TSTP Solution File: SEU570^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU570^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n032.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 03:28:15 EDT 2024

% Result   : Theorem 0.14s 0.42s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  246
% Syntax   : Number of formulae    :  297 (  24 unt; 156 typ;   0 def)
%            Number of atoms       : 1118 ( 326 equ;   0 cnn)
%            Maximal formula atoms :  340 (   7 avg)
%            Number of connectives : 4397 ( 406   ~; 454   |; 275   &;2570   @)
%                                         ( 149 <=>; 543  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  396 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  306 ( 306   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  159 ( 156 usr;  94 con; 0-4 aty)
%            Number of variables   :  935 (  63   ^ 768   !; 104   ?; 935   :)

% 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,
    epred1_0: $o ).

thf(decl_124,type,
    esk1_2: $i > $i > $i ).

thf(decl_125,type,
    esk2_2: $i > $i > $i ).

thf(decl_126,type,
    esk3_2: $i > $i > $i ).

thf(decl_127,type,
    esk4_1: $i > $i ).

thf(decl_128,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_129,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_130,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_131,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_132,type,
    esk9_1: $i > $i ).

thf(decl_133,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_134,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_135,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_136,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_137,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_138,type,
    esk15_2: $i > $i > $i ).

thf(decl_139,type,
    esk16_2: $i > $i > $i ).

thf(decl_140,type,
    esk17_1: $i > $i ).

thf(decl_141,type,
    esk18_1: $i > $i ).

thf(decl_142,type,
    esk19_1: $i > $i ).

thf(decl_143,type,
    esk20_2: $i > $i > $i ).

thf(decl_144,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_145,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_146,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_147,type,
    esk24_1: $i > $i ).

thf(decl_148,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_149,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_150,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_151,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_152,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_153,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_154,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_155,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_156,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_157,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_158,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_159,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_160,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_161,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_162,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_163,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_164,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_165,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_166,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_167,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_168,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_169,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_170,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_171,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_172,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_173,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_174,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_175,type,
    esk52_2: $i > $i > $i ).

thf(decl_176,type,
    esk53_2: $i > $i > $i ).

thf(decl_177,type,
    esk54_0: $i ).

thf(decl_178,type,
    esk55_0: $i ).

thf(decl_179,type,
    esk56_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/sandbox2/benchmark/theBenchmark.p',replAx) ).

thf(exu,axiom,
    ( exu
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] :
          ( ( X1 @ X2 )
          & ! [X3: $i] :
              ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE1) ).

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

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuI1) ).

thf(exuI3,axiom,
    ( exuI3
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] : ( X1 @ X2 )
       => ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
         => ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).

thf(exuI2,axiom,
    ( exuI2
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).

thf(exuE3u,axiom,
    ( exuE3u
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).

thf(exu__Cong,axiom,
    ( exu__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
        <=> ( exu
            @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).

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

thf(descr__Cong,axiom,
    ( descr__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
         => ( ( exu
              @ ^ [X2: $i] : ( X17 @ X2 ) )
           => ( ( descr
                @ ^ [X2: $i] : ( X1 @ X2 ) )
              = ( descr
                @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).

thf(dsetconstrI,axiom,
    ( dsetconstrI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).

thf(dsetconstrEL,axiom,
    ( dsetconstrEL
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [X3: $i] : ( X1 @ X3 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [X3: $i] : ( X1 @ X3 ) ) )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).

thf(setbeta,axiom,
    ( setbeta
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) )
        <=> ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(setunionE,axiom,
    ( setunionE
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
       => ! [X13: $o] :
            ( ! [X5: $i] :
                ( ( in @ X2 @ X5 )
               => ( ( in @ X5 @ X4 )
                 => X13 ) )
           => X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).

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

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

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

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

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

thf(upairsetE,axiom,
    ( upairsetE
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
       => ( ( X14 = X2 )
          | ( X14 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).

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

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

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

thf(quantDeMorgan1,axiom,
    ( quantDeMorgan1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).

thf(quantDeMorgan2,axiom,
    ( quantDeMorgan2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) )
       => ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).

thf(quantDeMorgan3,axiom,
    ( quantDeMorgan3
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).

thf(quantDeMorgan4,axiom,
    ( quantDeMorgan4
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).

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

thf(prop2set2propI,axiom,
    ( prop2set2propI
  <=> ! [X16: $o] :
        ( X16
       => ( set2prop @ ( prop2set @ X16 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notdexE) ).

thf(notdallE,axiom,
    ( notdallE
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).

thf(inCongP,axiom,
    ( inCongP
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X4 )
             => ( in @ X3 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).

thf(in__Cong,axiom,
    ( in__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X4 )
            <=> ( in @ X3 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).

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

thf(setadjoin__Cong,axiom,
    ( setadjoin__Cong
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ! [X14: $i,X18: $i] :
            ( ( X14 = X18 )
           => ( ( setadjoin @ X2 @ X14 )
              = ( setadjoin @ X3 @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).

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

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

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

thf(subsetI1,axiom,
    ( subsetI1
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).

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

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

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

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

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

thf(subsetE2,axiom,
    ( subsetE2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).

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

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

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

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

thf(c_0_89,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_90,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_91,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_92,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_93,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_94,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_95,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_96,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_97,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_98,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_99,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_100,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_101,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_102,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_103,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_104,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X260: $i] :
                  ( ( X6 @ X2 @ X260 )
                  & ! [X261: $i] :
                      ( ( X6 @ X2 @ X261 )
                     => ( X260 = X261 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_89,c_0_90]) ).

thf(c_0_105,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X262: $i] :
              ( ( X1 @ X262 )
              & ! [X263: $i] :
                  ( ( X1 @ X263 )
                 => ( X262 = X263 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_91,c_0_90]) ).

thf(c_0_106,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_107,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_108,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_109,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X264: $i] :
              ( ( X1 @ X264 )
              & ! [X265: $i] :
                  ( ( X1 @ X265 )
                 => ( X264 = X265 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_92,c_0_90]) ).

thf(c_0_110,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X266: $i] :
              ( ( X1 @ X266 )
              & ! [X267: $i] :
                  ( ( X1 @ X267 )
                 => ( X266 = X267 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_93,c_0_90]) ).

thf(c_0_111,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_112,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_94]) ).

thf(c_0_113,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_95,c_0_94]) ).

thf(c_0_114,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_94]) ).

thf(c_0_115,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_116,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X268: $i] :
              ( ( X1 @ X268 )
              & ! [X269: $i] :
                  ( ( X1 @ X269 )
                 => ( X268 = X269 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_96,c_0_90]) ).

thf(c_0_117,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_94]) ).

thf(c_0_118,plain,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) )
            = emptyset )
         => ~ $true ) ) ),
    inference(fof_simplification,[status(thm)],[emptyE1]) ).

thf(c_0_119,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X270: $i] :
              ( ( X1 @ X270 )
              & ! [X271: $i] :
                  ( ( X1 @ X271 )
                 => ( X270 = X271 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_97,c_0_90]) ).

thf(c_0_120,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X272: $i] :
                ( ( X1 @ X272 )
                & ! [X273: $i] :
                    ( ( X1 @ X273 )
                   => ( X272 = X273 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_98,c_0_90]) ).

thf(c_0_121,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X274: $i] :
              ( ( X1 @ X274 )
              & ! [X275: $i] :
                  ( ( X1 @ X275 )
                 => ( X274 = X275 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_99,c_0_90]) ).

thf(c_0_122,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X276: $i] :
              ( ( X1 @ X276 )
              & ! [X277: $i] :
                  ( ( X1 @ X277 )
                 => ( X276 = X277 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_100,c_0_90]) ).

thf(c_0_123,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X278: $i] :
                ( ( X1 @ X278 )
                & ! [X279: $i] :
                    ( ( X1 @ X279 )
                   => ( X278 = X279 ) ) )
          <=> ? [X280: $i] :
                ( ( X17 @ X280 )
                & ! [X281: $i] :
                    ( ( X17 @ X281 )
                   => ( X280 = X281 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_101,c_0_90]) ).

thf(c_0_124,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X282: $i] :
              ( ( X1 @ X282 )
              & ! [X283: $i] :
                  ( ( X1 @ X283 )
                 => ( X282 = X283 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_102,c_0_90]) ).

thf(c_0_125,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X284: $i] :
                ( ( X1 @ X284 )
                & ! [X285: $i] :
                    ( ( X1 @ X285 )
                   => ( X284 = X285 ) ) )
           => ( ? [X286: $i] :
                  ( ( X17 @ X286 )
                  & ! [X287: $i] :
                      ( ( X17 @ X287 )
                     => ( X286 = X287 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_103,c_0_90]) ).

