,c_0_97]) ).

thf(c_0_129,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X290: $i] :
              ( ( X1 @ X290 )
              & ! [X291: $i] :
                  ( ( X1 @ X291 )
                 => ( X290 = X291 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_107,c_0_97]) ).

thf(c_0_130,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X292: $i] :
                ( ( X1 @ X292 )
                & ! [X293: $i] :
                    ( ( X1 @ X293 )
                   => ( X292 = X293 ) ) )
          <=> ? [X294: $i] :
                ( ( X17 @ X294 )
                & ! [X295: $i] :
                    ( ( X17 @ X295 )
                   => ( X294 = X295 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_108,c_0_97]) ).

thf(c_0_131,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X296: $i] :
              ( ( X1 @ X296 )
              & ! [X297: $i] :
                  ( ( X1 @ X297 )
                 => ( X296 = X297 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_109,c_0_97]) ).

thf(c_0_132,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X298: $i] :
                ( ( X1 @ X298 )
                & ! [X299: $i] :
                    ( ( X1 @ X299 )
                   => ( X298 = X299 ) ) )
           => ( ? [X300: $i] :
                  ( ( X17 @ X300 )
                  & ! [X301: $i] :
                      ( ( X17 @ X301 )
                     => ( X300 = X301 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_110,c_0_97]) ).

thf(c_0_133,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_134,plain,
    ( epred1_0
  <=> ! [X331: $i] :
      ? [X332: $i] :
        ( ! [X333: $i] :
            ( ( in @ X333 @ X332 )
           => ! [X334: $i] :
                ( ( in @ X334 @ X333 )
               => ( in @ X334 @ X331 ) ) )
        & ! [X335: $i,X336: $i] :
            ( ( ( in @ X335 @ X331 )
              & ( in @ X336 @ X331 ) )
           => ( ! [X337: $i] :
                  ( ( in @ X337 @ X332 )
                 => ( ( in @ X335 @ X337 )
                  <=> ( in @ X336 @ X337 ) ) )
             => ( X335 = X336 ) ) )
        & ! [X338: $i,X339: $i] :
            ( ( ( in @ X338 @ X332 )
              & ( in @ X339 @ X332 ) )
           => ( ! [X340: $i] :
                  ( ( in @ X340 @ X338 )
                 => ( in @ X340 @ X339 ) )
              | ! [X341: $i] :
                  ( ( in @ X341 @ X339 )
                 => ( in @ X341 @ X338 ) ) ) )
        & ! [X342: $i] :
            ( ( ! [X343: $i] :
                  ( ( in @ X343 @ X342 )
                 => ( in @ X343 @ X331 ) )
              & ? [X344: $i] : ( in @ X344 @ X342 ) )
           => ? [X345: $i,X346: $i] :
                ( ( in @ X345 @ X332 )
                & ( in @ X346 @ X342 )
                & ~ ? [X347: $i] :
                      ( ( in @ X347 @ X345 )
                      & ( in @ X347 @ X342 ) )
                & ! [X348: $i] :
                    ( ( in @ X348 @ X332 )
                   => ( ! [X349: $i] :
                          ( ( in @ X349 @ X348 )
                         => ( in @ X349 @ X345 ) )
                      | ( in @ X346 @ X348 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_135,negated_conjecture,
    ~ ( ! [X302: $i,X303: $i] :
          ( ! [X304: $i] :
              ( ( in @ X304 @ X302 )
            <=> ( in @ X304 @ X303 ) )
         => ( X302 = X303 ) )
     => ( ! [X305: $i] :
            ~ ( in @ X305 @ emptyset )
       => ( ! [X306: $i,X307: $i,X308: $i] :
              ( ( in @ X308 @ ( setadjoin @ X306 @ X307 ) )
            <=> ( ( X308 = X306 )
                | ( in @ X308 @ X307 ) ) )
         => ( ! [X309: $i,X310: $i] :
                ( ( in @ X310 @ ( powerset @ X309 ) )
              <=> ! [X311: $i] :
                    ( ( in @ X311 @ X310 )
                   => ( in @ X311 @ X309 ) ) )
           => ( ! [X312: $i,X313: $i] :
                  ( ( in @ X313 @ ( setunion @ X312 ) )
                <=> ? [X314: $i] :
                      ( ( in @ X313 @ X314 )
                      & ( in @ X314 @ X312 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X315: $i] :
                      ( ( in @ X315 @ omega )
                     => ( in @ ( setadjoin @ X315 @ X315 ) @ omega ) )
                 => ( ! [X316: $i] :
                        ( ( ( in @ emptyset @ X316 )
                          & ! [X317: $i] :
                              ( ( ( in @ X317 @ omega )
                                & ( in @ X317 @ X316 ) )
                             => ( in @ ( setadjoin @ X317 @ X317 ) @ X316 ) ) )
                       => ! [X318: $i] :
                            ( ( in @ X318 @ omega )
                           => ( in @ X318 @ X316 ) ) )
                   => ( ! [X319: $i > $i > $o,X320: $i] :
                          ( ! [X321: $i] :
                              ( ( in @ X321 @ X320 )
                             => ? [X322: $i] :
                                  ( ( X319 @ X321 @ X322 )
                                  & ! [X323: $i] :
                                      ( ( X319 @ X321 @ X323 )
                                     => ( X322 = X323 ) ) ) )
                         => ? [X324: $i] :
                            ! [X325: $i] :
                              ( ( in @ X325 @ X324 )
                            <=> ? [X326: $i] :
                                  ( ( in @ X326 @ X320 )
                                  & ( X319 @ X326 @ X325 ) ) ) )
                     => ( ! [X327: $i] :
                            ( ? [X328: $i] : ( in @ X328 @ X327 )
                           => ? [X329: $i] :
                                ( ( in @ X329 @ X327 )
                                & ~ ? [X330: $i] :
                                      ( ( in @ X330 @ X329 )
                                      & ( in @ X330 @ X327 ) ) ) )
                       => ( epred1_0
                         => ( ! [X350: $i > $o] :
                                ( ? [X351: $i] :
                                    ( ( X350 @ X351 )
                                    & ! [X352: $i] :
                                        ( ( X350 @ X352 )
                                       => ( X351 = X352 ) ) )
                               => ( X350
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X350 @ Z0 ) ) ) )
                           => ( ! [X353: $i,X354: $i > $o,X355: $i] :
                                  ( ( in @ X355 @ X353 )
                                 => ( ( X354 @ X355 )
                                   => ( in @ X355 @ ( dsetconstr @ X353 @ X354 ) ) ) )
                             => ( ! [X356: $i,X357: $i > $o,X358: $i] :
                                    ( ( in @ X358 @ ( dsetconstr @ X356 @ X357 ) )
                                   => ( in @ X358 @ X356 ) )
                               => ( ! [X359: $i,X360: $i > $o,X361: $i] :
                                      ( ( in @ X361 @ ( dsetconstr @ X359 @ X360 ) )
                                     => ( X360 @ X361 ) )
                                 => ( ! [X362: $i > $o] :
                                        ( ? [X363: $i] :
                                            ( ( X362 @ X363 )
                                            & ! [X364: $i] :
                                                ( ( X362 @ X364 )
                                               => ( X363 = X364 ) ) )
                                       => ? [X365: $i] :
                                            ( ( X362 @ X365 )
                                            & ! [X366: $i] :
                                                ( ( X362 @ X366 )
                                               => ( X365 = X366 ) ) ) )
                                   => ( ! [X367: $o,X368: $i] :
                                          ( ( in @ X368 @ ( prop2set @ X367 ) )
                                         => X367 )
                                     => ( ! [X369: $i] :
                                            ( ( in @ X369 @ emptyset )
                                           => ! [X370: $o] : X370 )
                                       => ( ! [X371: $i] :
                                              ( ( in @ X371 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X372: $i] :
                                                ~ ( in @ X372 @ emptyset )
                                           => ( ! [X373: $i > $o] :
                                                  ( ? [X374: $i] :
                                                      ( ( X373 @ X374 )
                                                      & ! [X375: $i] :
                                                          ( ( X373 @ X375 )
                                                         => ( X374 = X375 ) ) )
                                                 => ? [X376: $i] : ( X373 @ X376 ) )
                                             => ( ! [X377: $i,X378: $i] :
                                                    ( ! [X379: $i] :
                                                        ( ( in @ X379 @ X377 )
                                                       => ( in @ X379 @ X378 ) )
                                                   => ( ! [X380: $i] :
                                                          ( ( in @ X380 @ X378 )
                                                         => ( in @ X380 @ X377 ) )
                                                     => ( X377 = X378 ) ) )
                                               => ( ! [X381: $i] :
                                                      ( ! [X382: $i] :
                                                          ~ ( in @ X382 @ X381 )
                                                     => ( X381 = emptyset ) )
                                                 => ( ! [X383: $i] :
                                                        ( ! [X384: $i] :
                                                            ~ ( in @ X384 @ X383 )
                                                       => ( X383 = emptyset ) )
                                                   => ( ! [X385: $i,X386: $i > $o,X387: $i] :
                                                          ( ( in @ X387 @ X385 )
                                                         => ( ( in @ X387 @ ( dsetconstr @ X385 @ X386 ) )
                                                          <=> ( X386 @ X387 ) ) )
                                                     => ( ! [X388: $i] :
                                                            ( ( X388 != emptyset )
                                                           => ? [X389: $i] : ( in @ X389 @ X388 ) )
                                                       => ( ! [X390: $i,X391: $i > $o,X392: $i] :
                                                              ( ( in @ X392 @ X390 )
                                                             => ( ( X391 @ X392 )
                                                               => ( ( dsetconstr @ X390 @ X391 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X393: $i] :
                                                                ( ? [X394: $i] : ( in @ X394 @ X393 )
                                                               => ( X393 != emptyset ) )
                                                           => ( ! [X395: $i,X396: $i] : ( in @ X395 @ ( setadjoin @ X395 @ X396 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X397: $i,X398: $i,X399: $i] :
                                                                      ( ( in @ X399 @ X398 )
