TSTP Solution File: SEU623^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU623^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 03:28:38 EDT 2024

% Result   : Theorem 0.57s 0.59s
% Output   : CNFRefutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  339
% Syntax   : Number of formulae    :  371 (   5 unt; 199 typ;   0 def)
%            Number of atoms       : 1428 ( 201 equ;   0 cnn)
%            Maximal formula atoms :  418 (   8 avg)
%            Number of connectives : 4788 ( 362   ~; 331   |; 262   &;2936   @)
%                                         ( 197 <=>; 700  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  529 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  251 ( 251   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  202 ( 199 usr; 147 con; 0-4 aty)
%            Number of variables   : 1193 (  59   ^1069   !;  65   ?;1193   :)

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

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

thf(decl_24,type,
    setextAx: $o ).

thf(decl_25,type,
    emptyset: $i ).

thf(decl_26,type,
    emptysetAx: $o ).

thf(decl_27,type,
    setadjoin: $i > $i > $i ).

thf(decl_28,type,
    setadjoinAx: $o ).

thf(decl_29,type,
    powerset: $i > $i ).

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

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

thf(decl_32,type,
    setunionAx: $o ).

thf(decl_33,type,
    omega: $i ).

thf(decl_34,type,
    omega0Ax: $o ).

thf(decl_35,type,
    omegaSAx: $o ).

thf(decl_36,type,
    omegaIndAx: $o ).

thf(decl_37,type,
    replAx: $o ).

thf(decl_38,type,
    foundationAx: $o ).

thf(decl_39,type,
    wellorderingAx: $o ).

thf(decl_40,type,
    descr: ( $i > $o ) > $i ).

thf(decl_41,type,
    descrp: $o ).

thf(decl_42,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(decl_43,type,
    dsetconstrI: $o ).

thf(decl_44,type,
    dsetconstrEL: $o ).

thf(decl_45,type,
    dsetconstrER: $o ).

thf(decl_46,type,
    exuE1: $o ).

thf(decl_47,type,
    prop2set: $o > $i ).

thf(decl_48,type,
    prop2setE: $o ).

thf(decl_49,type,
    emptysetE: $o ).

thf(decl_50,type,
    emptysetimpfalse: $o ).

thf(decl_51,type,
    notinemptyset: $o ).

thf(decl_52,type,
    exuE3e: $o ).

thf(decl_53,type,
    setext: $o ).

thf(decl_54,type,
    emptyI: $o ).

thf(decl_55,type,
    noeltsimpempty: $o ).

thf(decl_56,type,
    setbeta: $o ).

thf(decl_57,type,
    nonempty: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_135,type,
    binunion: $i > $i > $i ).

thf(decl_136,type,
    binunionIL: $o ).

thf(decl_137,type,
    upairset2IR: $o ).

thf(decl_138,type,
    binunionIR: $o ).

thf(decl_139,type,
    binunionEcases: $o ).

thf(decl_140,type,
    binunionE: $o ).

thf(decl_141,type,
    binunionLsub: $o ).

thf(decl_142,type,
    binunionRsub: $o ).

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

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

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

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

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

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

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

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

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

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

thf(decl_153,type,
    binintersectSubset4: $o ).

thf(decl_154,type,
    binintersectSubset1: $o ).

thf(decl_155,type,
    bs114d: $o ).

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

thf(decl_158,type,
    setminusI: $o ).

thf(decl_159,type,
    setminusEL: $o ).

thf(decl_160,type,
    setminusER: $o ).

thf(decl_161,type,
    setminusSubset2: $o ).

thf(decl_162,type,
    setminusERneg: $o ).

thf(decl_163,type,
    setminusELneg: $o ).

thf(decl_164,type,
    setminusILneg: $o ).

thf(decl_165,type,
    setminusIRneg: $o ).

thf(decl_166,type,
    setminusLsub: $o ).

thf(decl_167,type,
    setminusSubset1: $o ).

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

thf(decl_169,type,
    symdiffE: $o ).

thf(decl_170,type,
    symdiffI1: $o ).

thf(decl_171,type,
    symdiffI2: $o ).

thf(decl_172,type,
    symdiffIneg1: $o ).

thf(decl_173,type,
    symdiffIneg2: $o ).

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

thf(decl_175,type,
    secondinupair: $o ).

thf(decl_176,type,
    setukpairIL: $o ).

thf(decl_177,type,
    setukpairIR: $o ).

thf(decl_178,type,
    kpairiskpair: $o ).

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

thf(decl_180,type,
    kpairp: $o ).

thf(decl_182,type,
    singletonsubset: $o ).

thf(decl_183,type,
    singletoninpowerset: $o ).

thf(decl_184,type,
    epred1_0: $o ).

thf(decl_185,type,
    esk1_2: $i > $i > $i ).

thf(decl_186,type,
    esk2_2: $i > $i > $i ).

thf(decl_187,type,
    esk3_2: $i > $i > $i ).

thf(decl_188,type,
    esk4_1: $i > $i ).

thf(decl_189,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_190,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_191,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_192,type,
    esk8_1: $i > $i ).

thf(decl_193,type,
    esk9_1: ( $i > $o ) > $i ).

thf(decl_194,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_195,type,
    esk11_2: $i > $i > $i ).

thf(decl_196,type,
    esk12_2: $i > $i > $i ).

thf(decl_197,type,
    esk13_1: $i > $i ).

thf(decl_198,type,
    esk14_1: $i > $i ).

thf(decl_199,type,
    esk15_1: $i > $i ).

thf(decl_200,type,
    esk16_2: $i > $i > $i ).

thf(decl_201,type,
    esk17_3: $i > $i > $o > $i ).

thf(decl_202,type,
    esk18_1: ( $i > $o ) > $i ).

thf(decl_203,type,
    esk19_1: $i > $i ).

thf(decl_204,type,
    esk20_2: $i > ( $i > $o ) > $i ).

thf(decl_205,type,
    esk21_2: $i > ( $i > $o ) > $i ).

thf(decl_206,type,
    esk22_2: $i > ( $i > $o ) > $i ).

thf(decl_207,type,
    esk23_2: $i > ( $i > $o ) > $i ).

thf(decl_208,type,
    esk24_2: $i > ( $i > $o ) > $i ).

thf(decl_209,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_210,type,
    esk26_2: ( $i > $o ) > $i > $i ).