thf(c_0_126,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_127,plain,
    ( epred1_0
  <=> ! [X317: $i] :
      ? [X318: $i] :
        ( ! [X319: $i] :
            ( ( in @ X319 @ X318 )
           => ! [X320: $i] :
                ( ( in @ X320 @ X319 )
               => ( in @ X320 @ X317 ) ) )
        & ! [X321: $i,X322: $i] :
            ( ( ( in @ X321 @ X317 )
              & ( in @ X322 @ X317 ) )
           => ( ! [X323: $i] :
                  ( ( in @ X323 @ X318 )
                 => ( ( in @ X321 @ X323 )
                  <=> ( in @ X322 @ X323 ) ) )
             => ( X321 = X322 ) ) )
        & ! [X324: $i,X325: $i] :
            ( ( ( in @ X324 @ X318 )
              & ( in @ X325 @ X318 ) )
           => ( ! [X326: $i] :
                  ( ( in @ X326 @ X324 )
                 => ( in @ X326 @ X325 ) )
              | ! [X327: $i] :
                  ( ( in @ X327 @ X325 )
                 => ( in @ X327 @ X324 ) ) ) )
        & ! [X328: $i] :
            ( ( ! [X329: $i] :
                  ( ( in @ X329 @ X328 )
                 => ( in @ X329 @ X317 ) )
              & ? [X330: $i] : ( in @ X330 @ X328 ) )
           => ? [X331: $i,X332: $i] :
                ( ( in @ X331 @ X318 )
                & ( in @ X332 @ X328 )
                & ~ ? [X333: $i] :
                      ( ( in @ X333 @ X331 )
                      & ( in @ X333 @ X328 ) )
                & ! [X334: $i] :
                    ( ( in @ X334 @ X318 )
                   => ( ! [X335: $i] :
                          ( ( in @ X335 @ X334 )
                         => ( in @ X335 @ X331 ) )
                      | ( in @ X332 @ X334 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_128,negated_conjecture,
    ~ ( ! [X288: $i,X289: $i] :
          ( ! [X290: $i] :
              ( ( in @ X290 @ X288 )
            <=> ( in @ X290 @ X289 ) )
         => ( X288 = X289 ) )
     => ( ! [X291: $i] :
            ~ ( in @ X291 @ emptyset )
       => ( ! [X292: $i,X293: $i,X294: $i] :
              ( ( in @ X294 @ ( setadjoin @ X292 @ X293 ) )
            <=> ( ( X294 = X292 )
                | ( in @ X294 @ X293 ) ) )
         => ( ! [X295: $i,X296: $i] :
                ( ( in @ X296 @ ( powerset @ X295 ) )
              <=> ! [X297: $i] :
                    ( ( in @ X297 @ X296 )
                   => ( in @ X297 @ X295 ) ) )
           => ( ! [X298: $i,X299: $i] :
                  ( ( in @ X299 @ ( setunion @ X298 ) )
                <=> ? [X300: $i] :
                      ( ( in @ X299 @ X300 )
                      & ( in @ X300 @ X298 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X301: $i] :
                      ( ( in @ X301 @ omega )
                     => ( in @ ( setadjoin @ X301 @ X301 ) @ omega ) )
                 => ( ! [X302: $i] :
                        ( ( ( in @ emptyset @ X302 )
                          & ! [X303: $i] :
                              ( ( ( in @ X303 @ omega )
                                & ( in @ X303 @ X302 ) )
                             => ( in @ ( setadjoin @ X303 @ X303 ) @ X302 ) ) )
                       => ! [X304: $i] :
                            ( ( in @ X304 @ omega )
                           => ( in @ X304 @ X302 ) ) )
                   => ( ! [X305: $i > $i > $o,X306: $i] :
                          ( ! [X307: $i] :
                              ( ( in @ X307 @ X306 )
                             => ? [X308: $i] :
                                  ( ( X305 @ X307 @ X308 )
                                  & ! [X309: $i] :
                                      ( ( X305 @ X307 @ X309 )
                                     => ( X308 = X309 ) ) ) )
                         => ? [X310: $i] :
                            ! [X311: $i] :
                              ( ( in @ X311 @ X310 )
                            <=> ? [X312: $i] :
                                  ( ( in @ X312 @ X306 )
                                  & ( X305 @ X312 @ X311 ) ) ) )
                     => ( ! [X313: $i] :
                            ( ? [X314: $i] : ( in @ X314 @ X313 )
                           => ? [X315: $i] :
                                ( ( in @ X315 @ X313 )
                                & ~ ? [X316: $i] :
                                      ( ( in @ X316 @ X315 )
                                      & ( in @ X316 @ X313 ) ) ) )
                       => ( epred1_0
                         => ( ! [X336: $i > $o] :
                                ( ? [X337: $i] :
                                    ( ( X336 @ X337 )
                                    & ! [X338: $i] :
                                        ( ( X336 @ X338 )
                                       => ( X337 = X338 ) ) )
                               => ( X336
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X336 @ Z0 ) ) ) )
                           => ( ! [X339: $i,X340: $i > $o,X341: $i] :
                                  ( ( in @ X341 @ X339 )
                                 => ( ( X340 @ X341 )
                                   => ( in @ X341 @ ( dsetconstr @ X339 @ X340 ) ) ) )
                             => ( ! [X342: $i,X343: $i > $o,X344: $i] :
                                    ( ( in @ X344 @ ( dsetconstr @ X342 @ X343 ) )
                                   => ( in @ X344 @ X342 ) )
                               => ( ! [X345: $i,X346: $i > $o,X347: $i] :
                                      ( ( in @ X347 @ ( dsetconstr @ X345 @ X346 ) )
                                     => ( X346 @ X347 ) )
                                 => ( ! [X348: $i > $o] :
                                        ( ? [X349: $i] :
                                            ( ( X348 @ X349 )
                                            & ! [X350: $i] :
                                                ( ( X348 @ X350 )
                                               => ( X349 = X350 ) ) )
                                       => ? [X351: $i] :
                                            ( ( X348 @ X351 )
                                            & ! [X352: $i] :
                                                ( ( X348 @ X352 )
                                               => ( X351 = X352 ) ) ) )
                                   => ( ! [X353: $o,X354: $i] :
                                          ( ( in @ X354 @ ( prop2set @ X353 ) )
                                         => X353 )
                                     => ( ! [X355: $i] :
                                            ( ( in @ X355 @ emptyset )
                                           => ! [X356: $o] : X356 )
                                       => ( ! [X357: $i] :
                                              ( ( in @ X357 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X358: $i] :
                                                ~ ( in @ X358 @ emptyset )
                                           => ( ! [X359: $i > $o] :
                                                  ( ? [X360: $i] :
                                                      ( ( X359 @ X360 )
                                                      & ! [X361: $i] :
                                                          ( ( X359 @ X361 )
                                                         => ( X360 = X361 ) ) )
                                                 => ? [X362: $i] : ( X359 @ X362 ) )
                                             => ( ! [X363: $i,X364: $i] :
                                                    ( ! [X365: $i] :
                                                        ( ( in @ X365 @ X363 )
                                                       => ( in @ X365 @ X364 ) )
                                                   => ( ! [X366: $i] :
                                                          ( ( in @ X366 @ X364 )
                                                         => ( in @ X366 @ X363 ) )
                                                     => ( X363 = X364 ) ) )
                                               => ( ! [X367: $i] :
                                                      ( ! [X368: $i] :
                                                          ~ ( in @ X368 @ X367 )
                                                     => ( X367 = emptyset ) )
                                                 => ( ! [X369: $i] :
                                                        ( ! [X370: $i] :
                                                            ~ ( in @ X370 @ X369 )
                                                       => ( X369 = emptyset ) )
                                                   => ( ! [X371: $i,X372: $i > $o,X373: $i] :
                                                          ( ( in @ X373 @ X371 )
                                                         => ( ( in @ X373 @ ( dsetconstr @ X371 @ X372 ) )
                                                          <=> ( X372 @ X373 ) ) )
                                                     => ( ! [X374: $i] :
                                                            ( ( X374 != emptyset )
                                                           => ? [X375: $i] : ( in @ X375 @ X374 ) )
                                                       => ( ! [X376: $i,X377: $i > $o,X378: $i] :
                                                              ( ( in @ X378 @ X376 )
                                                             => ( ( X377 @ X378 )
                                                               => ( ( dsetconstr @ X376 @ X377 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X379: $i] :
                                                                ( ? [X380: $i] : ( in @ X380 @ X379 )
                                                               => ( X379 != emptyset ) )
                                                           => ( ! [X381: $i,X382: $i] : ( in @ X381 @ ( setadjoin @ X381 @ X382 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X383: $i,X384: $i,X385: $i] :
                                                                      ( ( in @ X385 @ X384 )
                                                                     => ( in @ X385 @ ( setadjoin @ X383 @ X384 ) ) )
                                                                 => ( ! [X386: $i,X387: $i,X388: $i] :
                                                                        ( ( in @ X388 @ ( setadjoin @ X386 @ X387 ) )
                                                                       => ! [X389: $o] :
                                                                            ( ( ( X388 = X386 )
                                                                             => X389 )
                                                                           => ( ( ( in @ X388 @ X387 )
                                                                               => X389 )
                                                                             => X389 ) ) )
                                                                   => ( ! [X390: $i,X391: $i,X392: $i] :
                                                                          ( ( in @ X392 @ ( setadjoin @ X390 @ X391 ) )
                                                                         => ( ( X392 = X390 )
                                                                            | ( in @ X392 @ X391 ) ) )
                                                                     => ( ! [X393: $i] :
                                                                            ( ( dsetconstr @ X393
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X393 )
                                                                       => ( ! [X394: $i,X395: $i] :
                                                                              ( ! [X396: $i] :
                                                                                  ( ( in @ X396 @ X395 )
                                                                                 => ( in @ X396 @ X394 ) )
                                                                             => ( in @ X395 @ ( powerset @ X394 ) ) )
                                                                         => ( ! [X397: $i] : ( in @ emptyset @ ( powerset @ X397 ) )
                                                                           => ( ! [X398: $i] : ( in @ emptyset @ ( powerset @ X398 ) )
                                                                             => ( ! [X399: $i,X400: $i,X401: $i] :
                                                                                    ( ( in @ X400 @ ( powerset @ X399 ) )
                                                                                   => ( ( in @ X401 @ X400 )
                                                                                     => ( in @ X401 @ X399 ) ) )
                                                                               => ( ! [X402: $i,X403: $i,X404: $i] :
                                                                                      ( ( in @ X403 @ X404 )
                                                                                     => ( ( in @ X404 @ X402 )
                                                                                       => ( in @ X403 @ ( setunion @ X402 ) ) ) )
                                                                                 => ( ! [X405: $i,X406: $i] :
                                                                                        ( ( in @ X406 @ ( setunion @ X405 ) )
                                                                                       => ! [X407: $o] :
                                                                                            ( ! [X408: $i] :
                                                                                                ( ( in @ X406 @ X408 )
                                                                                               => ( ( in @ X408 @ X405 )
                                                                                                 => X407 ) )
                                                                                           => X407 ) )
                                                                                   => ( ! [X409: $i,X410: $i] :
                                                                                          ( ( in @ X410 @ X409 )
                                                                                         => ( in @ X410 @ ( powerset @ ( setunion @ X409 ) ) ) )
                                                                                     => ( ! [X411: $i > $o] :
                                                                                            ( ? [X412: $i] :
                                                                                                ( ( X411 @ X412 )
                                                                                                & ! [X413: $i] :
                                                                                                    ( ( X411 @ X413 )
                                                                                                   => ( X412 = X413 ) ) )
                                                                                           => ? [X414: $i] :
                                                                                              ! [X415: $i] :
                                                                                                ( ( X411 @ X415 )
                                                                                              <=> ( X415 = X414 ) ) )
                                                                                       => ( ! [X416: $i] :
                                                                                              ( ( X416 != emptyset )
                                                                                             => ? [X417: $i] :
                                                                                                  ( ( in @ X417 @ X416 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X418: $i,X419: $i] :
                                                                                                ( ( in @ X418 @ ( setadjoin @ X419 @ emptyset ) )
                                                                                               => ( X418 = X419 ) )
                                                                                           => ( ! [X420: $i,X421: $i] :
                                                                                                  ( ( X420 != X421 )
                                                                                                 => ~ ( in @ X421 @ ( setadjoin @ X420 @ emptyset ) ) )
                                                                                             => ( ! [X422: $i,X423: $i] :
                                                                                                    ( ( X422 = X423 )
                                                                                                   => ( in @ X422 @ ( setadjoin @ X423 @ emptyset ) ) )
                                                                                               => ( ! [X424: $i,X425: $i] :
                                                                                                      ( ( in @ X424 @ ( setadjoin @ X425 @ emptyset ) )
                                                                                                     => ( in @ X425 @ ( setadjoin @ X424 @ emptyset ) ) )