                                                                     => ( in @ X399 @ ( setadjoin @ X397 @ X398 ) ) )
                                                                 => ( ! [X400: $i,X401: $i,X402: $i] :
                                                                        ( ( in @ X402 @ ( setadjoin @ X400 @ X401 ) )
                                                                       => ! [X403: $o] :
                                                                            ( ( ( X402 = X400 )
                                                                             => X403 )
                                                                           => ( ( ( in @ X402 @ X401 )
                                                                               => X403 )
                                                                             => X403 ) ) )
                                                                   => ( ! [X404: $i,X405: $i,X406: $i] :
                                                                          ( ( in @ X406 @ ( setadjoin @ X404 @ X405 ) )
                                                                         => ( ( X406 = X404 )
                                                                            | ( in @ X406 @ X405 ) ) )
                                                                     => ( ! [X407: $i] :
                                                                            ( ( dsetconstr @ X407
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X407 )
                                                                       => ( ! [X408: $i,X409: $i] :
                                                                              ( ! [X410: $i] :
                                                                                  ( ( in @ X410 @ X409 )
                                                                                 => ( in @ X410 @ X408 ) )
                                                                             => ( in @ X409 @ ( powerset @ X408 ) ) )
                                                                         => ( ! [X411: $i] : ( in @ emptyset @ ( powerset @ X411 ) )
                                                                           => ( ! [X412: $i] : ( in @ emptyset @ ( powerset @ X412 ) )
                                                                             => ( ! [X413: $i,X414: $i,X415: $i] :
                                                                                    ( ( in @ X414 @ ( powerset @ X413 ) )
                                                                                   => ( ( in @ X415 @ X414 )
                                                                                     => ( in @ X415 @ X413 ) ) )
                                                                               => ( ! [X416: $i,X417: $i,X418: $i] :
                                                                                      ( ( in @ X417 @ X418 )
                                                                                     => ( ( in @ X418 @ X416 )
                                                                                       => ( in @ X417 @ ( setunion @ X416 ) ) ) )
                                                                                 => ( ! [X419: $i,X420: $i] :
                                                                                        ( ( in @ X420 @ ( setunion @ X419 ) )
                                                                                       => ! [X421: $o] :
                                                                                            ( ! [X422: $i] :
                                                                                                ( ( in @ X420 @ X422 )
                                                                                               => ( ( in @ X422 @ X419 )
                                                                                                 => X421 ) )
                                                                                           => X421 ) )
                                                                                   => ( ! [X423: $i,X424: $i] :
                                                                                          ( ( in @ X424 @ X423 )
                                                                                         => ( in @ X424 @ ( powerset @ ( setunion @ X423 ) ) ) )
                                                                                     => ( ! [X425: $i > $o] :
                                                                                            ( ? [X426: $i] :
                                                                                                ( ( X425 @ X426 )
                                                                                                & ! [X427: $i] :
                                                                                                    ( ( X425 @ X427 )
                                                                                                   => ( X426 = X427 ) ) )
                                                                                           => ? [X428: $i] :
                                                                                              ! [X429: $i] :
                                                                                                ( ( X425 @ X429 )
                                                                                              <=> ( X429 = X428 ) ) )
                                                                                       => ( ! [X430: $i] :
                                                                                              ( ( X430 != emptyset )
                                                                                             => ? [X431: $i] :
                                                                                                  ( ( in @ X431 @ X430 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X432: $i,X433: $i] :
                                                                                                ( ( in @ X432 @ ( setadjoin @ X433 @ emptyset ) )
                                                                                               => ( X432 = X433 ) )
                                                                                           => ( ! [X434: $i,X435: $i] :
                                                                                                  ( ( X434 != X435 )
                                                                                                 => ~ ( in @ X435 @ ( setadjoin @ X434 @ emptyset ) ) )
                                                                                             => ( ! [X436: $i,X437: $i] :
                                                                                                    ( ( X436 = X437 )
                                                                                                   => ( in @ X436 @ ( setadjoin @ X437 @ emptyset ) ) )
                                                                                               => ( ! [X438: $i,X439: $i] :
                                                                                                      ( ( in @ X438 @ ( setadjoin @ X439 @ emptyset ) )
                                                                                                     => ( in @ X439 @ ( setadjoin @ X438 @ emptyset ) ) )
                                                                                                 => ( ! [X440: $i,X441: $i,X442: $i] :
                                                                                                        ( ( in @ X442 @ ( setadjoin @ X440 @ ( setadjoin @ X441 @ emptyset ) ) )
                                                                                                       => ( ( X442 = X440 )
                                                                                                          | ( X442 = X441 ) ) )
                                                                                                   => ( ! [X443: $i,X444: $i] : ( in @ X443 @ ( setadjoin @ X443 @ ( setadjoin @ X444 @ emptyset ) ) )
                                                                                                     => ( ! [X445: $i,X446: $i] : ( in @ X446 @ ( setadjoin @ X445 @ ( setadjoin @ X446 @ emptyset ) ) )
                                                                                                       => ( ! [X447: $i,X448: $i > $o] :
                                                                                                              ( ? [X449: $i] :
                                                                                                                  ( ( in @ X449 @ X447 )
                                                                                                                  & ( X448 @ X449 ) )
                                                                                                             => ( ( ( dsetconstr @ X447 @ X448 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X450: $i > $o,X451: $i] :
                                                                                                                ( ( in @ X451 @ emptyset )
                                                                                                               => ( X450 @ X451 ) )
                                                                                                           => ( ! [X452: $i,X453: $i > $o] :
                                                                                                                  ( ~ ! [X454: $i] :
                                                                                                                        ( ( in @ X454 @ X452 )
                                                                                                                       => ( X453 @ X454 ) )
                                                                                                                 => ? [X455: $i] :
                                                                                                                      ( ( in @ X455 @ X452 )
                                                                                                                      & ~ ( X453 @ X455 ) ) )
                                                                                                             => ( ! [X456: $i,X457: $i > $o] :
                                                                                                                    ( ! [X458: $i] :
                                                                                                                        ( ( in @ X458 @ X456 )
                                                                                                                       => ~ ( X457 @ X458 ) )
                                                                                                                   => ~ ? [X459: $i] :
                                                                                                                          ( ( in @ X459 @ X456 )
                                                                                                                          & ( X457 @ X459 ) ) )
                                                                                                               => ( ! [X460: $i,X461: $i > $o] :