thf(decl_211,type,
    esk27_1: ( $i > $o ) > $i ).

thf(decl_212,type,
    esk28_1: ( $i > $o ) > $i ).

thf(decl_213,type,
    esk29_2: ( $i > $o ) > $i > $i ).

thf(decl_214,type,
    esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_215,type,
    esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_216,type,
    esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_217,type,
    esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_218,type,
    esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_219,type,
    esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_220,type,
    esk36_2: $i > $i > $i ).

thf(decl_221,type,
    esk37_2: $i > $i > $i ).

thf(decl_222,type,
    esk38_2: $i > $i > $i ).

thf(decl_223,type,
    esk39_0: $i ).

thf(decl_224,type,
    esk40_0: $i ).

thf(decl_225,type,
    esk41_0: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(singletoninpowunion,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( uniqinunit
                                                                                         => ( notinsingleton
                                                                                           => ( eqinunit
                                                                                             => ( singletonsswitch
                                                                                               => ( upairsetE
                                                                                                 => ( upairsetIL
                                                                                                   => ( upairsetIR
                                                                                                     => ( emptyE1
                                                                                                       => ( vacuousDall
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( emptyset__Cong
                                                                                                                                         => ( setadjoin__Cong
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( emptysetsubset
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( setadjoinSub
                                                                                                                                                                                 => ( setadjoinSub2
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( subsetemptysetimpeq
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( upairset2IR
                                                                                                                                                                                                         => ( binunionIR
                                                                                                                                                                                                           => ( binunionEcases
                                                                                                                                                                                                             => ( binunionE
                                                                                                                                                                                                               => ( binunionLsub
                                                                                                                                                                                                                 => ( binunionRsub
                                                                                                                                                                                                                   => ( binintersectI
                                                                                                                                                                                                                     => ( binintersectSubset5
                                                                                                                                                                                                                       => ( binintersectEL
                                                                                                                                                                                                                         => ( binintersectLsub
                                                                                                                                                                                                                           => ( binintersectSubset2
                                                                                                                                                                                                                             => ( binintersectSubset3
                                                                                                                                                                                                                               => ( binintersectER
                                                                                                                                                                                                                                 => ( disjointsetsI1
                                                                                                                                                                                                                                   => ( binintersectRsub
                                                                                                                                                                                                                                     => ( binintersectSubset4
                                                                                                                                                                                                                                       => ( binintersectSubset1
                                                                                                                                                                                                                                         => ( bs114d
                                                                                                                                                                                                                                           => ( setminusI
                                                                                                                                                                                                                                             => ( setminusEL
                                                                                                                                                                                                                                               => ( setminusER
                                                                                                                                                                                                                                                 => ( setminusSubset2
                                                                                                                                                                                                                                                   => ( setminusERneg
                                                                                                                                                                                                                                                     => ( setminusELneg
                                                                                                                                                                                                                                                       => ( setminusILneg
                                                                                                                                                                                                                                                         => ( setminusIRneg
                                                                                                                                                                                                                                                           => ( setminusLsub
                                                                                                                                                                                                                                                             => ( setminusSubset1
                                                                                                                                                                                                                                                               => ( symdiffE
                                                                                                                                                                                                                                                                 => ( symdiffI1
                                                                                                                                                                                                                                                                   => ( symdiffI2
                                                                                                                                                                                                                                                                     => ( symdiffIneg1
                                                                                                                                                                                                                                                                       => ( symdiffIneg2
                                                                                                                                                                                                                                                                         => ( secondinupair
                                                                                                                                                                                                                                                                           => ( setukpairIL
                                                                                                                                                                                                                                                                             => ( setukpairIR
                                                                                                                                                                                                                                                                               => ( kpairiskpair
                                                                                                                                                                                                                                                                                 => ( kpairp
                                                                                                                                                                                                                                                                                   => ( singletonsubset
                                                                                                                                                                                                                                                                                     => ( singletoninpowerset
                                                                                                                                                                                                                                                                                       => ! [X4: $i,X5: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(symdiffI2,axiom,
    ( symdiffI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).

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

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

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

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

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

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

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

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

thf(binintersectSubset4,axiom,
    ( binintersectSubset4
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( ( binintersect @ X4 @ X5 )
          = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).

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

thf(binintersectSubset1,axiom,
    ( binintersectSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X4 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).

thf(bs114d,axiom,
    ( bs114d
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
        = ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).

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

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

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

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

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

thf(setminusSubset2,axiom,
    ( setminusSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( setminus @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).

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

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

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

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

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

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

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

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

thf(setminusSubset1,axiom,
    ( setminusSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( setminus @ X4 @ X5 )
          = emptyset )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).

thf(symdiffE,axiom,
    ( symdiffE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
       => ! [X20: $o] :
            ( ( ( in @ X2 @ X4 )
             => ( ~ ( in @ X2 @ X5 )
               => X20 ) )
           => ( ( ~ ( in @ X2 @ X4 )
               => ( ( in @ X2 @ X5 )
                 => X20 ) )
             => X20 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).

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

thf(symdiffI1,axiom,
    ( symdiffI1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).

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

thf(symdiffIneg1,axiom,
    ( symdiffIneg1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).

thf(symdiffIneg2,axiom,
    ( symdiffIneg2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_0_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,plain,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ ( powerset @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[sepInPowerset]) ).