                                                                                                 => ( ! [X426: $i,X427: $i,X428: $i] :
                                                                                                        ( ( in @ X428 @ ( setadjoin @ X426 @ ( setadjoin @ X427 @ emptyset ) ) )
                                                                                                       => ( ( X428 = X426 )
                                                                                                          | ( X428 = X427 ) ) )
                                                                                                   => ( ! [X429: $i,X430: $i] : ( in @ X429 @ ( setadjoin @ X429 @ ( setadjoin @ X430 @ emptyset ) ) )
                                                                                                     => ( ! [X431: $i,X432: $i] : ( in @ X432 @ ( setadjoin @ X431 @ ( setadjoin @ X432 @ emptyset ) ) )
                                                                                                       => ( ! [X433: $i,X434: $i > $o] :
                                                                                                              ( ? [X435: $i] :
                                                                                                                  ( ( in @ X435 @ X433 )
                                                                                                                  & ( X434 @ X435 ) )
                                                                                                             => ( ( ( dsetconstr @ X433 @ X434 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X436: $i > $o,X437: $i] :
                                                                                                                ( ( in @ X437 @ emptyset )
                                                                                                               => ( X436 @ X437 ) )
                                                                                                           => ( ! [X438: $i,X439: $i > $o] :
                                                                                                                  ( ~ ! [X440: $i] :
                                                                                                                        ( ( in @ X440 @ X438 )
                                                                                                                       => ( X439 @ X440 ) )
                                                                                                                 => ? [X441: $i] :
                                                                                                                      ( ( in @ X441 @ X438 )
                                                                                                                      & ~ ( X439 @ X441 ) ) )
                                                                                                             => ( ! [X442: $i,X443: $i > $o] :
                                                                                                                    ( ! [X444: $i] :
                                                                                                                        ( ( in @ X444 @ X442 )
                                                                                                                       => ~ ( X443 @ X444 ) )
                                                                                                                   => ~ ? [X445: $i] :
                                                                                                                          ( ( in @ X445 @ X442 )
                                                                                                                          & ( X443 @ X445 ) ) )
                                                                                                               => ( ! [X446: $i,X447: $i > $o] :
                                                                                                                      ( ~ ? [X448: $i] :
                                                                                                                            ( ( in @ X448 @ X446 )
                                                                                                                            & ( X447 @ X448 ) )
                                                                                                                     => ! [X449: $i] :
                                                                                                                          ( ( in @ X449 @ X446 )
                                                                                                                         => ~ ( X447 @ X449 ) ) )
                                                                                                                 => ( ! [X450: $i,X451: $i > $o] :
                                                                                                                        ( ? [X452: $i] :
                                                                                                                            ( ( in @ X452 @ X450 )
                                                                                                                            & ~ ( X451 @ X452 ) )
                                                                                                                       => ~ ! [X453: $i] :
                                                                                                                              ( ( in @ X453 @ X450 )
                                                                                                                             => ( X451 @ X453 ) ) )
                                                                                                                   => ( ! [X454: $o] :
                                                                                                                          ( X454
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X454 ) ) )
                                                                                                                     => ( ! [X455: $o] :
                                                                                                                            ( X455
                                                                                                                           => ( set2prop @ ( prop2set @ 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 > $o] :
                                                                                                                                  ( ? [X465: $i] :
                                                                                                                                      ( ( X464 @ X465 )
                                                                                                                                      & ! [X466: $i] :
                                                                                                                                          ( ( X464 @ X466 )
                                                                                                                                         => ( X465 = X466 ) ) )
                                                                                                                                 => ? [X467: $i] :
                                                                                                                                      ( ( X464 @ X467 )
                                                                                                                                      & ! [X468: $i] :
                                                                                                                                          ( ( X464 @ X468 )
                                                                                                                                         => ( X467 = X468 ) ) ) )
                                                                                                                             => ( ! [X469: $i > $o] :
                                                                                                                                    ( ? [X470: $i] : ( X469 @ X470 )
                                                                                                                                   => ( ! [X471: $i,X472: $i] :
                                                                                                                                          ( ( X469 @ X471 )
                                                                                                                                         => ( ( X469 @ X472 )
                                                                                                                                           => ( X471 = X472 ) ) )
                                                                                                                                     => ? [X473: $i] :
                                                                                                                                          ( ( X469 @ X473 )
                                                                                                                                          & ! [X474: $i] :
                                                                                                                                              ( ( X469 @ X474 )
                                                                                                                                             => ( X473 = X474 ) ) ) ) )
                                                                                                                               => ( ! [X475: $i > $o] :
                                                                                                                                      ( ? [X476: $i] :
                                                                                                                                        ! [X477: $i] :
                                                                                                                                          ( ( X475 @ X477 )
                                                                                                                                        <=> ( X477 = X476 ) )
                                                                                                                                     => ? [X478: $i] :
                                                                                                                                          ( ( X475 @ X478 )
                                                                                                                                          & ! [X479: $i] :
                                                                                                                                              ( ( X475 @ X479 )
                                                                                                                                             => ( X478 = X479 ) ) ) )
                                                                                                                                 => ( ! [X480: $i,X481: $i] :
                                                                                                                                        ( ( X480 = X481 )
                                                                                                                                       => ! [X482: $i,X483: $i] :
                                                                                                                                            ( ( X482 = X483 )
                                                                                                                                           => ( ( in @ X482 @ X480 )
                                                                                                                                             => ( in @ X483 @ X481 ) ) ) )
                                                                                                                                   => ( ! [X484: $i,X485: $i] :
                                                                                                                                          ( ( X484 = X485 )
                                                                                                                                         => ! [X486: $i,X487: $i] :
                                                                                                                                              ( ( X486 = X487 )
                                                                                                                                             => ( ( in @ X486 @ X484 )
                                                                                                                                              <=> ( in @ X487 @ X485 ) ) ) )
                                                                                                                                     => ( ! [X488: $i > $o] :
                                                                                                                                            ( ? [X489: $i] :
                                                                                                                                                ( ( X488 @ X489 )
                                                                                                                                                & ! [X490: $i] :
                                                                                                                                                    ( ( X488 @ X490 )
                                                                                                                                                   => ( X489 = X490 ) ) )
                                                                                                                                           => ! [X491: $i,X492: $i] :
                                                                                                                                                ( ( X488 @ X491 )
                                                                                                                                               => ( ( X488 @ X492 )
                                                                                                                                                 => ( X491 = X492 ) ) ) )
                                                                                                                                       => ( ! [X493: $i > $o,X494: $i > $o] :
                                                                                                                                              ( ! [X495: $i,X496: $i] :
                                                                                                                                                  ( ( X495 = X496 )
                                                                                                                                                 => ( ( X493 @ X495 )
                                                                                                                                                  <=> ( X494 @ X496 ) ) )
                                                                                                                                             => ( ? [X497: $i] :
                                                                                                                                                    ( ( X493 @ X497 )
                                                                                                                                                    & ! [X498: $i] :
                                                                                                                                                        ( ( X493 @ X498 )
                                                                                                                                                       => ( X497 = X498 ) ) )
                                                                                                                                              <=> ? [X499: $i] :
                                                                                                                                                    ( ( X494 @ X499 )
                                                                                                                                                    & ! [X500: $i] :
                                                                                                                                                        ( ( X494 @ X500 )
                                                                                                                                                       => ( X499 = X500 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X501: $i,X502: $i] :
                                                                                                                                                  ( ( X501 = X502 )