                                                                                                                      ( ~ ? [X462: $i] :
                                                                                                                            ( ( in @ X462 @ X460 )
                                                                                                                            & ( X461 @ X462 ) )
                                                                                                                     => ! [X463: $i] :
                                                                                                                          ( ( in @ X463 @ X460 )
                                                                                                                         => ~ ( X461 @ X463 ) ) )
                                                                                                                 => ( ! [X464: $i,X465: $i > $o] :
                                                                                                                        ( ? [X466: $i] :
                                                                                                                            ( ( in @ X466 @ X464 )
                                                                                                                            & ~ ( X465 @ X466 ) )
                                                                                                                       => ~ ! [X467: $i] :
                                                                                                                              ( ( in @ X467 @ X464 )
                                                                                                                             => ( X465 @ X467 ) ) )
                                                                                                                   => ( ! [X468: $o] :
                                                                                                                          ( X468
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X468 ) ) )
                                                                                                                     => ( ! [X469: $o] :
                                                                                                                            ( X469
                                                                                                                           => ( set2prop @ ( prop2set @ X469 ) ) )
                                                                                                                       => ( ! [X470: $i,X471: $i > $o] :
                                                                                                                              ( ~ ? [X472: $i] :
                                                                                                                                    ( ( in @ X472 @ X470 )
                                                                                                                                    & ( X471 @ X472 ) )
                                                                                                                             => ! [X473: $i] :
                                                                                                                                  ( ( in @ X473 @ X470 )
                                                                                                                                 => ~ ( X471 @ X473 ) ) )
                                                                                                                         => ( ! [X474: $i,X475: $i > $o] :
                                                                                                                                ( ~ ! [X476: $i] :
                                                                                                                                      ( ( in @ X476 @ X474 )
                                                                                                                                     => ( X475 @ X476 ) )
                                                                                                                               => ? [X477: $i] :
                                                                                                                                    ( ( in @ X477 @ X474 )
                                                                                                                                    & ~ ( X475 @ X477 ) ) )
                                                                                                                           => ( ! [X478: $i > $o] :
                                                                                                                                  ( ? [X479: $i] :
                                                                                                                                      ( ( X478 @ X479 )
                                                                                                                                      & ! [X480: $i] :
                                                                                                                                          ( ( X478 @ X480 )
                                                                                                                                         => ( X479 = X480 ) ) )
                                                                                                                                 => ? [X481: $i] :
                                                                                                                                      ( ( X478 @ X481 )
                                                                                                                                      & ! [X482: $i] :
                                                                                                                                          ( ( X478 @ X482 )
                                                                                                                                         => ( X481 = X482 ) ) ) )
                                                                                                                             => ( ! [X483: $i > $o] :
                                                                                                                                    ( ? [X484: $i] : ( X483 @ X484 )
                                                                                                                                   => ( ! [X485: $i,X486: $i] :
                                                                                                                                          ( ( X483 @ X485 )
                                                                                                                                         => ( ( X483 @ X486 )
                                                                                                                                           => ( X485 = X486 ) ) )
                                                                                                                                     => ? [X487: $i] :
                                                                                                                                          ( ( X483 @ X487 )
                                                                                                                                          & ! [X488: $i] :
                                                                                                                                              ( ( X483 @ X488 )
                                                                                                                                             => ( X487 = X488 ) ) ) ) )
                                                                                                                               => ( ! [X489: $i > $o] :
                                                                                                                                      ( ? [X490: $i] :
                                                                                                                                        ! [X491: $i] :
                                                                                                                                          ( ( X489 @ X491 )
                                                                                                                                        <=> ( X491 = X490 ) )
                                                                                                                                     => ? [X492: $i] :
                                                                                                                                          ( ( X489 @ X492 )
                                                                                                                                          & ! [X493: $i] :
                                                                                                                                              ( ( X489 @ X493 )
                                                                                                                                             => ( X492 = X493 ) ) ) )
                                                                                                                                 => ( ! [X494: $i,X495: $i] :
                                                                                                                                        ( ( X494 = X495 )
                                                                                                                                       => ! [X496: $i,X497: $i] :
                                                                                                                                            ( ( X496 = X497 )
                                                                                                                                           => ( ( in @ X496 @ X494 )
                                                                                                                                             => ( in @ X497 @ X495 ) ) ) )
                                                                                                                                   => ( ! [X498: $i,X499: $i] :
                                                                                                                                          ( ( X498 = X499 )
                                                                                                                                         => ! [X500: $i,X501: $i] :
                                                                                                                                              ( ( X500 = X501 )
                                                                                                                                             => ( ( in @ X500 @ X498 )
                                                                                                                                              <=> ( in @ X501 @ X499 ) ) ) )