thf(c_0_150,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_151,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_152,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_153,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_154,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_155,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_156,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_157,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_158,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_159,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_160,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_161,plain,
    ( epred1_0
  <=> ! [X418: $i] :
      ? [X419: $i] :
        ( ! [X420: $i] :
            ( ( in @ X420 @ X419 )
           => ! [X421: $i] :
                ( ( in @ X421 @ X420 )
               => ( in @ X421 @ X418 ) ) )
        & ! [X422: $i,X423: $i] :
            ( ( ( in @ X422 @ X418 )
              & ( in @ X423 @ X418 ) )
           => ( ! [X424: $i] :
                  ( ( in @ X424 @ X419 )
                 => ( ( in @ X422 @ X424 )
                  <=> ( in @ X423 @ X424 ) ) )
             => ( X422 = X423 ) ) )
        & ! [X425: $i,X426: $i] :
            ( ( ( in @ X425 @ X419 )
              & ( in @ X426 @ X419 ) )
           => ( ! [X427: $i] :
                  ( ( in @ X427 @ X425 )
                 => ( in @ X427 @ X426 ) )
              | ! [X428: $i] :
                  ( ( in @ X428 @ X426 )
                 => ( in @ X428 @ X425 ) ) ) )
        & ! [X429: $i] :
            ( ( ! [X430: $i] :
                  ( ( in @ X430 @ X429 )
                 => ( in @ X430 @ X418 ) )
              & ? [X431: $i] : ( in @ X431 @ X429 ) )
           => ? [X432: $i,X433: $i] :
                ( ( in @ X432 @ X419 )
                & ( in @ X433 @ X429 )
                & ~ ? [X434: $i] :
                      ( ( in @ X434 @ X432 )
                      & ( in @ X434 @ X429 ) )
                & ! [X435: $i] :
                    ( ( in @ X435 @ X419 )
                   => ( ! [X436: $i] :
                          ( ( in @ X436 @ X435 )
                         => ( in @ X436 @ X432 ) )
                      | ( in @ X433 @ X435 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_162,negated_conjecture,
    ~ ( ! [X391: $i,X392: $i] :
          ( ! [X393: $i] :
              ( ( in @ X393 @ X391 )
            <=> ( in @ X393 @ X392 ) )
         => ( X391 = X392 ) )
     => ( ! [X394: $i] :
            ~ ( in @ X394 @ emptyset )
       => ( ! [X395: $i,X396: $i,X397: $i] :
              ( ( in @ X397 @ ( setadjoin @ X395 @ X396 ) )
            <=> ( ( X397 = X395 )
                | ( in @ X397 @ X396 ) ) )
         => ( ! [X398: $i,X399: $i] :
                ( ( in @ X399 @ ( powerset @ X398 ) )
              <=> ! [X400: $i] :
                    ( ( in @ X400 @ X399 )
                   => ( in @ X400 @ X398 ) ) )
           => ( ! [X401: $i,X402: $i] :
                  ( ( in @ X402 @ ( setunion @ X401 ) )
                <=> ? [X403: $i] :
                      ( ( in @ X402 @ X403 )
                      & ( in @ X403 @ X401 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X404: $i] :
                      ( ( in @ X404 @ omega )
                     => ( in @ ( setadjoin @ X404 @ X404 ) @ omega ) )
                 => ( ! [X405: $i] :
                        ( ( ( in @ emptyset @ X405 )
                          & ! [X406: $i] :
                              ( ( ( in @ X406 @ omega )
                                & ( in @ X406 @ X405 ) )
                             => ( in @ ( setadjoin @ X406 @ X406 ) @ X405 ) ) )
                       => ! [X407: $i] :
                            ( ( in @ X407 @ omega )
                           => ( in @ X407 @ X405 ) ) )
                   => ( ! [X408: $i > $i > $o,X409: $i] :
                          ( ! [X410: $i] :
                              ( ( in @ X410 @ X409 )
                             => ( exu @ ( X408 @ X410 ) ) )
                         => ? [X411: $i] :
                            ! [X412: $i] :
                              ( ( in @ X412 @ X411 )
                            <=> ? [X413: $i] :
                                  ( ( in @ X413 @ X409 )
                                  & ( X408 @ X413 @ X412 ) ) ) )
                     => ( ! [X414: $i] :
                            ( ? [X415: $i] : ( in @ X415 @ X414 )
                           => ? [X416: $i] :
                                ( ( in @ X416 @ X414 )
                                & ~ ? [X417: $i] :
                                      ( ( in @ X417 @ X416 )
                                      & ( in @ X417 @ X414 ) ) ) )
                       => ( epred1_0
                         => ( ! [X437: $i > $o] :
                                ( ( exu @ X437 )
                               => ( X437
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X437 @ Z0 ) ) ) )
                           => ( ! [X438: $i,X439: $i > $o,X440: $i] :
                                  ( ( in @ X440 @ X438 )
                                 => ( ( X439 @ X440 )
                                   => ( in @ X440 @ ( dsetconstr @ X438 @ X439 ) ) ) )
                             => ( ! [X441: $i,X442: $i > $o,X443: $i] :
                                    ( ( in @ X443 @ ( dsetconstr @ X441 @ X442 ) )
                                   => ( in @ X443 @ X441 ) )
                               => ( ! [X444: $i,X445: $i > $o,X446: $i] :
                                      ( ( in @ X446 @ ( dsetconstr @ X444 @ X445 ) )
                                     => ( X445 @ X446 ) )
                                 => ( ! [X447: $i > $o] :
                                        ( ( exu @ X447 )
                                       => ? [X448: $i] :
                                            ( ( X447 @ X448 )
                                            & ! [X449: $i] :
                                                ( ( X447 @ X449 )
                                               => ( X448 = X449 ) ) ) )
                                   => ( ! [X450: $o,X451: $i] :
                                          ( ( in @ X451 @ ( prop2set @ X450 ) )
                                         => X450 )
                                     => ( ! [X452: $i] :
                                            ( ( in @ X452 @ emptyset )
                                           => ! [X453: $o] : X453 )
                                       => ( ! [X454: $i] :
                                              ( ( in @ X454 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X455: $i] :
                                                ~ ( in @ X455 @ emptyset )
                                           => ( ! [X456: $i > $o] :
                                                  ( ( exu @ X456 )
                                                 => ? [X457: $i] : ( X456 @ X457 ) )
                                             => ( ! [X458: $i,X459: $i] :
                                                    ( ! [X460: $i] :
                                                        ( ( in @ X460 @ X458 )
                                                       => ( in @ X460 @ X459 ) )
                                                   => ( ! [X461: $i] :
                                                          ( ( in @ X461 @ X459 )
                                                         => ( in @ X461 @ X458 ) )
                                                     => ( X458 = X459 ) ) )
                                               => ( ! [X462: $i] :
                                                      ( ! [X463: $i] :
                                                          ~ ( in @ X463 @ X462 )
                                                     => ( X462 = emptyset ) )
                                                 => ( ! [X464: $i] :
                                                        ( ! [X465: $i] :
                                                            ~ ( in @ X465 @ X464 )
                                                       => ( X464 = emptyset ) )
                                                   => ( ! [X466: $i,X467: $i > $o,X468: $i] :
                                                          ( ( in @ X468 @ X466 )
                                                         => ( ( in @ X468 @ ( dsetconstr @ X466 @ X467 ) )
                                                          <=> ( X467 @ X468 ) ) )
                                                     => ( ! [X469: $i] :
                                                            ( ( nonempty @ X469 )
                                                           => ? [X470: $i] : ( in @ X470 @ X469 ) )
                                                       => ( ! [X471: $i,X472: $i > $o,X473: $i] :
                                                              ( ( in @ X473 @ X471 )
                                                             => ( ( X472 @ X473 )
                                                               => ( nonempty @ ( dsetconstr @ X471 @ X472 ) ) ) )
                                                         => ( ! [X474: $i] :
                                                                ( ? [X475: $i] : ( in @ X475 @ X474 )
                                                               => ( nonempty @ X474 ) )
                                                           => ( ! [X476: $i,X477: $i] : ( in @ X476 @ ( setadjoin @ X476 @ X477 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X478: $i,X479: $i,X480: $i] :
                                                                      ( ( in @ X480 @ X479 )
                                                                     => ( in @ X480 @ ( setadjoin @ X478 @ X479 ) ) )
                                                                 => ( ! [X481: $i,X482: $i,X483: $i] :
                                                                        ( ( in @ X483 @ ( setadjoin @ X481 @ X482 ) )
                                                                       => ! [X484: $o] :
                                                                            ( ( ( X483 = X481 )
                                                                             => X484 )
                                                                           => ( ( ( in @ X483 @ X482 )
                                                                               => X484 )
                                                                             => X484 ) ) )
                                                                   => ( ! [X485: $i,X486: $i,X487: $i] :
                                                                          ( ( in @ X487 @ ( setadjoin @ X485 @ X486 ) )
                                                                         => ( ( X487 = X485 )
                                                                            | ( in @ X487 @ X486 ) ) )
                                                                     => ( ! [X488: $i] :
                                                                            ( ( dsetconstr @ X488
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X488 )
                                                                       => ( ! [X489: $i,X490: $i] :
                                                                              ( ! [X491: $i] :
                                                                                  ( ( in @ X491 @ X490 )
                                                                                 => ( in @ X491 @ X489 ) )
                                                                             => ( in @ X490 @ ( powerset @ X489 ) ) )
                                                                         => ( ! [X492: $i] : ( in @ emptyset @ ( powerset @ X492 ) )
                                                                           => ( ! [X493: $i] : ( in @ emptyset @ ( powerset @ X493 ) )
                                                                             => ( ! [X494: $i,X495: $i,X496: $i] :
                                                                                    ( ( in @ X495 @ ( powerset @ X494 ) )
                                                                                   => ( ( in @ X496 @ X495 )
                                                                                     => ( in @ X496 @ X494 ) ) )
                                                                               => ( ! [X497: $i,X498: $i,X499: $i] :
                                                                                      ( ( in @ X498 @ X499 )
                                                                                     => ( ( in @ X499 @ X497 )
                                                                                       => ( in @ X498 @ ( setunion @ X497 ) ) ) )
                                                                                 => ( ! [X500: $i,X501: $i] :