                                                                                                                                                 => ! [X503: $i,X504: $i] :
                                                                                                                                                      ( ( X503 = X504 )
                                                                                                                                                     => ( ( setadjoin @ X501 @ X503 )
                                                                                                                                                        = ( setadjoin @ X502 @ X504 ) ) ) )
                                                                                                                                             => ( ! [X505: $i,X506: $i] :
                                                                                                                                                    ( ( X505 = X506 )
                                                                                                                                                   => ( ( powerset @ X505 )
                                                                                                                                                      = ( powerset @ X506 ) ) )
                                                                                                                                               => ( ! [X507: $i,X508: $i] :
                                                                                                                                                      ( ( X507 = X508 )
                                                                                                                                                     => ( ( setunion @ X507 )
                                                                                                                                                        = ( setunion @ X508 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X509: $i > $o] :
                                                                                                                                                          ( ? [X510: $i] :
                                                                                                                                                              ( ( X509 @ X510 )
                                                                                                                                                              & ! [X511: $i] :
                                                                                                                                                                  ( ( X509 @ X511 )
                                                                                                                                                                 => ( X510 = X511 ) ) )
                                                                                                                                                         => ! [X512: $i,X513: $i] :
                                                                                                                                                              ( ( X509 @ X512 )
                                                                                                                                                             => ( ( X509 @ X513 )
                                                                                                                                                               => ( X512 = X513 ) ) ) )
                                                                                                                                                     => ( ! [X514: $i > $o,X515: $i > $o] :
                                                                                                                                                            ( ! [X516: $i,X517: $i] :
                                                                                                                                                                ( ( X516 = X517 )
                                                                                                                                                               => ( ( X514 @ X516 )
                                                                                                                                                                <=> ( X515 @ X517 ) ) )
                                                                                                                                                           => ( ? [X518: $i] :
                                                                                                                                                                  ( ( X514 @ X518 )
                                                                                                                                                                  & ! [X519: $i] :
                                                                                                                                                                      ( ( X514 @ X519 )
                                                                                                                                                                     => ( X518 = X519 ) ) )
                                                                                                                                                             => ( ? [X520: $i] :
                                                                                                                                                                    ( ( X515 @ X520 )
                                                                                                                                                                    & ! [X521: $i] :
                                                                                                                                                                        ( ( X515 @ X521 )
                                                                                                                                                                       => ( X520 = X521 ) ) )
                                                                                                                                                               => ( ( descr @ X514 )
                                                                                                                                                                  = ( descr @ X515 ) ) ) ) )
                                                                                                                                                       => ( ! [X522: $i,X523: $i] :
                                                                                                                                                              ( ( X522 = X523 )
                                                                                                                                                             => ! [X524: $i > $o,X525: $i > $o] :
                                                                                                                                                                  ( ! [X526: $i] :
                                                                                                                                                                      ( ( in @ X526 @ X522 )
                                                                                                                                                                     => ! [X527: $i] :
                                                                                                                                                                          ( ( in @ X527 @ X523 )
                                                                                                                                                                         => ( ( X526 = X527 )
                                                                                                                                                                           => ( ( X524 @ X526 )
                                                                                                                                                                            <=> ( X525 @ X527 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X522 @ X524 )
                                                                                                                                                                    = ( dsetconstr @ X523 @ X525 ) ) ) )
                                                                                                                                                         => ( ! [X528: $i,X529: $i] :
                                                                                                                                                                ( ! [X530: $i] :
                                                                                                                                                                    ( ( in @ X530 @ X528 )
                                                                                                                                                                   => ( in @ X530 @ X529 ) )
                                                                                                                                                               => ( subset @ X528 @ X529 ) )
                                                                                                                                                           => ( ! [X531: $i,X532: $i] :
                                                                                                                                                                  ( ( X531 = X532 )
                                                                                                                                                                 => ( subset @ X532 @ X531 ) )
                                                                                                                                                             => ( ! [X533: $i,X534: $i] :
                                                                                                                                                                    ( ( X533 = X534 )
                                                                                                                                                                   => ( subset @ X533 @ X534 ) )
                                                                                                                                                               => ( ! [X535: $i,X536: $i] :
                                                                                                                                                                      ( ! [X537: $i] :
                                                                                                                                                                          ( ( in @ X537 @ X535 )
                                                                                                                                                                         => ( in @ X537 @ X536 ) )
                                                                                                                                                                     => ( subset @ X535 @ X536 ) )
                                                                                                                                                                 => ( ! [X538: $i] : ( subset @ emptyset @ X538 )
                                                                                                                                                                   => ( ! [X539: $i,X540: $i,X541: $i] :
                                                                                                                                                                          ( ( subset @ X539 @ X540 )
                                                                                                                                                                         => ( ( in @ X541 @ X539 )
                                                                                                                                                                           => ( in @ X541 @ X540 ) ) )
                                                                                                                                                                     => ( ! [X542: $i,X543: $i,X544: $i] :
                                                                                                                                                                            ( ( subset @ X542 @ X543 )
                                                                                                                                                                           => ( ~ ( in @ X544 @ X543 )
                                                                                                                                                                             => ~ ( in @ X544 @ X542 ) ) )
                                                                                                                                                                       => ( ! [X545: $i,X546: $i,X547: $i] :
                                                                                                                                                                              ( ( in @ X547 @ X545 )
                                                                                                                                                                             => ( ~ ( in @ X547 @ X546 )
                                                                                                                                                                               => ~ ( subset @ X545 @ X546 ) ) )
                                                                                                                                                                         => ( ! [X548: $i,X549: $i] :
                                                                                                                                                                                ( ~ ( subset @ X548 @ X549 )
                                                                                                                                                                               => ( X548 != X549 ) )
                                                                                                                                                                           => ( ! [X550: $i,X551: $i,X552: $i] :
                                                                                                                                                                                  ( ( in @ X552 @ X550 )
                                                                                                                                                                                 => ( ~ ( in @ X552 @ X551 )
                                                                                                                                                                                   => ( X550 != X551 ) ) )
                                                                                                                                                                             => ( ! [X553: $i] : ( subset @ X553 @ X553 )
                                                                                                                                                                               => ! [X4: $i,X5: $i,X7: $i] :
                                                                                                                                                                                    ( ( subset @ X4 @ X5 )
                                                                                                                                                                                   => ( ( subset @ X5 @ X7 )
                                                                                                                                                                                     => ( subset @ X4 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(assume_negation,[status(cth)],[subsetTrans]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_104]),foundationAx]),wellorderingAx]),c_0_105]),c_0_106]),c_0_107]),c_0_108]),c_0_109]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_110]),setext]),emptyI]),noeltsimpempty]),c_0_111]),c_0_112]),c_0_113]),c_0_114]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_115]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_116]),c_0_117]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_118]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_119]),c_0_120]),c_0_121]),inCongP]),in__Cong]),c_0_122]),c_0_123]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_124]),c_0_125]),c_0_126]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl])])]),c_0_127]) ).