                                                                                                                                     => ( ! [X502: $i > $o] :
                                                                                                                                            ( ? [X503: $i] :
                                                                                                                                                ( ( X502 @ X503 )
                                                                                                                                                & ! [X504: $i] :
                                                                                                                                                    ( ( X502 @ X504 )
                                                                                                                                                   => ( X503 = X504 ) ) )
                                                                                                                                           => ! [X505: $i,X506: $i] :
                                                                                                                                                ( ( X502 @ X505 )
                                                                                                                                               => ( ( X502 @ X506 )
                                                                                                                                                 => ( X505 = X506 ) ) ) )
                                                                                                                                       => ( ! [X507: $i > $o,X508: $i > $o] :
                                                                                                                                              ( ! [X509: $i,X510: $i] :
                                                                                                                                                  ( ( X509 = X510 )
                                                                                                                                                 => ( ( X507 @ X509 )
                                                                                                                                                  <=> ( X508 @ X510 ) ) )
                                                                                                                                             => ( ? [X511: $i] :
                                                                                                                                                    ( ( X507 @ X511 )
                                                                                                                                                    & ! [X512: $i] :
                                                                                                                                                        ( ( X507 @ X512 )
                                                                                                                                                       => ( X511 = X512 ) ) )
                                                                                                                                              <=> ? [X513: $i] :
                                                                                                                                                    ( ( X508 @ X513 )
                                                                                                                                                    & ! [X514: $i] :
                                                                                                                                                        ( ( X508 @ X514 )
                                                                                                                                                       => ( X513 = X514 ) ) ) ) )
                                                                                                                                         => ( ( 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] :
                                                                                                                                                          ( ? [X524: $i] :
                                                                                                                                                              ( ( X523 @ X524 )
                                                                                                                                                              & ! [X525: $i] :
                                                                                                                                                                  ( ( X523 @ X525 )
                                                                                                                                                                 => ( X524 = X525 ) ) )
                                                                                                                                                         => ! [X526: $i,X527: $i] :
                                                                                                                                                              ( ( X523 @ X526 )
                                                                                                                                                             => ( ( X523 @ X527 )
                                                                                                                                                               => ( X526 = X527 ) ) ) )
                                                                                                                                                     => ( ! [X528: $i > $o,X529: $i > $o] :
                                                                                                                                                            ( ! [X530: $i,X531: $i] :
                                                                                                                                                                ( ( X530 = X531 )
                                                                                                                                                               => ( ( X528 @ X530 )
                                                                                                                                                                <=> ( X529 @ X531 ) ) )
                                                                                                                                                           => ( ? [X532: $i] :
                                                                                                                                                                  ( ( X528 @ X532 )
                                                                                                                                                                  & ! [X533: $i] :
                                                                                                                                                                      ( ( X528 @ X533 )
                                                                                                                                                                     => ( X532 = X533 ) ) )
                                                                                                                                                             => ( ? [X534: $i] :
                                                                                                                                                                    ( ( X529 @ X534 )
                                                                                                                                                                    & ! [X535: $i] :
                                                                                                                                                                        ( ( X529 @ X535 )
                                                                                                                                                                       => ( X534 = X535 ) ) )
                                                                                                                                                               => ( ( descr @ X528 )
                                                                                                                                                                  = ( descr @ X529 ) ) ) ) )
                                                                                                                                                       => ( ! [X536: $i,X537: $i] :
                                                                                                                                                              ( ( X536 = X537 )
                                                                                                                                                             => ! [X538: $i > $o,X539: $i > $o] :
                                                                                                                                                                  ( ! [X540: $i] :
                                                                                                                                                                      ( ( in @ X540 @ X536 )
                                                                                                                                                                     => ! [X541: $i] :
                                                                                                                                                                          ( ( in @ X541 @ X537 )
                                                                                                                                                                         => ( ( X540 = X541 )
                                                                                                                                                                           => ( ( X538 @ X540 )
                                                                                                                                                                            <=> ( X539 @ X541 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X536 @ X538 )
                                                                                                                                                                    = ( dsetconstr @ X537 @ X539 ) ) ) )
                                                                                                                                                         => ( ! [X542: $i,X543: $i] :
                                                                                                                                                                ( ! [X544: $i] :