                                                                                        ( ( in @ X501 @ ( setunion @ X500 ) )
                                                                                       => ! [X502: $o] :
                                                                                            ( ! [X503: $i] :
                                                                                                ( ( in @ X501 @ X503 )
                                                                                               => ( ( in @ X503 @ X500 )
                                                                                                 => X502 ) )
                                                                                           => X502 ) )
                                                                                   => ( ! [X504: $i,X505: $i] :
                                                                                          ( ( in @ X505 @ X504 )
                                                                                         => ( in @ X505 @ ( powerset @ ( setunion @ X504 ) ) ) )
                                                                                     => ( ! [X506: $i > $o] :
                                                                                            ( ( exu @ X506 )
                                                                                           => ? [X507: $i] :
                                                                                              ! [X508: $i] :
                                                                                                ( ( X506 @ X508 )
                                                                                              <=> ( X508 = X507 ) ) )
                                                                                       => ( ! [X509: $i] :
                                                                                              ( ( nonempty @ X509 )
                                                                                             => ? [X510: $i] :
                                                                                                  ( ( in @ X510 @ X509 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X511: $i,X512: $i] :
                                                                                                ( ( in @ X511 @ ( setadjoin @ X512 @ emptyset ) )
                                                                                               => ( X511 = X512 ) )
                                                                                           => ( ! [X513: $i,X514: $i] :
                                                                                                  ( ( X513 != X514 )
                                                                                                 => ~ ( in @ X514 @ ( setadjoin @ X513 @ emptyset ) ) )
                                                                                             => ( ! [X515: $i,X516: $i] :
                                                                                                    ( ( X515 = X516 )
                                                                                                   => ( in @ X515 @ ( setadjoin @ X516 @ emptyset ) ) )
                                                                                               => ( ! [X517: $i,X518: $i] :
                                                                                                      ( ( in @ X517 @ ( setadjoin @ X518 @ emptyset ) )
                                                                                                     => ( in @ X518 @ ( setadjoin @ X517 @ emptyset ) ) )
                                                                                                 => ( ! [X519: $i,X520: $i,X521: $i] :
                                                                                                        ( ( in @ X521 @ ( setadjoin @ X519 @ ( setadjoin @ X520 @ emptyset ) ) )
                                                                                                       => ( ( X521 = X519 )
                                                                                                          | ( X521 = X520 ) ) )
                                                                                                   => ( ! [X522: $i,X523: $i] : ( in @ X522 @ ( setadjoin @ X522 @ ( setadjoin @ X523 @ emptyset ) ) )
                                                                                                     => ( ! [X524: $i,X525: $i] : ( in @ X525 @ ( setadjoin @ X524 @ ( setadjoin @ X525 @ emptyset ) ) )
                                                                                                       => ( ! [X526: $i,X527: $i > $o] :
                                                                                                              ( ? [X528: $i] :
                                                                                                                  ( ( in @ X528 @ X526 )
                                                                                                                  & ( X527 @ X528 ) )
                                                                                                             => ( ( ( dsetconstr @ X526 @ X527 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X529: $i > $o,X530: $i] :
                                                                                                                ( ( in @ X530 @ emptyset )
                                                                                                               => ( X529 @ X530 ) )
                                                                                                           => ( ! [X531: $i,X532: $i > $o] :
                                                                                                                  ( ~ ! [X533: $i] :
                                                                                                                        ( ( in @ X533 @ X531 )
                                                                                                                       => ( X532 @ X533 ) )
                                                                                                                 => ? [X534: $i] :
                                                                                                                      ( ( in @ X534 @ X531 )
                                                                                                                      & ~ ( X532 @ X534 ) ) )
                                                                                                             => ( ! [X535: $i,X536: $i > $o] :
                                                                                                                    ( ! [X537: $i] :
                                                                                                                        ( ( in @ X537 @ X535 )
                                                                                                                       => ~ ( X536 @ X537 ) )
                                                                                                                   => ~ ? [X538: $i] :
                                                                                                                          ( ( in @ X538 @ X535 )
                                                                                                                          & ( X536 @ X538 ) ) )
                                                                                                               => ( ! [X539: $i,X540: $i > $o] :
                                                                                                                      ( ~ ? [X541: $i] :
                                                                                                                            ( ( in @ X541 @ X539 )
                                                                                                                            & ( X540 @ X541 ) )
                                                                                                                     => ! [X542: $i] :
                                                                                                                          ( ( in @ X542 @ X539 )
                                                                                                                         => ~ ( X540 @ X542 ) ) )
                                                                                                                 => ( ! [X543: $i,X544: $i > $o] :
                                                                                                                        ( ? [X545: $i] :
                                                                                                                            ( ( in @ X545 @ X543 )
                                                                                                                            & ~ ( X544 @ X545 ) )
                                                                                                                       => ~ ! [X546: $i] :
                                                                                                                              ( ( in @ X546 @ X543 )
                                                                                                                             => ( X544 @ X546 ) ) )
                                                                                                                   => ( ! [X547: $o] :
                                                                                                                          ( X547
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X547 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X548: $i,X549: $i > $o] :
                                                                                                                              ( ~ ? [X550: $i] :
                                                                                                                                    ( ( in @ X550 @ X548 )
                                                                                                                                    & ( X549 @ X550 ) )
                                                                                                                             => ! [X551: $i] :
                                                                                                                                  ( ( in @ X551 @ X548 )
                                                                                                                                 => ~ ( X549 @ X551 ) ) )
                                                                                                                         => ( ! [X552: $i,X553: $i > $o] :
                                                                                                                                ( ~ ! [X554: $i] :
                                                                                                                                      ( ( in @ X554 @ X552 )
                                                                                                                                     => ( X553 @ X554 ) )
                                                                                                                               => ? [X555: $i] :
                                                                                                                                    ( ( in @ X555 @ X552 )
                                                                                                                                    & ~ ( X553 @ X555 ) ) )
                                                                                                                           => ( ! [X556: $i > $o] :
                                                                                                                                  ( ? [X557: $i] :
                                                                                                                                      ( ( X556 @ X557 )
                                                                                                                                      & ! [X558: $i] :
                                                                                                                                          ( ( X556 @ X558 )
                                                                                                                                         => ( X557 = X558 ) ) )
                                                                                                                                 => ( exu @ X556 ) )