thf(c_0_129,negated_conjecture,
    ! [X554: $i,X555: $i,X557: $i,X558: $i,X559: $i,X560: $i,X561: $i,X562: $i,X563: $i,X564: $i,X565: $i,X567: $i,X568: $i,X570: $i,X571: $i,X572: $i,X573: $i,X574: $i,X576: $i,X577: $i > $i > $o,X578: $i,X580: $i,X583: $i,X585: $i,X586: $i,X587: $i,X588: $i,X590: $i,X591: $i > $o,X592: $i,X594: $i,X595: $i > $o,X596: $i,X597: $i,X598: $i > $o,X599: $i,X600: $i,X601: $i > $o,X602: $i,X603: $i > $o,X604: $i,X607: $i,X608: $o,X609: $i,X610: $i,X611: $o,X612: $i,X613: $i,X614: $i > $o,X615: $i,X618: $i,X619: $i,X622: $i,X624: $i,X626: $i,X627: $i > $o,X628: $i,X629: $i,X631: $i,X632: $i > $o,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X641: $i,X642: $i,X643: $i,X644: $o,X645: $i,X646: $i,X647: $i,X648: $i,X649: $i,X650: $i,X652: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i,X660: $i,X661: $i,X662: $o,X664: $i,X665: $i,X666: $i > $o,X667: $i,X670: $i,X671: $i,X672: $i,X674: $i,X675: $i,X676: $i,X677: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $i,X686: $i,X687: $i,X688: $i,X689: $i,X690: $i > $o,X691: $i,X692: $i > $o,X693: $i,X694: $i,X695: $i > $o,X696: $i,X698: $i,X699: $i > $o,X701: $i,X702: $i,X703: $i > $o,X705: $i,X706: $i,X707: $i > $o,X708: $i,X710: $o,X711: $o,X712: $i,X713: $i > $o,X715: $i,X716: $i,X717: $i > $o,X718: $i,X720: $i > $o,X721: $i,X724: $i,X725: $i > $o,X726: $i,X730: $i,X731: $i > $o,X732: $i,X735: $i,X736: $i,X737: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $i,X743: $i,X744: $i > $o,X745: $i,X747: $i,X748: $i,X749: $i > $o,X750: $i > $o,X753: $i,X756: $i,X757: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i > $o,X770: $i,X772: $i,X773: $i,X774: $i > $o,X775: $i > $o,X778: $i,X780: $i,X782: $i,X783: $i,X784: $i > $o,X785: $i > $o,X788: $i,X789: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X554 @ X555 ) @ X554 )
        | ~ ( in @ ( esk1_2 @ X554 @ X555 ) @ X555 )
        | ( X554 = X555 ) )
      & ( ( in @ ( esk1_2 @ X554 @ X555 ) @ X554 )
        | ( in @ ( esk1_2 @ X554 @ X555 ) @ X555 )
        | ( X554 = X555 ) )
      & ~ ( in @ X557 @ emptyset )
      & ( ~ ( in @ X560 @ ( setadjoin @ X558 @ X559 ) )
        | ( X560 = X558 )
        | ( in @ X560 @ X559 ) )
      & ( ( X560 != X558 )
        | ( in @ X560 @ ( setadjoin @ X558 @ X559 ) ) )
      & ( ~ ( in @ X560 @ X559 )
        | ( in @ X560 @ ( setadjoin @ X558 @ X559 ) ) )
      & ( ~ ( in @ X562 @ ( powerset @ X561 ) )
        | ~ ( in @ X563 @ X562 )
        | ( in @ X563 @ X561 ) )
      & ( ( in @ ( esk2_2 @ X564 @ X565 ) @ X565 )
        | ( in @ X565 @ ( powerset @ X564 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X564 @ X565 ) @ X564 )
        | ( in @ X565 @ ( powerset @ X564 ) ) )
      & ( ( in @ X568 @ ( esk3_2 @ X567 @ X568 ) )
        | ~ ( in @ X568 @ ( setunion @ X567 ) ) )
      & ( ( in @ ( esk3_2 @ X567 @ X568 ) @ X567 )
        | ~ ( in @ X568 @ ( setunion @ X567 ) ) )
      & ( ~ ( in @ X571 @ X572 )
        | ~ ( in @ X572 @ X570 )
        | ( in @ X571 @ ( setunion @ X570 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X573 @ omega )
        | ( in @ ( setadjoin @ X573 @ X573 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X574 ) @ omega )
        | ~ ( in @ emptyset @ X574 )
        | ~ ( in @ X576 @ omega )
        | ( in @ X576 @ X574 ) )
      & ( ( in @ ( esk4_1 @ X574 ) @ X574 )
        | ~ ( in @ emptyset @ X574 )
        | ~ ( in @ X576 @ omega )
        | ( in @ X576 @ X574 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X574 ) @ ( esk4_1 @ X574 ) ) @ X574 )
        | ~ ( in @ emptyset @ X574 )
        | ~ ( in @ X576 @ omega )
        | ( in @ X576 @ X574 ) )
      & ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
      & ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
      & ( ~ ( in @ X586 @ X578 )
        | ~ ( X577 @ X586 @ X585 )
        | ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
        | ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
      & ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ~ ( in @ X586 @ X578 )
        | ~ ( X577 @ X586 @ X585 )
        | ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X580
         != ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
        | ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X580
         != ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ~ ( in @ X586 @ X578 )
        | ~ ( X577 @ X586 @ X585 )
        | ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
        | ( X580
         != ( esk6_3 @ X577 @ X578 @ X580 ) )
        | ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
      & ( ( in @ ( esk9_1 @ X587 ) @ X587 )
        | ~ ( in @ X588 @ X587 ) )
      & ( ~ ( in @ X590 @ ( esk9_1 @ X587 ) )
        | ~ ( in @ X590 @ X587 )
        | ~ ( in @ X588 @ X587 ) )
      & epred1_0
      & ( ( X591 @ ( esk10_2 @ X591 @ X592 ) )
        | ~ ( X591 @ X592 )
        | ( X591 @ ( descr @ X591 ) ) )
      & ( ( X592
         != ( esk10_2 @ X591 @ X592 ) )
        | ~ ( X591 @ X592 )
        | ( X591 @ ( descr @ X591 ) ) )
      & ( ~ ( in @ X596 @ X594 )
        | ~ ( X595 @ X596 )
        | ( in @ X596 @ ( dsetconstr @ X594 @ X595 ) ) )
      & ( ~ ( in @ X599 @ ( dsetconstr @ X597 @ X598 ) )
        | ( in @ X599 @ X597 ) )
      & ( ~ ( in @ X602 @ ( dsetconstr @ X600 @ X601 ) )
        | ( X601 @ X602 ) )
      & ( ( X603 @ ( esk12_1 @ X603 ) )
        | ( X603 @ ( esk11_2 @ X603 @ X604 ) )
        | ~ ( X603 @ X604 ) )
      & ( ~ ( X603 @ X607 )
        | ( ( esk12_1 @ X603 )
          = X607 )
        | ( X603 @ ( esk11_2 @ X603 @ X604 ) )
        | ~ ( X603 @ X604 ) )
      & ( ( X603 @ ( esk12_1 @ X603 ) )
        | ( X604
         != ( esk11_2 @ X603 @ X604 ) )
        | ~ ( X603 @ X604 ) )
      & ( ~ ( X603 @ X607 )
        | ( ( esk12_1 @ X603 )
          = X607 )
        | ( X604
         != ( esk11_2 @ X603 @ X604 ) )
        | ~ ( X603 @ X604 ) )
      & ( ~ ( in @ X609 @ ( prop2set @ X608 ) )
        | X608 )
      & ( ~ ( in @ X610 @ emptyset )
        | X611 )
      & ( ~ ( in @ X612 @ emptyset )
        | ~ $true )
      & ~ ( in @ X613 @ emptyset )
      & ( ( X614 @ ( esk13_2 @ X614 @ X615 ) )
        | ~ ( X614 @ X615 )
        | ( X614 @ ( esk14_1 @ X614 ) ) )
      & ( ( X615
         != ( esk13_2 @ X614 @ X615 ) )
        | ~ ( X614 @ X615 )
        | ( X614 @ ( esk14_1 @ X614 ) ) )
      & ( ( in @ ( esk16_2 @ X618 @ X619 ) @ X619 )
        | ( X618 = X619 )
        | ( in @ ( esk15_2 @ X618 @ X619 ) @ X618 ) )
      & ( ~ ( in @ ( esk16_2 @ X618 @ X619 ) @ X618 )
        | ( X618 = X619 )