                                                                                                                                                                    ( ( in @ X544 @ X542 )
                                                                                                                                                                   => ( in @ X544 @ X543 ) )
                                                                                                                                                               => ( subset @ X542 @ X543 ) )
                                                                                                                                                           => ( ! [X545: $i,X546: $i] :
                                                                                                                                                                  ( ( X545 = X546 )
                                                                                                                                                                 => ( subset @ X546 @ X545 ) )
                                                                                                                                                             => ( ! [X547: $i,X548: $i] :
                                                                                                                                                                    ( ( X547 = X548 )
                                                                                                                                                                   => ( subset @ X547 @ X548 ) )
                                                                                                                                                               => ( ! [X549: $i,X550: $i] :
                                                                                                                                                                      ( ! [X551: $i] :
                                                                                                                                                                          ( ( in @ X551 @ X549 )
                                                                                                                                                                         => ( in @ X551 @ X550 ) )
                                                                                                                                                                     => ( subset @ X549 @ X550 ) )
                                                                                                                                                                 => ( ! [X552: $i] : ( subset @ emptyset @ X552 )
                                                                                                                                                                   => ( ! [X553: $i,X554: $i,X555: $i] :
                                                                                                                                                                          ( ( subset @ X553 @ X554 )
                                                                                                                                                                         => ( ( in @ X555 @ X553 )
                                                                                                                                                                           => ( in @ X555 @ X554 ) ) )
                                                                                                                                                                     => ( ! [X556: $i,X557: $i,X558: $i] :
                                                                                                                                                                            ( ( subset @ X556 @ X557 )
                                                                                                                                                                           => ( ~ ( in @ X558 @ X557 )
                                                                                                                                                                             => ~ ( in @ X558 @ X556 ) ) )
                                                                                                                                                                       => ( ! [X559: $i,X560: $i,X561: $i] :
                                                                                                                                                                              ( ( in @ X561 @ X559 )
                                                                                                                                                                             => ( ~ ( in @ X561 @ X560 )
                                                                                                                                                                               => ~ ( subset @ X559 @ X560 ) ) )
                                                                                                                                                                         => ( ! [X562: $i,X563: $i] :
                                                                                                                                                                                ( ~ ( subset @ X562 @ X563 )
                                                                                                                                                                               => ( X562 != X563 ) )
                                                                                                                                                                           => ( ! [X564: $i,X565: $i,X566: $i] :
                                                                                                                                                                                  ( ( in @ X566 @ X564 )
                                                                                                                                                                                 => ( ~ ( in @ X566 @ X565 )
                                                                                                                                                                                   => ( X564 != X565 ) ) )
                                                                                                                                                                             => ( ! [X567: $i] : ( subset @ X567 @ X567 )
                                                                                                                                                                               => ( ! [X568: $i,X569: $i,X570: $i] :
                                                                                                                                                                                      ( ( subset @ X568 @ X569 )
                                                                                                                                                                                     => ( ( subset @ X569 @ X570 )
                                                                                                                                                                                       => ( subset @ X568 @ X570 ) ) )
                                                                                                                                                                                 => ( ! [X571: $i,X572: $i] : ( subset @ X572 @ ( setadjoin @ X571 @ X572 ) )
                                                                                                                                                                                   => ( ! [X573: $i,X574: $i,X575: $i] :
                                                                                                                                                                                          ( ( subset @ X573 @ X575 )
                                                                                                                                                                                         => ( subset @ X573 @ ( setadjoin @ X574 @ X575 ) ) )
                                                                                                                                                                                     => ( ! [X576: $i,X577: $i] :
                                                                                                                                                                                            ( ( subset @ X576 @ X577 )
                                                                                                                                                                                           => ( in @ X576 @ ( powerset @ X577 ) ) )
                                                                                                                                                                                       => ( ! [X578: $i,X579: $i] :
                                                                                                                                                                                              ( ( subset @ X578 @ X579 )
                                                                                                                                                                                             => ( ( subset @ X579 @ X578 )
                                                                                                                                                                                               => ( X578 = X579 ) ) )
                                                                                                                                                                                         => ( ! [X580: $i] :
                                                                                                                                                                                                ( ( subset @ X580 @ emptyset )
                                                                                                                                                                                               => ( X580 = emptyset ) )
                                                                                                                                                                                           => ( ! [X581: $i,X582: $i] :
                                                                                                                                                                                                  ( ( subset @ X582 @ X581 )
                                                                                                                                                                                                 => ( in @ X582 @ ( powerset @ X581 ) ) )
                                                                                                                                                                                             => ! [X4: $i,X5: $i] :