                                                                                                                             => ( ! [X559: $i > $o] :
                                                                                                                                    ( ? [X560: $i] : ( X559 @ X560 )
                                                                                                                                   => ( ! [X561: $i,X562: $i] :
                                                                                                                                          ( ( X559 @ X561 )
                                                                                                                                         => ( ( X559 @ X562 )
                                                                                                                                           => ( X561 = X562 ) ) )
                                                                                                                                     => ( exu @ X559 ) ) )
                                                                                                                               => ( ! [X563: $i > $o] :
                                                                                                                                      ( ? [X564: $i] :
                                                                                                                                        ! [X565: $i] :
                                                                                                                                          ( ( X563 @ X565 )
                                                                                                                                        <=> ( X565 = X564 ) )
                                                                                                                                     => ( exu @ X563 ) )
                                                                                                                                 => ( ! [X566: $i,X567: $i] :
                                                                                                                                        ( ( X566 = X567 )
                                                                                                                                       => ! [X568: $i,X569: $i] :
                                                                                                                                            ( ( X568 = X569 )
                                                                                                                                           => ( ( in @ X568 @ X566 )
                                                                                                                                             => ( in @ X569 @ X567 ) ) ) )
                                                                                                                                   => ( ! [X570: $i,X571: $i] :
                                                                                                                                          ( ( X570 = X571 )
                                                                                                                                         => ! [X572: $i,X573: $i] :
                                                                                                                                              ( ( X572 = X573 )
                                                                                                                                             => ( ( in @ X572 @ X570 )
                                                                                                                                              <=> ( in @ X573 @ X571 ) ) ) )
                                                                                                                                     => ( ! [X574: $i > $o] :
                                                                                                                                            ( ( exu @ X574 )
                                                                                                                                           => ! [X575: $i,X576: $i] :
                                                                                                                                                ( ( X574 @ X575 )
                                                                                                                                               => ( ( X574 @ X576 )
                                                                                                                                                 => ( X575 = X576 ) ) ) )
                                                                                                                                       => ( ! [X577: $i > $o,X578: $i > $o] :
                                                                                                                                              ( ! [X579: $i,X580: $i] :
                                                                                                                                                  ( ( X579 = X580 )
                                                                                                                                                 => ( ( X577 @ X579 )
                                                                                                                                                  <=> ( X578 @ X580 ) ) )
                                                                                                                                             => ( ( exu @ X577 )
                                                                                                                                              <=> ( exu @ X578 ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X581: $i,X582: $i] :
                                                                                                                                                  ( ( X581 = X582 )
                                                                                                                                                 => ! [X583: $i,X584: $i] :
                                                                                                                                                      ( ( X583 = X584 )
                                                                                                                                                     => ( ( setadjoin @ X581 @ X583 )
                                                                                                                                                        = ( setadjoin @ X582 @ X584 ) ) ) )
                                                                                                                                             => ( ! [X585: $i,X586: $i] :
                                                                                                                                                    ( ( X585 = X586 )
                                                                                                                                                   => ( ( powerset @ X585 )
                                                                                                                                                      = ( powerset @ X586 ) ) )
                                                                                                                                               => ( ! [X587: $i,X588: $i] :
                                                                                                                                                      ( ( X587 = X588 )
                                                                                                                                                     => ( ( setunion @ X587 )
                                                                                                                                                        = ( setunion @ X588 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X589: $i > $o] :
                                                                                                                                                          ( ( exu @ X589 )
                                                                                                                                                         => ! [X590: $i,X591: $i] :
                                                                                                                                                              ( ( X589 @ X590 )
                                                                                                                                                             => ( ( X589 @ X591 )
                                                                                                                                                               => ( X590 = X591 ) ) ) )
                                                                                                                                                     => ( ! [X592: $i > $o,X593: $i > $o] :
                                                                                                                                                            ( ! [X594: $i,X595: $i] :
                                                                                                                                                                ( ( X594 = X595 )
                                                                                                                                                               => ( ( X592 @ X594 )
                                                                                                                                                                <=> ( X593 @ X595 ) ) )
                                                                                                                                                           => ( ( exu @ X592 )
                                                                                                                                                             => ( ( exu @ X593 )
                                                                                                                                                               => ( ( descr @ X592 )
                                                                                                                                                                  = ( descr @ X593 ) ) ) ) )
                                                                                                                                                       => ( ! [X596: $i,X597: $i] :
                                                                                                                                                              ( ( X596 = X597 )
                                                                                                                                                             => ! [X598: $i > $o,X599: $i > $o] :
                                                                                                                                                                  ( ! [X600: $i] :
                                                                                                                                                                      ( ( in @ X600 @ X596 )
                                                                                                                                                                     => ! [X601: $i] :
                                                                                                                                                                          ( ( in @ X601 @ X597 )
                                                                                                                                                                         => ( ( X600 = X601 )
                                                                                                                                                                           => ( ( X598 @ X600 )
                                                                                                                                                                            <=> ( X599 @ X601 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X596 @ X598 )
                                                                                                                                                                    = ( dsetconstr @ X597 @ X599 ) ) ) )