        | ( in @ ( esk15_2 @ X618 @ X619 ) @ X618 ) )
      & ( ( in @ ( esk16_2 @ X618 @ X619 ) @ X619 )
        | ( X618 = X619 )
        | ~ ( in @ ( esk15_2 @ X618 @ X619 ) @ X619 ) )
      & ( ~ ( in @ ( esk16_2 @ X618 @ X619 ) @ X618 )
        | ( X618 = X619 )
        | ~ ( in @ ( esk15_2 @ X618 @ X619 ) @ X619 ) )
      & ( ( in @ ( esk17_1 @ X622 ) @ X622 )
        | ( X622 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X624 ) @ X624 )
        | ( X624 = emptyset ) )
      & ( ~ ( in @ X628 @ ( dsetconstr @ X626 @ X627 ) )
        | ( X627 @ X628 )
        | ~ ( in @ X628 @ X626 ) )
      & ( ~ ( X627 @ X628 )
        | ( in @ X628 @ ( dsetconstr @ X626 @ X627 ) )
        | ~ ( in @ X628 @ X626 ) )
      & ( ( X629 = emptyset )
        | ( in @ ( esk19_1 @ X629 ) @ X629 ) )
      & ( ~ ( in @ X633 @ X631 )
        | ~ ( X632 @ X633 )
        | ( ( dsetconstr @ X631 @ X632 )
         != emptyset ) )
      & ( ~ ( in @ X635 @ X634 )
        | ( X634 != emptyset ) )
      & ( in @ X636 @ ( setadjoin @ X636 @ X637 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X640 @ X639 )
        | ( in @ X640 @ ( setadjoin @ X638 @ X639 ) ) )
      & ( ( in @ X643 @ X642 )
        | X644
        | ( X643 = X641 )
        | ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
      & ( ~ X644
        | X644
        | ( X643 = X641 )
        | ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
      & ( ( in @ X643 @ X642 )
        | X644
        | ~ X644
        | ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
      & ( ~ X644
        | X644
        | ~ X644
        | ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
      & ( ~ ( in @ X647 @ ( setadjoin @ X645 @ X646 ) )
        | ( X647 = X645 )
        | ( in @ X647 @ X646 ) )
      & ( ( dsetconstr @ X648
          @ ^ [Z0: $i] : $true )
        = X648 )
      & ( ( in @ ( esk20_2 @ X649 @ X650 ) @ X650 )
        | ( in @ X650 @ ( powerset @ X649 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X649 @ X650 ) @ X649 )
        | ( in @ X650 @ ( powerset @ X649 ) ) )
      & ( in @ emptyset @ ( powerset @ X652 ) )
      & ( in @ emptyset @ ( powerset @ X653 ) )
      & ( ~ ( in @ X655 @ ( powerset @ X654 ) )
        | ~ ( in @ X656 @ X655 )
        | ( in @ X656 @ X654 ) )
      & ( ~ ( in @ X658 @ X659 )
        | ~ ( in @ X659 @ X657 )
        | ( in @ X658 @ ( setunion @ X657 ) ) )
      & ( ( in @ X661 @ ( esk21_3 @ X660 @ X661 @ X662 ) )
        | X662
        | ~ ( in @ X661 @ ( setunion @ X660 ) ) )
      & ( ( in @ ( esk21_3 @ X660 @ X661 @ X662 ) @ X660 )
        | X662
        | ~ ( in @ X661 @ ( setunion @ X660 ) ) )
      & ( ~ X662
        | X662
        | ~ ( in @ X661 @ ( setunion @ X660 ) ) )
      & ( ~ ( in @ X665 @ X664 )
        | ( in @ X665 @ ( powerset @ ( setunion @ X664 ) ) ) )
      & ( ~ ( X666 @ X670 )
        | ( X670
          = ( esk23_1 @ X666 ) )
        | ( X666 @ ( esk22_2 @ X666 @ X667 ) )
        | ~ ( X666 @ X667 ) )
      & ( ( X671
         != ( esk23_1 @ X666 ) )
        | ( X666 @ X671 )
        | ( X666 @ ( esk22_2 @ X666 @ X667 ) )
        | ~ ( X666 @ X667 ) )
      & ( ~ ( X666 @ X670 )
        | ( X670
          = ( esk23_1 @ X666 ) )
        | ( X667
         != ( esk22_2 @ X666 @ X667 ) )
        | ~ ( X666 @ X667 ) )
      & ( ( X671
         != ( esk23_1 @ X666 ) )
        | ( X666 @ X671 )
        | ( X667
         != ( esk22_2 @ X666 @ X667 ) )
        | ~ ( X666 @ X667 ) )
      & ( ( in @ ( esk24_1 @ X672 ) @ X672 )
        | ( X672 = emptyset ) )
      & ( $true
        | ( X672 = emptyset ) )
      & ( ~ ( in @ X674 @ ( setadjoin @ X675 @ emptyset ) )
        | ( X674 = X675 ) )
      & ( ( X676 = X677 )
        | ~ ( in @ X677 @ ( setadjoin @ X676 @ emptyset ) ) )
      & ( ( X678 != X679 )
        | ( in @ X678 @ ( setadjoin @ X679 @ emptyset ) ) )
      & ( ~ ( in @ X680 @ ( setadjoin @ X681 @ emptyset ) )
        | ( in @ X681 @ ( setadjoin @ X680 @ emptyset ) ) )
      & ( ~ ( in @ X684 @ ( setadjoin @ X682 @ ( setadjoin @ X683 @ emptyset ) ) )
        | ( X684 = X682 )
        | ( X684 = X683 ) )
      & ( in @ X685 @ ( setadjoin @ X685 @ ( setadjoin @ X686 @ emptyset ) ) )
      & ( in @ X688 @ ( setadjoin @ X687 @ ( setadjoin @ X688 @ emptyset ) ) )
      & ( ~ ( in @ X691 @ X689 )
        | ~ ( X690 @ X691 )
        | ( ( dsetconstr @ X689 @ X690 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X693 @ emptyset )
        | ( X692 @ X693 ) )
      & ( ( in @ ( esk25_2 @ X694 @ X695 ) @ X694 )
        | ~ ( in @ X696 @ X694 )
        | ( X695 @ X696 ) )
      & ( ~ ( X695 @ ( esk25_2 @ X694 @ X695 ) )
        | ~ ( in @ X696 @ X694 )
        | ( X695 @ X696 ) )
      & ( ( in @ ( esk26_2 @ X698 @ X699 ) @ X698 )
        | ~ ( in @ X701 @ X698 )
        | ~ ( X699 @ X701 ) )
      & ( ( X699 @ ( esk26_2 @ X698 @ X699 ) )
        | ~ ( in @ X701 @ X698 )
        | ~ ( X699 @ X701 ) )
      & ( ( in @ ( esk27_2 @ X702 @ X703 ) @ X702 )
        | ~ ( in @ X705 @ X702 )
        | ~ ( X703 @ X705 ) )
      & ( ( X703 @ ( esk27_2 @ X702 @ X703 ) )
        | ~ ( in @ X705 @ X702 )
        | ~ ( X703 @ X705 ) )
      & ( ( in @ ( esk28_2 @ X706 @ X707 ) @ X706 )
        | ~ ( in @ X708 @ X706 )
        | ( X707 @ X708 ) )
      & ( ~ ( X707 @ ( esk28_2 @ X706 @ X707 ) )
        | ~ ( in @ X708 @ X706 )
        | ( X707 @ X708 ) )
      & ( ~ X710
        | ( in @ emptyset @ ( prop2set @ X710 ) ) )
      & ( ~ X711
        | ( set2prop @ ( prop2set @ X711 ) ) )
      & ( ( in @ ( esk29_2 @ X712 @ X713 ) @ X712 )
        | ~ ( in @ X715 @ X712 )
        | ~ ( X713 @ X715 ) )
      & ( ( X713 @ ( esk29_2 @ X712 @ X713 ) )
        | ~ ( in @ X715 @ X712 )
        | ~ ( X713 @ X715 ) )
      & ( ( in @ ( esk30_2 @ X716 @ X717 ) @ X716 )
        | ~ ( in @ X718 @ X716 )
        | ( X717 @ X718 ) )
      & ( ~ ( X717 @ ( esk30_2 @ X716 @ X717 ) )
        | ~ ( in @ X718 @ X716 )
        | ( X717 @ X718 ) )
      & ( ( X720 @ ( esk32_1 @ X720 ) )
        | ( X720 @ ( esk31_2 @ X720 @ X721 ) )
        | ~ ( X720 @ X721 ) )
      & ( ~ ( X720 @ X724 )
        | ( ( esk32_1 @ X720 )
          = X724 )
        | ( X720 @ ( esk31_2 @ X720 @ X721 ) )
        | ~ ( X720 @ X721 ) )
      & ( ( X720 @ ( esk32_1 @ X720 ) )
        | ( X721
         != ( esk31_2 @ X720 @ X721 ) )
        | ~ ( X720 @ X721 ) )
      & ( ~ ( X720 @ X724 )
        | ( ( esk32_1 @ X720 )
          = X724 )
        | ( X721
         != ( esk31_2 @ X720 @ X721 ) )
        | ~ ( X720 @ X721 ) )
      & ( ( X725 @ ( esk35_1 @ X725 ) )