                                                                                                                                                                                                  ( ( in @ X5 @ ( powerset @ X4 ) )
                                                                                                                                                                                                 => ( subset @ X5 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(assume_negation,[status(cth)],[powersetE1]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_111]),foundationAx]),wellorderingAx]),c_0_112]),c_0_113]),c_0_114]),c_0_115]),c_0_116]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_117]),setext]),emptyI]),noeltsimpempty]),c_0_118]),c_0_119]),c_0_120]),c_0_121]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_122]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_123]),c_0_124]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_125]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_126]),c_0_127]),c_0_128]),inCongP]),in__Cong]),c_0_129]),c_0_130]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_131]),c_0_132]),c_0_133]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1])])]),c_0_134]) ).

thf(c_0_136,negated_conjecture,
    ! [X583: $i,X584: $i,X586: $i,X587: $i,X588: $i,X589: $i,X590: $i,X591: $i,X592: $i,X593: $i,X594: $i,X596: $i,X597: $i,X599: $i,X600: $i,X601: $i,X602: $i,X603: $i,X605: $i,X606: $i > $i > $o,X607: $i,X609: $i,X612: $i,X614: $i,X615: $i,X616: $i,X617: $i,X619: $i,X620: $i > $o,X621: $i,X623: $i,X624: $i > $o,X625: $i,X626: $i,X627: $i > $o,X628: $i,X629: $i,X630: $i > $o,X631: $i,X632: $i > $o,X633: $i,X636: $i,X637: $o,X638: $i,X639: $i,X640: $o,X641: $i,X642: $i,X643: $i > $o,X644: $i,X647: $i,X648: $i,X651: $i,X653: $i,X655: $i,X656: $i > $o,X657: $i,X658: $i,X660: $i,X661: $i > $o,X662: $i,X663: $i,X664: $i,X665: $i,X666: $i,X667: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $o,X674: $i,X675: $i,X676: $i,X677: $i,X678: $i,X679: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $i,X686: $i,X687: $i,X688: $i,X689: $i,X690: $i,X691: $o,X693: $i,X694: $i,X695: $i > $o,X696: $i,X699: $i,X700: $i,X701: $i,X703: $i,X704: $i,X705: $i,X706: $i,X707: $i,X708: $i,X709: $i,X710: $i,X711: $i,X712: $i,X713: $i,X714: $i,X715: $i,X716: $i,X717: $i,X718: $i,X719: $i > $o,X720: $i,X721: $i > $o,X722: $i,X723: $i,X724: $i > $o,X725: $i,X727: $i,X728: $i > $o,X730: $i,X731: $i,X732: $i > $o,X734: $i,X735: $i,X736: $i > $o,X737: $i,X739: $o,X740: $o,X741: $i,X742: $i > $o,X744: $i,X745: $i,X746: $i > $o,X747: $i,X749: $i > $o,X750: $i,X753: $i,X754: $i > $o,X755: $i,X759: $i,X760: $i > $o,X761: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X770: $i,X771: $i,X772: $i,X773: $i > $o,X774: $i,X776: $i,X777: $i,X778: $i > $o,X779: $i > $o,X782: $i,X785: $i,X786: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i > $o,X799: $i,X801: $i,X802: $i,X803: $i > $o,X804: $i > $o,X807: $i,X809: $i,X811: $i,X812: $i,X813: $i > $o,X814: $i > $o,X817: $i,X818: $i,X820: $i,X821: $i,X822: $i,X823: $i,X824: $i,X825: $i,X827: $i,X828: $i,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X838: $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] :
      ( ( ~ ( in @ ( esk1_2 @ X583 @ X584 ) @ X583 )
        | ~ ( in @ ( esk1_2 @ X583 @ X584 ) @ X584 )
        | ( X583 = X584 ) )
      & ( ( in @ ( esk1_2 @ X583 @ X584 ) @ X583 )
        | ( in @ ( esk1_2 @ X583 @ X584 ) @ X584 )
        | ( X583 = X584 ) )
      & ~ ( in @ X586 @ emptyset )
      & ( ~ ( in @ X589 @ ( setadjoin @ X587 @ X588 ) )
        | ( X589 = X587 )
        | ( in @ X589 @ X588 ) )
      & ( ( X589 != X587 )
        | ( in @ X589 @ ( setadjoin @ X587 @ X588 ) ) )
      & ( ~ ( in @ X589 @ X588 )
        | ( in @ X589 @ ( setadjoin @ X587 @ X588 ) ) )
      & ( ~ ( in @ X591 @ ( powerset @ X590 ) )
        | ~ ( in @ X592 @ X591 )
        | ( in @ X592 @ X590 ) )
      & ( ( in @ ( esk2_2 @ X593 @ X594 ) @ X594 )
        | ( in @ X594 @ ( powerset @ X593 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X593 @ X594 ) @ X593 )
        | ( in @ X594 @ ( powerset @ X593 ) ) )
      & ( ( in @ X597 @ ( esk3_2 @ X596 @ X597 ) )
        | ~ ( in @ X597 @ ( setunion @ X596 ) ) )
      & ( ( in @ ( esk3_2 @ X596 @ X597 ) @ X596 )
        | ~ ( in @ X597 @ ( setunion @ X596 ) ) )
      & ( ~ ( in @ X600 @ X601 )
        | ~ ( in @ X601 @ X599 )
        | ( in @ X600 @ ( setunion @ X599 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X602 @ omega )
        | ( in @ ( setadjoin @ X602 @ X602 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X603 ) @ omega )
        | ~ ( in @ emptyset @ X603 )
        | ~ ( in @ X605 @ omega )
        | ( in @ X605 @ X603 ) )
      & ( ( in @ ( esk4_1 @ X603 ) @ X603 )
        | ~ ( in @ emptyset @ X603 )
        | ~ ( in @ X605 @ omega )
        | ( in @ X605 @ X603 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X603 ) @ ( esk4_1 @ X603 ) ) @ X603 )
        | ~ ( in @ emptyset @ X603 )
        | ~ ( in @ X605 @ omega )
        | ( in @ X605 @ X603 ) )
      & ( ( in @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X607 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( in @ ( esk5_2 @ X606 @ X607 ) @ X607 ) )
      & ( ( X606 @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X612 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( in @ ( esk5_2 @ X606 @ X607 ) @ X607 ) )
      & ( ~ ( in @ X615 @ X607 )
        | ~ ( X606 @ X615 @ X614 )
        | ( in @ X614 @ ( esk7_2 @ X606 @ X607 ) )
        | ( in @ ( esk5_2 @ X606 @ X607 ) @ X607 ) )
      & ( ( in @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X607 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X606 @ ( esk5_2 @ X606 @ X607 ) @ ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ( X606 @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X612 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X606 @ ( esk5_2 @ X606 @ X607 ) @ ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ~ ( in @ X615 @ X607 )
        | ~ ( X606 @ X615 @ X614 )
        | ( in @ X614 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X606 @ ( esk5_2 @ X606 @ X607 ) @ ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ( in @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X607 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X609
         != ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ( X606 @ ( esk8_3 @ X606 @ X607 @ X612 ) @ X612 )
        | ~ ( in @ X612 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X609
         != ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ~ ( in @ X615 @ X607 )
        | ~ ( X606 @ X615 @ X614 )
        | ( in @ X614 @ ( esk7_2 @ X606 @ X607 ) )
        | ( X609
         != ( esk6_3 @ X606 @ X607 @ X609 ) )
        | ~ ( X606 @ ( esk5_2 @ X606 @ X607 ) @ X609 ) )
      & ( ( in @ ( esk9_1 @ X616 ) @ X616 )
        | ~ ( in @ X617 @ X616 ) )
      & ( ~ ( in @ X619 @ ( esk9_1 @ X616 ) )
        | ~ ( in @ X619 @ X616 )
        | ~ ( in @ X617 @ X616 ) )
      & epred1_0
      & ( ( X620 @ ( esk10_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 )
        | ( X620 @ ( descr @ X620 ) ) )
      & ( ( X621
         != ( esk10_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 )
        | ( X620 @ ( descr @ X620 ) ) )
      & ( ~ ( in @ X625 @ X623 )
        | ~ ( X624 @ X625 )
        | ( in @ X625 @ ( dsetconstr @ X623 @ X624 ) ) )
      & ( ~ ( in @ X628 @ ( dsetconstr @ X626 @ X627 ) )
        | ( in @ X628 @ X626 ) )
      & ( ~ ( in @ X631 @ ( dsetconstr @ X629 @ X630 ) )
        | ( X630 @ X631 ) )
      & ( ( X632 @ ( esk12_1 @ X632 ) )
        | ( X632 @ ( esk11_2 @ X632 @ X633 ) )
        | ~ ( X632 @ X633 ) )
      & ( ~ ( X632 @ X636 )
        | ( ( esk12_1 @ X632 )
          = X636 )
        | ( X632 @ ( esk11_2 @ X632 @ X633 ) )
        | ~ ( X632 @ X633 ) )
      & ( ( X632 @ ( esk12_1 @ X632 ) )
        | ( X633
         != ( esk11_2 @ X632 @ X633 ) )
        | ~ ( X632 @ X633 ) )
      & ( ~ ( X632 @ X636 )
        | ( ( esk12_1 @ X632 )
          = X636 )
        | ( X633
         != ( esk11_2 @ X632 @ X633 ) )
        | ~ ( X632 @ X633 ) )
      & ( ~ ( in @ X638 @ ( prop2set @ X637 ) )
        | X637 )
      & ( ~ ( in @ X639 @ emptyset )
        | X640 )
      & ( ~ ( in @ X641 @ emptyset )
        | ~ $true )
      & ~ ( in @ X642 @ emptyset )
      & ( ( X643 @ ( esk13_2 @ X643 @ X644 ) )
        | ~ ( X643 @ X644 )
        | ( X643 @ ( esk14_1 @ X643 ) ) )
      & ( ( X644
         != ( esk13_2 @ X643 @ X644 ) )
        | ~ ( X643 @ X644 )
        | ( X643 @ ( esk14_1 @ X643 ) ) )
      & ( ( in @ ( esk16_2 @ X647 @ X648 ) @ X648 )
        | ( X647 = X648 )
        | ( in @ ( esk15_2 @ X647 @ X648 ) @ X647 ) )
      & ( ~ ( in @ ( esk16_2 @ X647 @ X648 ) @ X647 )
        | ( X647 = X648 )
        | ( in @ ( esk15_2 @ X647 @ X648 ) @ X647 ) )
      & ( ( in @ ( esk16_2 @ X647 @ X648 ) @ X648 )
        | ( X647 = X648 )
        | ~ ( in @ ( esk15_2 @ X647 @ X648 ) @ X648 ) )
      & ( ~ ( in @ ( esk16_2 @ X647 @ X648 ) @ X647 )
        | ( X647 = X648 )
        | ~ ( in @ ( esk15_2 @ X647 @ X648 ) @ X648 ) )
      & ( ( in @ ( esk17_1 @ X651 ) @ X651 )
        | ( X651 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X653 ) @ X653 )
        | ( X653 = emptyset ) )
      & ( ~ ( in @ X657 @ ( dsetconstr @ X655 @ X656 ) )
        | ( X656 @ X657 )
        | ~ ( in @ X657 @ X655 ) )
      & ( ~ ( X656 @ X657 )
        | ( in @ X657 @ ( dsetconstr @ X655 @ X656 ) )
        | ~ ( in @ X657 @ X655 ) )
      & ( ( X658 = emptyset )
        | ( in @ ( esk19_1 @ X658 ) @ X658 ) )
      & ( ~ ( in @ X662 @ X660 )
        | ~ ( X661 @ X662 )
        | ( ( dsetconstr @ X660 @ X661 )
         != emptyset ) )
      & ( ~ ( in @ X664 @ X663 )
        | ( X663 != emptyset ) )
      & ( in @ X665 @ ( setadjoin @ X665 @ X666 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X669 @ X668 )
        | ( in @ X669 @ ( setadjoin @ X667 @ X668 ) ) )
      & ( ( in @ X672 @ X671 )
        | X673
        | ( X672 = X670 )
        | ~ ( in @ X672 @ ( setadjoin @ X670 @ X671 ) ) )
      & ( ~ X673
        | X673
        | ( X672 = X670 )
        | ~ ( in @ X672 @ ( setadjoin @ X670 @ X671 ) ) )
      & ( ( in @ X672 @ X671 )
        | X673
        | ~ X673
        | ~ ( in @ X672 @ ( setadjoin @ X670 @ X671 ) ) )
      & ( ~ X673
        | X673
        | ~ X673
        | ~ ( in @ X672 @ ( setadjoin @ X670 @ X671 ) ) )
      & ( ~ ( in @ X676 @ ( setadjoin @ X674 @ X675 ) )
        | ( X676 = X674 )
        | ( in @ X676 @ X675 ) )
      & ( ( dsetconstr @ X677
          @ ^ [Z0: $i] : $true )
        = X677 )
      & ( ( in @ ( esk20_2 @ X678 @ X679 ) @ X679 )
        | ( in @ X679 @ ( powerset @ X678 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X678 @ X679 ) @ X678 )
        | ( in @ X679 @ ( powerset @ X678 ) ) )
      & ( in @ emptyset @ ( powerset @ X681 ) )
      & ( in @ emptyset @ ( powerset @ X682 ) )
      & ( ~ ( in @ X684 @ ( powerset @ X683 ) )
        | ~ ( in @ X685 @ X684 )
        | ( in @ X685 @ X683 ) )
      & ( ~ ( in @ X687 @ X688 )
        | ~ ( in @ X688 @ X686 )
        | ( in @ X687 @ ( setunion @ X686 ) ) )
      & ( ( in @ X690 @ ( esk21_3 @ X689 @ X690 @ X691 ) )
        | X691
        | ~ ( in @ X690 @ ( setunion @ X689 ) ) )
      & ( ( in @ ( esk21_3 @ X689 @ X690 @ X691 ) @ X689 )
        | X691
        | ~ ( in @ X690 @ ( setunion @ X689 ) ) )
      & ( ~ X691
        | X691
        | ~ ( in @ X690 @ ( setunion @ X689 ) ) )
      & ( ~ ( in @ X694 @ X693 )
        | ( in @ X694 @ ( powerset @ ( setunion @ X693 ) ) ) )
      & ( ~ ( X695 @ X699 )
        | ( X699
          = ( esk23_1 @ X695 ) )