                                                                                                                                                         => ( ! [X602: $i,X603: $i] :
                                                                                                                                                                ( ! [X604: $i] :
                                                                                                                                                                    ( ( in @ X604 @ X602 )
                                                                                                                                                                   => ( in @ X604 @ X603 ) )
                                                                                                                                                               => ( subset @ X602 @ X603 ) )
                                                                                                                                                           => ( ! [X605: $i,X606: $i] :
                                                                                                                                                                  ( ( X605 = X606 )
                                                                                                                                                                 => ( subset @ X606 @ X605 ) )
                                                                                                                                                             => ( ! [X607: $i,X608: $i] :
                                                                                                                                                                    ( ( X607 = X608 )
                                                                                                                                                                   => ( subset @ X607 @ X608 ) )
                                                                                                                                                               => ( ! [X609: $i,X610: $i] :
                                                                                                                                                                      ( ! [X611: $i] :
                                                                                                                                                                          ( ( in @ X611 @ X609 )
                                                                                                                                                                         => ( in @ X611 @ X610 ) )
                                                                                                                                                                     => ( subset @ X609 @ X610 ) )
                                                                                                                                                                 => ( ! [X612: $i] : ( subset @ emptyset @ X612 )
                                                                                                                                                                   => ( ! [X613: $i,X614: $i,X615: $i] :
                                                                                                                                                                          ( ( subset @ X613 @ X614 )
                                                                                                                                                                         => ( ( in @ X615 @ X613 )
                                                                                                                                                                           => ( in @ X615 @ X614 ) ) )
                                                                                                                                                                     => ( ! [X616: $i,X617: $i,X618: $i] :
                                                                                                                                                                            ( ( subset @ X616 @ X617 )
                                                                                                                                                                           => ( ~ ( in @ X618 @ X617 )
                                                                                                                                                                             => ~ ( in @ X618 @ X616 ) ) )
                                                                                                                                                                       => ( ! [X619: $i,X620: $i,X621: $i] :
                                                                                                                                                                              ( ( in @ X621 @ X619 )
                                                                                                                                                                             => ( ~ ( in @ X621 @ X620 )
                                                                                                                                                                               => ~ ( subset @ X619 @ X620 ) ) )
                                                                                                                                                                         => ( ! [X622: $i,X623: $i] :
                                                                                                                                                                                ( ~ ( subset @ X622 @ X623 )
                                                                                                                                                                               => ( X622 != X623 ) )
                                                                                                                                                                           => ( ! [X624: $i,X625: $i,X626: $i] :
                                                                                                                                                                                  ( ( in @ X626 @ X624 )
                                                                                                                                                                                 => ( ~ ( in @ X626 @ X625 )
                                                                                                                                                                                   => ( X624 != X625 ) ) )
                                                                                                                                                                             => ( ! [X627: $i] : ( subset @ X627 @ X627 )
                                                                                                                                                                               => ( ! [X628: $i,X629: $i,X630: $i] :
                                                                                                                                                                                      ( ( subset @ X628 @ X629 )
                                                                                                                                                                                     => ( ( subset @ X629 @ X630 )
                                                                                                                                                                                       => ( subset @ X628 @ X630 ) ) )
                                                                                                                                                                                 => ( ! [X631: $i,X632: $i] : ( subset @ X632 @ ( setadjoin @ X631 @ X632 ) )
                                                                                                                                                                                   => ( ! [X633: $i,X634: $i,X635: $i] :
                                                                                                                                                                                          ( ( subset @ X633 @ X635 )
                                                                                                                                                                                         => ( subset @ X633 @ ( setadjoin @ X634 @ X635 ) ) )
                                                                                                                                                                                     => ( ! [X636: $i,X637: $i] :
                                                                                                                                                                                            ( ( subset @ X636 @ X637 )
                                                                                                                                                                                           => ( in @ X636 @ ( powerset @ X637 ) ) )
                                                                                                                                                                                       => ( ! [X638: $i,X639: $i] :
                                                                                                                                                                                              ( ( subset @ X638 @ X639 )
                                                                                                                                                                                             => ( ( subset @ X639 @ X638 )
                                                                                                                                                                                               => ( X638 = X639 ) ) )
                                                                                                                                                                                         => ( ! [X640: $i] :
                                                                                                                                                                                                ( ( subset @ X640 @ emptyset )
                                                                                                                                                                                               => ( X640 = emptyset ) )
                                                                                                                                                                                           => ( ! [X641: $i,X642: $i] :
                                                                                                                                                                                                  ( ( subset @ X642 @ X641 )
                                                                                                                                                                                                 => ( in @ X642 @ ( powerset @ X641 ) ) )
                                                                                                                                                                                             => ( ! [X643: $i,X644: $i] :
                                                                                                                                                                                                    ( ( in @ X644 @ ( powerset @ X643 ) )
                                                                                                                                                                                                   => ( subset @ X644 @ X643 ) )
                                                                                                                                                                                               => ( ! [X645: $i] : ( in @ X645 @ ( powerset @ X645 ) )
                                                                                                                                                                                                 => ( ! [X646: $i,X647: $i] :
                                                                                                                                                                                                        ( ( subset @ X646 @ X647 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X646 ) @ ( powerset @ X647 ) ) )