        | ( X725 @ ( esk33_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ~ ( X725 @ X730 )
        | ( ( esk35_1 @ X725 )
          = X730 )
        | ( X725 @ ( esk33_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ( X725 @ ( esk35_1 @ X725 ) )
        | ( X725 @ ( esk34_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ~ ( X725 @ X730 )
        | ( ( esk35_1 @ X725 )
          = X730 )
        | ( X725 @ ( esk34_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ( X725 @ ( esk35_1 @ X725 ) )
        | ( ( esk33_1 @ X725 )
         != ( esk34_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ~ ( X725 @ X730 )
        | ( ( esk35_1 @ X725 )
          = X730 )
        | ( ( esk33_1 @ X725 )
         != ( esk34_1 @ X725 ) )
        | ~ ( X725 @ X726 ) )
      & ( ( X731 @ ( esk37_1 @ X731 ) )
        | ~ ( X731 @ ( esk36_2 @ X731 @ X732 ) )
        | ( ( esk36_2 @ X731 @ X732 )
         != X732 ) )
      & ( ~ ( X731 @ X735 )
        | ( ( esk37_1 @ X731 )
          = X735 )
        | ~ ( X731 @ ( esk36_2 @ X731 @ X732 ) )
        | ( ( esk36_2 @ X731 @ X732 )
         != X732 ) )
      & ( ( X731 @ ( esk37_1 @ X731 ) )
        | ( X731 @ ( esk36_2 @ X731 @ X732 ) )
        | ( ( esk36_2 @ X731 @ X732 )
          = X732 ) )
      & ( ~ ( X731 @ X735 )
        | ( ( esk37_1 @ X731 )
          = X735 )
        | ( X731 @ ( esk36_2 @ X731 @ X732 ) )
        | ( ( esk36_2 @ X731 @ X732 )
          = X732 ) )
      & ( ( X736 != X737 )
        | ( X738 != X739 )
        | ~ ( in @ X738 @ X736 )
        | ( in @ X739 @ X737 ) )
      & ( ~ ( in @ X742 @ X740 )
        | ( in @ X743 @ X741 )
        | ( X742 != X743 )
        | ( X740 != X741 ) )
      & ( ~ ( in @ X743 @ X741 )
        | ( in @ X742 @ X740 )
        | ( X742 != X743 )
        | ( X740 != X741 ) )
      & ( ( X744 @ ( esk38_2 @ X744 @ X745 ) )
        | ~ ( X744 @ X745 )
        | ~ ( X744 @ X747 )
        | ~ ( X744 @ X748 )
        | ( X747 = X748 ) )
      & ( ( X745
         != ( esk38_2 @ X744 @ X745 ) )
        | ~ ( X744 @ X745 )
        | ~ ( X744 @ X747 )
        | ~ ( X744 @ X748 )
        | ( X747 = X748 ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( ( esk39_2 @ X749 @ X750 )
          = ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X750 @ X756 )
        | ( ( esk42_2 @ X749 @ X750 )
          = X756 )
        | ( X753
         != ( esk41_3 @ X749 @ X750 @ X753 ) )
        | ~ ( X749 @ X753 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( ~ ( X749 @ X760 )
        | ( ( esk44_2 @ X749 @ X750 )
          = X760 )
        | ( X757
         != ( esk43_3 @ X749 @ X750 @ X757 ) )
        | ~ ( X750 @ X757 )
        | ( X749 @ ( esk39_2 @ X749 @ X750 ) )
        | ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
      & ( emptyset = emptyset )
      & ( ( X761 != X762 )
        | ( X763 != X764 )
        | ( ( setadjoin @ X761 @ X763 )
          = ( setadjoin @ X762 @ X764 ) ) )
      & ( ( X765 != X766 )
        | ( ( powerset @ X765 )
          = ( powerset @ X766 ) ) )
      & ( ( X767 != X768 )
        | ( ( setunion @ X767 )
          = ( setunion @ X768 ) ) )
      & ( omega = omega )
      & ( ( X769 @ ( esk45_2 @ X769 @ X770 ) )
        | ~ ( X769 @ X770 )
        | ~ ( X769 @ X772 )
        | ~ ( X769 @ X773 )
        | ( X772 = X773 ) )
      & ( ( X770
         != ( esk45_2 @ X769 @ X770 ) )
        | ~ ( X769 @ X770 )
        | ~ ( X769 @ X772 )
        | ~ ( X769 @ X773 )
        | ( X772 = X773 ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( ( esk46_2 @ X774 @ X775 )
          = ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( ( esk46_2 @ X774 @ X775 )
          = ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( ( esk46_2 @ X774 @ X775 )
          = ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( ( esk46_2 @ X774 @ X775 )
          = ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( X780
         != ( esk49_3 @ X774 @ X775 @ X780 ) )
        | ~ ( X775 @ X780 )
        | ( ( descr @ X774 )
          = ( descr @ X775 ) )
        | ( X778
         != ( esk48_3 @ X774 @ X775 @ X778 ) )
        | ~ ( X774 @ X778 )
        | ( X774 @ ( esk46_2 @ X774 @ X775 ) )
        | ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
      & ( ( in @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) @ X782 )
        | ( ( dsetconstr @ X782 @ X784 )
          = ( dsetconstr @ X783 @ X785 ) )
        | ( X782 != X783 ) )
      & ( ( in @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) @ X783 )
        | ( ( dsetconstr @ X782 @ X784 )
          = ( dsetconstr @ X783 @ X785 ) )
        | ( X782 != X783 ) )
      & ( ( ( esk50_4 @ X782 @ X783 @ X784 @ X785 )
          = ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
        | ( ( dsetconstr @ X782 @ X784 )
          = ( dsetconstr @ X783 @ X785 ) )
        | ( X782 != X783 ) )
      & ( ~ ( X784 @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) )
        | ~ ( X785 @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
        | ( ( dsetconstr @ X782 @ X784 )
          = ( dsetconstr @ X783 @ X785 ) )
        | ( X782 != X783 ) )
      & ( ( X784 @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) )
        | ( X785 @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
        | ( ( dsetconstr @ X782 @ X784 )
          = ( dsetconstr @ X783 @ X785 ) )
        | ( X782 != X783 ) )
      & ( ( in @ ( esk52_2 @ X788 @ X789 ) @ X788 )
        | ( subset @ X788 @ X789 ) )
      & ( ~ ( in @ ( esk52_2 @ X788 @ X789 ) @ X789 )
        | ( subset @ X788 @ X789 ) )
      & ( ( X791 != X792 )
        | ( subset @ X792 @ X791 ) )
      & ( ( X793 != X794 )
        | ( subset @ X793 @ X794 ) )
      & ( ( in @ ( esk53_2 @ X795 @ X796 ) @ X795 )
        | ( subset @ X795 @ X796 ) )
      & ( ~ ( in @ ( esk53_2 @ X795 @ X796 ) @ X796 )
        | ( subset @ X795 @ X796 ) )
      & ( subset @ emptyset @ X798 )
      & ( ~ ( subset @ X799 @ X800 )
        | ~ ( in @ X801 @ X799 )
        | ( in @ X801 @ X800 ) )
      & ( ~ ( subset @ X802 @ X803 )
        | ( in @ X804 @ X803 )
        | ~ ( in @ X804 @ X802 ) )
      & ( ~ ( in @ X807 @ X805 )
        | ( in @ X807 @ X806 )
        | ~ ( subset @ X805 @ X806 ) )
      & ( ( subset @ X808 @ X809 )
        | ( X808 != X809 ) )
      & ( ~ ( in @ X812 @ X810 )
        | ( in @ X812 @ X811 )
        | ( X810 != X811 ) )
      & ( subset @ X813 @ X813 )
      & ( subset @ esk54_0 @ esk55_0 )
      & ( subset @ esk55_0 @ esk56_0 )
      & ~ ( subset @ esk54_0 @ esk56_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_128])])])])])])]) ).