        | ( X695 @ ( esk22_2 @ X695 @ X696 ) )
        | ~ ( X695 @ X696 ) )
      & ( ( X700
         != ( esk23_1 @ X695 ) )
        | ( X695 @ X700 )
        | ( X695 @ ( esk22_2 @ X695 @ X696 ) )
        | ~ ( X695 @ X696 ) )
      & ( ~ ( X695 @ X699 )
        | ( X699
          = ( esk23_1 @ X695 ) )
        | ( X696
         != ( esk22_2 @ X695 @ X696 ) )
        | ~ ( X695 @ X696 ) )
      & ( ( X700
         != ( esk23_1 @ X695 ) )
        | ( X695 @ X700 )
        | ( X696
         != ( esk22_2 @ X695 @ X696 ) )
        | ~ ( X695 @ X696 ) )
      & ( ( in @ ( esk24_1 @ X701 ) @ X701 )
        | ( X701 = emptyset ) )
      & ( $true
        | ( X701 = emptyset ) )
      & ( ~ ( in @ X703 @ ( setadjoin @ X704 @ emptyset ) )
        | ( X703 = X704 ) )
      & ( ( X705 = X706 )
        | ~ ( in @ X706 @ ( setadjoin @ X705 @ emptyset ) ) )
      & ( ( X707 != X708 )
        | ( in @ X707 @ ( setadjoin @ X708 @ emptyset ) ) )
      & ( ~ ( in @ X709 @ ( setadjoin @ X710 @ emptyset ) )
        | ( in @ X710 @ ( setadjoin @ X709 @ emptyset ) ) )
      & ( ~ ( in @ X713 @ ( setadjoin @ X711 @ ( setadjoin @ X712 @ emptyset ) ) )
        | ( X713 = X711 )
        | ( X713 = X712 ) )
      & ( in @ X714 @ ( setadjoin @ X714 @ ( setadjoin @ X715 @ emptyset ) ) )
      & ( in @ X717 @ ( setadjoin @ X716 @ ( setadjoin @ X717 @ emptyset ) ) )
      & ( ~ ( in @ X720 @ X718 )
        | ~ ( X719 @ X720 )
        | ( ( dsetconstr @ X718 @ X719 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X722 @ emptyset )
        | ( X721 @ X722 ) )
      & ( ( in @ ( esk25_2 @ X723 @ X724 ) @ X723 )
        | ~ ( in @ X725 @ X723 )
        | ( X724 @ X725 ) )
      & ( ~ ( X724 @ ( esk25_2 @ X723 @ X724 ) )
        | ~ ( in @ X725 @ X723 )
        | ( X724 @ X725 ) )
      & ( ( in @ ( esk26_2 @ X727 @ X728 ) @ X727 )
        | ~ ( in @ X730 @ X727 )
        | ~ ( X728 @ X730 ) )
      & ( ( X728 @ ( esk26_2 @ X727 @ X728 ) )
        | ~ ( in @ X730 @ X727 )
        | ~ ( X728 @ X730 ) )
      & ( ( in @ ( esk27_2 @ X731 @ X732 ) @ X731 )
        | ~ ( in @ X734 @ X731 )
        | ~ ( X732 @ X734 ) )
      & ( ( X732 @ ( esk27_2 @ X731 @ X732 ) )
        | ~ ( in @ X734 @ X731 )
        | ~ ( X732 @ X734 ) )
      & ( ( in @ ( esk28_2 @ X735 @ X736 ) @ X735 )
        | ~ ( in @ X737 @ X735 )
        | ( X736 @ X737 ) )
      & ( ~ ( X736 @ ( esk28_2 @ X735 @ X736 ) )
        | ~ ( in @ X737 @ X735 )
        | ( X736 @ X737 ) )
      & ( ~ X739
        | ( in @ emptyset @ ( prop2set @ X739 ) ) )
      & ( ~ X740
        | ( set2prop @ ( prop2set @ X740 ) ) )
      & ( ( in @ ( esk29_2 @ X741 @ X742 ) @ X741 )
        | ~ ( in @ X744 @ X741 )
        | ~ ( X742 @ X744 ) )
      & ( ( X742 @ ( esk29_2 @ X741 @ X742 ) )
        | ~ ( in @ X744 @ X741 )
        | ~ ( X742 @ X744 ) )
      & ( ( in @ ( esk30_2 @ X745 @ X746 ) @ X745 )
        | ~ ( in @ X747 @ X745 )
        | ( X746 @ X747 ) )
      & ( ~ ( X746 @ ( esk30_2 @ X745 @ X746 ) )
        | ~ ( in @ X747 @ X745 )
        | ( X746 @ X747 ) )
      & ( ( X749 @ ( esk32_1 @ X749 ) )
        | ( X749 @ ( esk31_2 @ X749 @ X750 ) )
        | ~ ( X749 @ X750 ) )
      & ( ~ ( X749 @ X753 )
        | ( ( esk32_1 @ X749 )
          = X753 )
        | ( X749 @ ( esk31_2 @ X749 @ X750 ) )
        | ~ ( X749 @ X750 ) )
      & ( ( X749 @ ( esk32_1 @ X749 ) )
        | ( X750
         != ( esk31_2 @ X749 @ X750 ) )
        | ~ ( X749 @ X750 ) )
      & ( ~ ( X749 @ X753 )
        | ( ( esk32_1 @ X749 )
          = X753 )
        | ( X750
         != ( esk31_2 @ X749 @ X750 ) )
        | ~ ( X749 @ X750 ) )
      & ( ( X754 @ ( esk35_1 @ X754 ) )
        | ( X754 @ ( esk33_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ~ ( X754 @ X759 )
        | ( ( esk35_1 @ X754 )
          = X759 )
        | ( X754 @ ( esk33_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ( X754 @ ( esk35_1 @ X754 ) )
        | ( X754 @ ( esk34_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ~ ( X754 @ X759 )
        | ( ( esk35_1 @ X754 )
          = X759 )
        | ( X754 @ ( esk34_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ( X754 @ ( esk35_1 @ X754 ) )
        | ( ( esk33_1 @ X754 )
         != ( esk34_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ~ ( X754 @ X759 )
        | ( ( esk35_1 @ X754 )
          = X759 )
        | ( ( esk33_1 @ X754 )
         != ( esk34_1 @ X754 ) )
        | ~ ( X754 @ X755 ) )
      & ( ( X760 @ ( esk37_1 @ X760 ) )
        | ~ ( X760 @ ( esk36_2 @ X760 @ X761 ) )
        | ( ( esk36_2 @ X760 @ X761 )
         != X761 ) )
      & ( ~ ( X760 @ X764 )
        | ( ( esk37_1 @ X760 )
          = X764 )
        | ~ ( X760 @ ( esk36_2 @ X760 @ X761 ) )
        | ( ( esk36_2 @ X760 @ X761 )
         != X761 ) )
      & ( ( X760 @ ( esk37_1 @ X760 ) )
        | ( X760 @ ( esk36_2 @ X760 @ X761 ) )
        | ( ( esk36_2 @ X760 @ X761 )
          = X761 ) )
      & ( ~ ( X760 @ X764 )
        | ( ( esk37_1 @ X760 )
          = X764 )
        | ( X760 @ ( esk36_2 @ X760 @ X761 ) )
        | ( ( esk36_2 @ X760 @ X761 )
          = X761 ) )
      & ( ( X765 != X766 )
        | ( X767 != X768 )
        | ~ ( in @ X767 @ X765 )
        | ( in @ X768 @ X766 ) )
      & ( ~ ( in @ X771 @ X769 )
        | ( in @ X772 @ X770 )
        | ( X771 != X772 )
        | ( X769 != X770 ) )
      & ( ~ ( in @ X772 @ X770 )
        | ( in @ X771 @ X769 )
        | ( X771 != X772 )
        | ( X769 != X770 ) )
      & ( ( X773 @ ( esk38_2 @ X773 @ X774 ) )
        | ~ ( X773 @ X774 )
        | ~ ( X773 @ X776 )
        | ~ ( X773 @ X777 )
        | ( X776 = X777 ) )
      & ( ( X774
         != ( esk38_2 @ X773 @ X774 ) )
        | ~ ( X773 @ X774 )
        | ~ ( X773 @ X776 )
        | ~ ( X773 @ X777 )
        | ( X776 = X777 ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( ( esk39_2 @ X778 @ X779 )
          = ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ~ ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ~ ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X778 @ ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X779 @ ( esk42_2 @ X778 @ X779 ) )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X779 @ X785 )
        | ( ( esk42_2 @ X778 @ X779 )
          = X785 )
        | ( X782
         != ( esk41_3 @ X778 @ X779 @ X782 ) )
        | ~ ( X778 @ X782 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X779 @ ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ( X778 @ ( esk44_2 @ X778 @ X779 ) )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( ~ ( X778 @ X789 )
        | ( ( esk44_2 @ X778 @ X779 )
          = X789 )
        | ( X786
         != ( esk43_3 @ X778 @ X779 @ X786 ) )
        | ~ ( X779 @ X786 )
        | ( X778 @ ( esk39_2 @ X778 @ X779 ) )
        | ( X779 @ ( esk40_2 @ X778 @ X779 ) ) )
      & ( emptyset = emptyset )
      & ( ( X790 != X791 )
        | ( X792 != X793 )
        | ( ( setadjoin @ X790 @ X792 )
          = ( setadjoin @ X791 @ X793 ) ) )
      & ( ( X794 != X795 )
        | ( ( powerset @ X794 )
          = ( powerset @ X795 ) ) )
      & ( ( X796 != X797 )
        | ( ( setunion @ X796 )
          = ( setunion @ X797 ) ) )
      & ( omega = omega )
      & ( ( X798 @ ( esk45_2 @ X798 @ X799 ) )
        | ~ ( X798 @ X799 )
        | ~ ( X798 @ X801 )
        | ~ ( X798 @ X802 )
        | ( X801 = X802 ) )
      & ( ( X799
         != ( esk45_2 @ X798 @ X799 ) )
        | ~ ( X798 @ X799 )
        | ~ ( X798 @ X801 )
        | ~ ( X798 @ X802 )
        | ( X801 = X802 ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( ( esk46_2 @ X803 @ X804 )
          = ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( ( esk46_2 @ X803 @ X804 )
          = ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( ( esk46_2 @ X803 @ X804 )
          = ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( ( esk46_2 @ X803 @ X804 )
          = ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ~ ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ~ ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ~ ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ~ ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ~ ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ~ ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ~ ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ~ ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X803 @ ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X804 @ ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( X809
         != ( esk49_3 @ X803 @ X804 @ X809 ) )
        | ~ ( X804 @ X809 )
        | ( ( descr @ X803 )
          = ( descr @ X804 ) )
        | ( X807
         != ( esk48_3 @ X803 @ X804 @ X807 ) )
        | ~ ( X803 @ X807 )
        | ( X803 @ ( esk46_2 @ X803 @ X804 ) )
        | ( X804 @ ( esk47_2 @ X803 @ X804 ) ) )
      & ( ( in @ ( esk50_4 @ X811 @ X812 @ X813 @ X814 ) @ X811 )
        | ( ( dsetconstr @ X811 @ X813 )
          = ( dsetconstr @ X812 @ X814 ) )
        | ( X811 != X812 ) )
      & ( ( in @ ( esk51_4 @ X811 @ X812 @ X813 @ X814 ) @ X812 )
        | ( ( dsetconstr @ X811 @ X813 )
          = ( dsetconstr @ X812 @ X814 ) )
        | ( X811 != X812 ) )
      & ( ( ( esk50_4 @ X811 @ X812 @ X813 @ X814 )
          = ( esk51_4 @ X811 @ X812 @ X813 @ X814 ) )
        | ( ( dsetconstr @ X811 @ X813 )
          = ( dsetconstr @ X812 @ X814 ) )
        | ( X811 != X812 ) )
      & ( ~ ( X813 @ ( esk50_4 @ X811 @ X812 @ X813 @ X814 ) )
        | ~ ( X814 @ ( esk51_4 @ X811 @ X812 @ X813 @ X814 ) )
        | ( ( dsetconstr @ X811 @ X813 )
          = ( dsetconstr @ X812 @ X814 ) )
        | ( X811 != X812 ) )
      & ( ( X813 @ ( esk50_4 @ X811 @ X812 @ X813 @ X814 ) )
        | ( X814 @ ( esk51_4 @ X811 @ X812 @ X813 @ X814 ) )
        | ( ( dsetconstr @ X811 @ X813 )
          = ( dsetconstr @ X812 @ X814 ) )
        | ( X811 != X812 ) )
      & ( ( in @ ( esk52_2 @ X817 @ X818 ) @ X817 )
        | ( subset @ X817 @ X818 ) )
      & ( ~ ( in @ ( esk52_2 @ X817 @ X818 ) @ X818 )
        | ( subset @ X817 @ X818 ) )
      & ( ( X820 != X821 )
        | ( subset @ X821 @ X820 ) )
      & ( ( X822 != X823 )
        | ( subset @ X822 @ X823 ) )
      & ( ( in @ ( esk53_2 @ X824 @ X825 ) @ X824 )
        | ( subset @ X824 @ X825 ) )
      & ( ~ ( in @ ( esk53_2 @ X824 @ X825 ) @ X825 )
        | ( subset @ X824 @ X825 ) )
      & ( subset @ emptyset @ X827 )
      & ( ~ ( subset @ X828 @ X829 )
        | ~ ( in @ X830 @ X828 )
        | ( in @ X830 @ X829 ) )
      & ( ~ ( subset @ X831 @ X832 )
        | ( in @ X833 @ X832 )
        | ~ ( in @ X833 @ X831 ) )
      & ( ~ ( in @ X836 @ X834 )
        | ( in @ X836 @ X835 )
        | ~ ( subset @ X834 @ X835 ) )
      & ( ( subset @ X837 @ X838 )
        | ( X837 != X838 ) )
      & ( ~ ( in @ X841 @ X839 )
        | ( in @ X841 @ X840 )
        | ( X839 != X840 ) )
      & ( subset @ X842 @ X842 )
      & ( ~ ( subset @ X843 @ X844 )
        | ~ ( subset @ X844 @ X845 )
        | ( subset @ X843 @ X845 ) )
      & ( subset @ X847 @ ( setadjoin @ X846 @ X847 ) )
      & ( ~ ( subset @ X848 @ X850 )
        | ( subset @ X848 @ ( setadjoin @ X849 @ X850 ) ) )
      & ( ~ ( subset @ X851 @ X852 )
        | ( in @ X851 @ ( powerset @ X852 ) ) )
      & ( ~ ( subset @ X853 @ X854 )
        | ~ ( subset @ X854 @ X853 )
        | ( X853 = X854 ) )
      & ( ~ ( subset @ X855 @ emptyset )
        | ( X855 = emptyset ) )
      & ( ~ ( subset @ X857 @ X856 )
        | ( in @ X857 @ ( powerset @ X856 ) ) )
      & ( in @ esk55_0 @ ( powerset @ esk54_0 ) )
      & ~ ( subset @ esk55_0 @ esk54_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_135])])])])])])]) ).