                                                                                                                                                                                                   => ( ! [X648: $i,X649: $i > $o] : ( in @ ( dsetconstr @ X648 @ X649 ) @ ( powerset @ X648 ) )
                                                                                                                                                                                                     => ( ! [X650: $i,X651: $i > $o] : ( subset @ ( dsetconstr @ X650 @ X651 ) @ X650 )
                                                                                                                                                                                                       => ( ! [X652: $i,X653: $i,X654: $i] :
                                                                                                                                                                                                              ( ( in @ X654 @ X652 )
                                                                                                                                                                                                             => ( in @ X654 @ ( binunion @ X652 @ X653 ) ) )
                                                                                                                                                                                                         => ( ! [X655: $i,X656: $i] : ( in @ X656 @ ( setadjoin @ X655 @ ( setadjoin @ X656 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X657: $i,X658: $i,X659: $i] :
                                                                                                                                                                                                                  ( ( in @ X659 @ X658 )
                                                                                                                                                                                                                 => ( in @ X659 @ ( binunion @ X657 @ X658 ) ) )
                                                                                                                                                                                                             => ( ! [X660: $i,X661: $i,X662: $i,X663: $o] :
                                                                                                                                                                                                                    ( ( in @ X662 @ ( binunion @ X660 @ X661 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X662 @ X660 )
                                                                                                                                                                                                                       => X663 )
                                                                                                                                                                                                                     => ( ( ( in @ X662 @ X661 )
                                                                                                                                                                                                                         => X663 )
                                                                                                                                                                                                                       => X663 ) ) )
                                                                                                                                                                                                               => ( ! [X664: $i,X665: $i,X666: $i] :
                                                                                                                                                                                                                      ( ( in @ X666 @ ( binunion @ X664 @ X665 ) )
                                                                                                                                                                                                                     => ( ( in @ X666 @ X664 )
                                                                                                                                                                                                                        | ( in @ X666 @ X665 ) ) )
                                                                                                                                                                                                                 => ( ! [X667: $i,X668: $i] : ( subset @ X667 @ ( binunion @ X667 @ X668 ) )
                                                                                                                                                                                                                   => ( ! [X669: $i,X670: $i] : ( subset @ X670 @ ( binunion @ X669 @ X670 ) )
                                                                                                                                                                                                                     => ( ! [X671: $i,X672: $i,X673: $i] :
                                                                                                                                                                                                                            ( ( in @ X673 @ X671 )
                                                                                                                                                                                                                           => ( ( in @ X673 @ X672 )
                                                                                                                                                                                                                             => ( in @ X673 @ ( binintersect @ X671 @ X672 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X674: $i,X675: $i,X676: $i] :
                                                                                                                                                                                                                              ( ( subset @ X676 @ X674 )
                                                                                                                                                                                                                             => ( ( subset @ X676 @ X675 )
                                                                                                                                                                                                                               => ( subset @ X676 @ ( binintersect @ X674 @ X675 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X677: $i,X678: $i,X679: $i] :
                                                                                                                                                                                                                                ( ( in @ X679 @ ( binintersect @ X677 @ X678 ) )
                                                                                                                                                                                                                               => ( in @ X679 @ X677 ) )
                                                                                                                                                                                                                           => ( ! [X680: $i,X681: $i] : ( subset @ ( binintersect @ X680 @ X681 ) @ X680 )
                                                                                                                                                                                                                             => ( ! [X682: $i,X683: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X682 @ X683 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X682 @ X683 )
                                                                                                                                                                                                                                      = X682 ) )
                                                                                                                                                                                                                               => ( ! [X684: $i,X685: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X684 @ X685 )
                                                                                                                                                                                                                                        = X685 )
                                                                                                                                                                                                                                     => ( subset @ X685 @ X684 ) )
                                                                                                                                                                                                                                 => ( ! [X686: $i,X687: $i,X688: $i] :
                                                                                                                                                                                                                                        ( ( in @ X688 @ ( binintersect @ X686 @ X687 ) )
                                                                                                                                                                                                                                       => ( in @ X688 @ X687 ) )
                                                                                                                                                                                                                                   => ( ! [X689: $i,X690: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X691: $i] :
                                                                                                                                                                                                                                                ( ( in @ X691 @ X689 )
                                                                                                                                                                                                                                                & ( in @ X691 @ X690 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X689 @ X690 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X692: $i,X693: $i] : ( subset @ ( binintersect @ X692 @ X693 ) @ X693 )
                                                                                                                                                                                                                                       => ( ! [X694: $i,X695: $i] :
                                                                                                                                                                                                                                              ( ( subset @ X695 @ X694 )
                                                                                                                                                                                                                                             => ( ( binintersect @ X694 @ X695 )
                                                                                                                                                                                                                                                = X695 ) )
                                                                                                                                                                                                                                         => ( ! [X696: $i,X697: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ X696 @ X697 )
                                                                                                                                                                                                                                                  = X696 )
                                                                                                                                                                                                                                               => ( subset @ X696 @ X697 ) )