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

thf(c_0_131,negated_conjecture,
    subset @ esk55_0 @ esk56_0,
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

thf(c_0_132,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( subset @ X2 @ X3 )
      | ~ ( in @ ( esk52_2 @ X2 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

thf(c_0_133,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk56_0 )
      | ~ ( in @ X2 @ esk55_0 ) ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

thf(c_0_134,negated_conjecture,
    subset @ esk54_0 @ esk55_0,
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

thf(c_0_135,negated_conjecture,
    ! [X2: $i] :
      ( ( subset @ X2 @ esk56_0 )
      | ~ ( in @ ( esk52_2 @ X2 @ esk56_0 ) @ esk55_0 ) ),
    inference(spm,[status(thm)],[c_0_132,c_0_133]) ).

thf(c_0_136,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk55_0 )
      | ~ ( in @ X2 @ esk54_0 ) ),
    inference(spm,[status(thm)],[c_0_130,c_0_134]) ).

thf(c_0_137,negated_conjecture,
    ! [X2: $i] :
      ( ( subset @ X2 @ esk56_0 )
      | ~ ( in @ ( esk52_2 @ X2 @ esk56_0 ) @ esk54_0 ) ),
    inference(spm,[status(thm)],[c_0_135,c_0_136]) ).

thf(c_0_138,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ ( esk52_2 @ X2 @ X3 ) @ X2 )
      | ( subset @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

thf(c_0_139,negated_conjecture,
    ~ ( subset @ esk54_0 @ esk56_0 ),
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

thf(c_0_140,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09  % Problem    : SEU570^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Sun May 19 17:28:22 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.37  Running higher-order theorem proving
% 0.14/0.37  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42  # Version: 3.1.0-ho
% 0.14/0.42  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42  # Starting ehoh_best3_rw with 300s (1) cores
% 0.14/0.42  # Starting almost_fo_3 with 300s (1) cores
% 0.14/0.42  # Starting new_ho_13 with 300s (1) cores
% 0.14/0.42  # ehoh_best3_avoidappvar with pid 28695 completed with status 0
% 0.14/0.42  # Result found by ehoh_best3_avoidappvar
% 0.14/0.42  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42  # No SInE strategy applied
% 0.14/0.42  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42  # Starting ho_unfolding_3 with 811s (1) cores
% 0.14/0.42  # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.14/0.42  # Starting lpo1_def_fix with 136s (1) cores
% 0.14/0.42  # Starting full_lambda_2 with 136s (1) cores
% 0.14/0.42  # Starting new_ho_14 with 136s (1) cores
% 0.14/0.42  # ehoh_best3_avoidappvar with pid 28702 completed with status 0
% 0.14/0.42  # Result found by ehoh_best3_avoidappvar
% 0.14/0.42  # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42  # No SInE strategy applied
% 0.14/0.42  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42  # Starting ho_unfolding_3 with 811s (1) cores
% 0.14/0.42  # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.14/0.42  # Preprocessing time       : 0.003 s
% 0.14/0.42  # Presaturation interreduction done
% 0.14/0.42  
% 0.14/0.42  # Proof found!
% 0.14/0.42  # SZS status Theorem
% 0.14/0.42  # SZS output start CNFRefutation
% See solution above
% 0.14/0.42  # Parsed axioms                        : 190
% 0.14/0.42  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.42  # Initial clauses                      : 300
% 0.14/0.42  # Removed in clause preprocessing      : 115
% 0.14/0.42  # Initial clauses in saturation        : 185
% 0.14/0.42  # Processed clauses                    : 295
% 0.14/0.42  # ...of these trivial                  : 7
% 0.14/0.42  # ...subsumed                          : 42
% 0.14/0.42  # ...remaining for further processing  : 246
% 0.14/0.42  # Other redundant clauses eliminated   : 13
% 0.14/0.42  # Clauses deleted for lack of memory   : 0
% 0.14/0.42  # Backward-subsumed                    : 0
% 0.14/0.42  # Backward-rewritten                   : 5
% 0.14/0.42  # Generated clauses                    : 278
% 0.14/0.42  # ...of the previous two non-redundant : 245
% 0.14/0.42  # ...aggressively subsumed             : 0
% 0.14/0.42  # Contextual simplify-reflections      : 0
% 0.14/0.42  # Paramodulations                      : 254
% 0.14/0.42  # Factorizations                       : 2
% 0.14/0.42  # NegExts                              : 0
% 0.14/0.42  # Equation resolutions                 : 13
% 0.14/0.42  # Disequality decompositions           : 0
% 0.14/0.42  # Total rewrite steps                  : 52
% 0.14/0.42  # ...of those cached                   : 29
% 0.14/0.42  # Propositional unsat checks           : 0
% 0.14/0.42  #    Propositional check models        : 0
% 0.14/0.42  #    Propositional check unsatisfiable : 0
% 0.14/0.42  #    Propositional clauses             : 0
% 0.14/0.42  #    Propositional clauses after purity: 0
% 0.14/0.42  #    Propositional unsat core size     : 0
% 0.14/0.42  #    Propositional preprocessing time  : 0.000
% 0.14/0.42  #    Propositional encoding time       : 0.000
% 0.14/0.42  #    Propositional solver time         : 0.000
% 0.14/0.42  #    Success case prop preproc time    : 0.000
% 0.14/0.42  #    Success case prop encoding time   : 0.000
% 0.14/0.42  #    Success case prop solver time     : 0.000
% 0.14/0.42  # Current number of processed clauses  : 67
% 0.14/0.42  #    Positive orientable unit clauses  : 20
% 0.14/0.42  #    Positive unorientable unit clauses: 0
% 0.14/0.42  #    Negative unit clauses             : 2
% 0.14/0.42  #    Non-unit-clauses                  : 45
% 0.14/0.42  # Current number of unprocessed clauses: 288
% 0.14/0.42  # ...number of literals in the above   : 897
% 0.14/0.42  # Current number of archived formulas  : 0
% 0.14/0.42  # Current number of archived clauses   : 166
% 0.14/0.42  # Clause-clause subsumption calls (NU) : 5522
% 0.14/0.42  # Rec. Clause-clause subsumption calls : 1417
% 0.14/0.42  # Non-unit clause-clause subsumptions  : 30
% 0.14/0.42  # Unit Clause-clause subsumption calls : 40
% 0.14/0.42  # Rewrite failures with RHS unbound    : 0
% 0.14/0.42  # BW rewrite match attempts            : 17
% 0.14/0.42  # BW rewrite match successes           : 4
% 0.14/0.42  # Condensation attempts                : 0
% 0.14/0.42  # Condensation successes               : 0
% 0.14/0.42  # Termbank termtop insertions          : 43332
% 0.14/0.42  # Search garbage collected termcells   : 9904
% 0.14/0.42  
% 0.14/0.42  # -------------------------------------------------
% 0.14/0.42  # User time                : 0.032 s
% 0.14/0.42  # System time              : 0.007 s
% 0.14/0.42  # Total time               : 0.039 s
% 0.14/0.42  # Maximum resident set size: 4304 pages
% 0.14/0.42  
% 0.14/0.42  # -------------------------------------------------
% 0.14/0.42  # User time                : 0.103 s
% 0.14/0.42  # System time              : 0.020 s
% 0.14/0.42  # Total time               : 0.123 s
% 0.14/0.42  # Maximum resident set size: 1924 pages
% 0.14/0.42  % E---3.1 exiting
% 0.14/0.42  % E exiting
%------------------------------------------------------------------------------