thf(c_0_137,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i] :
      ( ( in @ X4 @ X3 )
      | ~ ( in @ X2 @ ( powerset @ X3 ) )
      | ~ ( in @ X4 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

thf(c_0_138,negated_conjecture,
    in @ esk55_0 @ ( powerset @ esk54_0 ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

thf(c_0_139,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( subset @ X2 @ X3 )
      | ~ ( in @ ( esk53_2 @ X2 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

thf(c_0_140,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk54_0 )
      | ~ ( in @ X2 @ esk55_0 ) ),
    inference(spm,[status(thm)],[c_0_137,c_0_138]) ).

thf(c_0_141,negated_conjecture,
    ! [X2: $i] :
      ( ( subset @ X2 @ esk54_0 )
      | ~ ( in @ ( esk53_2 @ X2 @ esk54_0 ) @ esk55_0 ) ),
    inference(spm,[status(thm)],[c_0_139,c_0_140]) ).

thf(c_0_142,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ ( esk53_2 @ X2 @ X3 ) @ X2 )
      | ( subset @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

thf(c_0_143,negated_conjecture,
    ~ ( subset @ esk55_0 @ esk54_0 ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

thf(c_0_144,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : SEU577^1 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.11  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sun May 19 18:16:22 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.48  Running higher-order theorem proving
% 0.17/0.48  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.55  # Version: 3.1.0-ho
% 0.65/0.55  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.65/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.55  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.65/0.55  # Starting ehoh_best3_rw with 300s (1) cores
% 0.65/0.55  # Starting almost_fo_3 with 300s (1) cores
% 0.65/0.55  # Starting new_ho_13 with 300s (1) cores
% 0.65/0.55  # ehoh_best3_avoidappvar with pid 16297 completed with status 0
% 0.65/0.55  # Result found by ehoh_best3_avoidappvar
% 0.65/0.55  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.65/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.55  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.65/0.55  # No SInE strategy applied
% 0.65/0.55  # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.65/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.55  # Starting ehoh_best3 with 811s (1) cores
% 0.65/0.55  # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.65/0.55  # Starting new_bool_3 with 136s (1) cores
% 0.65/0.55  # Starting new_bool_6 with 136s (1) cores
% 0.65/0.55  # Starting ehoh_best5 with 136s (1) cores
% 0.65/0.55  # ehoh_best3_avoidappvar with pid 16302 completed with status 0
% 0.65/0.55  # Result found by ehoh_best3_avoidappvar
% 0.65/0.55  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.65/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.55  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.65/0.55  # No SInE strategy applied
% 0.65/0.55  # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.65/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.55  # Starting ehoh_best3 with 811s (1) cores
% 0.65/0.55  # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.65/0.55  # Preprocessing time       : 0.005 s
% 0.65/0.55  # Presaturation interreduction done
% 0.65/0.55  
% 0.65/0.55  # Proof found!
% 0.65/0.55  # SZS status Theorem
% 0.65/0.55  # SZS output start CNFRefutation
% See solution above
% 0.65/0.56  # Parsed axioms                        : 204
% 0.65/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.65/0.56  # Initial clauses                      : 313
% 0.65/0.56  # Removed in clause preprocessing      : 122
% 0.65/0.56  # Initial clauses in saturation        : 191
% 0.65/0.56  # Processed clauses                    : 323
% 0.65/0.56  # ...of these trivial                  : 7
% 0.65/0.56  # ...subsumed                          : 47
% 0.65/0.56  # ...remaining for further processing  : 269
% 0.65/0.56  # Other redundant clauses eliminated   : 13
% 0.65/0.56  # Clauses deleted for lack of memory   : 0
% 0.65/0.56  # Backward-subsumed                    : 0
% 0.65/0.56  # Backward-rewritten                   : 5
% 0.65/0.56  # Generated clauses                    : 402
% 0.65/0.56  # ...of the previous two non-redundant : 360
% 0.65/0.56  # ...aggressively subsumed             : 0
% 0.65/0.56  # Contextual simplify-reflections      : 0
% 0.65/0.56  # Paramodulations                      : 378
% 0.65/0.56  # Factorizations                       : 2
% 0.65/0.56  # NegExts                              : 0
% 0.65/0.56  # Equation resolutions                 : 13
% 0.65/0.56  # Disequality decompositions           : 0
% 0.65/0.56  # Total rewrite steps                  : 59
% 0.65/0.56  # ...of those cached                   : 36
% 0.65/0.56  # Propositional unsat checks           : 0
% 0.65/0.56  #    Propositional check models        : 0
% 0.65/0.56  #    Propositional check unsatisfiable : 0
% 0.65/0.56  #    Propositional clauses             : 0
% 0.65/0.56  #    Propositional clauses after purity: 0
% 0.65/0.56  #    Propositional unsat core size     : 0
% 0.65/0.56  #    Propositional preprocessing time  : 0.000
% 0.65/0.56  #    Propositional encoding time       : 0.000
% 0.65/0.56  #    Propositional solver time         : 0.000
% 0.65/0.56  #    Success case prop preproc time    : 0.000
% 0.65/0.56  #    Success case prop encoding time   : 0.000
% 0.65/0.56  #    Success case prop solver time     : 0.000
% 0.65/0.56  # Current number of processed clauses  : 85
% 0.65/0.56  #    Positive orientable unit clauses  : 20
% 0.65/0.56  #    Positive unorientable unit clauses: 0
% 0.65/0.56  #    Negative unit clauses             : 2
% 0.65/0.56  #    Non-unit-clauses                  : 63
% 0.65/0.56  # Current number of unprocessed clauses: 379
% 0.65/0.56  # ...number of literals in the above   : 1165
% 0.65/0.56  # Current number of archived formulas  : 0
% 0.65/0.56  # Current number of archived clauses   : 171
% 0.65/0.56  # Clause-clause subsumption calls (NU) : 4840
% 0.65/0.56  # Rec. Clause-clause subsumption calls : 1681
% 0.65/0.56  # Non-unit clause-clause subsumptions  : 33
% 0.65/0.56  # Unit Clause-clause subsumption calls : 38
% 0.65/0.56  # Rewrite failures with RHS unbound    : 0
% 0.65/0.56  # BW rewrite match attempts            : 15
% 0.65/0.56  # BW rewrite match successes           : 4
% 0.65/0.56  # Condensation attempts                : 0
% 0.65/0.56  # Condensation successes               : 0
% 0.65/0.56  # Termbank termtop insertions          : 46889
% 0.65/0.56  # Search garbage collected termcells   : 10289
% 0.65/0.56  
% 0.65/0.56  # -------------------------------------------------
% 0.65/0.56  # User time                : 0.046 s
% 0.65/0.56  # System time              : 0.013 s
% 0.65/0.56  # Total time               : 0.059 s
% 0.65/0.56  # Maximum resident set size: 4548 pages
% 0.65/0.56  
% 0.65/0.56  # -------------------------------------------------
% 0.65/0.56  # User time                : 0.186 s
% 0.65/0.56  # System time              : 0.025 s
% 0.65/0.56  # Total time               : 0.211 s
% 0.65/0.56  # Maximum resident set size: 2060 pages
% 0.65/0.56  % E---3.1 exiting
% 0.65/0.56  % E exiting
%------------------------------------------------------------------------------