                                                                                                                                                                                                                                           => ( ! [X698: $i,X699: $i,X700: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ X698 @ ( binunion @ X699 @ X700 ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X698 @ X699 ) @ ( binintersect @ X698 @ X700 ) ) )
                                                                                                                                                                                                                                             => ( ! [X701: $i,X702: $i,X703: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X703 @ X701 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X703 @ X702 )
                                                                                                                                                                                                                                                     => ( in @ X703 @ ( setminus @ X701 @ X702 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X704: $i,X705: $i,X706: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X706 @ ( setminus @ X704 @ X705 ) )
                                                                                                                                                                                                                                                     => ( in @ X706 @ X704 ) )
                                                                                                                                                                                                                                                 => ( ! [X707: $i,X708: $i,X709: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X709 @ ( setminus @ X707 @ X708 ) )
                                                                                                                                                                                                                                                       => ~ ( in @ X709 @ X708 ) )
                                                                                                                                                                                                                                                   => ( ! [X710: $i,X711: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ X710 @ X711 )
                                                                                                                                                                                                                                                         => ( ( setminus @ X710 @ X711 )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [X712: $i,X713: $i,X714: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X714 @ ( setminus @ X712 @ X713 ) )
                                                                                                                                                                                                                                                           => ( ( in @ X714 @ X712 )
                                                                                                                                                                                                                                                             => ( in @ X714 @ X713 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X715: $i,X716: $i,X717: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ X717 @ ( setminus @ X715 @ X716 ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ X717 @ X716 )
                                                                                                                                                                                                                                                               => ~ ( in @ X717 @ X715 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X718: $i,X719: $i,X720: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ X720 @ X718 )
                                                                                                                                                                                                                                                               => ~ ( in @ X720 @ ( setminus @ X718 @ X719 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X721: $i,X722: $i,X723: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X723 @ X722 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X723 @ ( setminus @ X721 @ X722 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X724: $i,X725: $i] : ( subset @ ( setminus @ X724 @ X725 ) @ X724 )
                                                                                                                                                                                                                                                               => ( ! [X726: $i,X727: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ X726 @ X727 )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ X726 @ X727 ) )
                                                                                                                                                                                                                                                                 => ( ! [X728: $i,X729: $i,X730: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X730 @ ( symdiff @ X728 @ X729 ) )
                                                                                                                                                                                                                                                                       => ! [X731: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X730 @ X728 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X730 @ X729 )
                                                                                                                                                                                                                                                                               => X731 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X730 @ X728 )
                                                                                                                                                                                                                                                                               => ( ( in @ X730 @ X729 )
                                                                                                                                                                                                                                                                                 => X731 ) )
                                                                                                                                                                                                                                                                             => X731 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X732: $i,X733: $i,X734: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X734 @ X732 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X734 @ X733 )
                                                                                                                                                                                                                                                                           => ( in @ X734 @ ( symdiff @ X732 @ X733 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X735: $i,X736: $i,X737: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X737 @ X735 )
                                                                                                                                                                                                                                                                           => ( ( in @ X737 @ X736 )
                                                                                                                                                                                                                                                                             => ( in @ X737 @ ( symdiff @ X735 @ X736 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X738: $i,X739: $i,X740: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X740 @ X738 )
                                                                                                                                                                                                                                                                             => ( ( in @ X740 @ X739 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X740 @ ( symdiff @ X738 @ X739 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X741: $i,X742: $i,X743: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ X743 @ X741 )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ X743 @ X742 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X743 @ ( symdiff @ X741 @ X742 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X744: $i,X745: $i] : ( in @ X745 @ ( setadjoin @ X744 @ ( setadjoin @ X745 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X746: $i,X747: $i] : ( in @ X746 @ ( setunion @ ( setadjoin @ ( setadjoin @ X746 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X746 @ ( setadjoin @ X747 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X748: $i,X749: $i] : ( in @ X749 @ ( setunion @ ( setadjoin @ ( setadjoin @ X748 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X748 @ ( setadjoin @ X749 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X750: $i,X751: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X750 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X750 @ ( setadjoin @ X751 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X752: $i,X753: $i] : ( iskpair @ ( kpair @ X752 @ X753 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X754: $i,X755: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X755 @ X754 )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X755 @ emptyset ) @ X754 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X756: $i,X757: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X757 @ X756 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X757 @ emptyset ) @ ( powerset @ X756 ) ) )
                                                                                                                                                                                                                                                                                         => ! [X4: $i,X5: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[singletoninpowunion]),c_0_139]),symdiffI2]),singletoninpowerset]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),c_0_140]),binintersectER]),disjointsetsI1]),nonemptyImpWitness]),binintersectRsub]),binintersectSubset4]),uniqinunit]),binintersectSubset1]),bs114d]),notinsingleton]),setminusI]),setminusEL]),eqinunit]),setminusER]),setminusSubset2]),singletonsswitch]),setminusERneg]),setminusELneg]),upairsetE]),setminusILneg]),setminusIRneg]),upairsetIL]),setminusLsub]),setminusSubset1]),symdiffE]),upairsetIR]),symdiffI1]),powerset__Cong]),symdiffIneg1]),symdiffIneg2]),secondinupair]),vacuousDall]),setukpairIL]),setukpairIR]),quantDeMorgan1]),kpairiskpair]),kpairp]),quantDeMorgan2]),singletonsubset]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_141]),c_0_142]),c_0_143]),inCongP]),in__Cong]),c_0_144]),c_0_145]),emptyset__Cong]),setadjoin__Cong]),binintersectI]),binintersectSubset5]),binintersectEL]),setunion__Cong]),omega__Cong]),c_0_146]),c_0_147]),c_0_148]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetE]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_149]),c_0_150]),binunionIL]),upairset2IR]),binunionIR]),setunionI]),binunionEcases]),setunionE]),subPowSU]),binunionE]),binunionLsub]),binunionRsub]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_151]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_152]),nonemptyE1]),c_0_153]),noeltsimpempty]),emptyI]),setext]),c_0_154]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_155]),c_0_156]),c_0_157]),c_0_158]),c_0_159]),wellorderingAx]),foundationAx]),c_0_160]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_161]) ).

thf(c_0_163,negated_conjecture,
    ! [X758: $i,X759: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X771: $i,X772: $i,X774: $i,X775: $i,X776: $i,X777: $i,X778: $i,X780: $i,X781: $i > $i > $o,X782: $i,X785: $i,X787: $i,X788: $i,X789: $i,X790: $i,X792: $i,X793: $i > $o,X794: $i,X795: $i > $o,X796: $i,X797: $i,X798: $i > $o,X799: $i,X800: $i,X801: $i > $o,X802: $i,X803: $i > $o,X805: $i,X806: $o,X807: $i,X808: $i,X809: $o,X810: $i,X811: $i,X812: $i > $o,X814: $i,X815: $i,X818: $i,X820: $i,X822: $i,X823: $i > $o,X824: $i,X825: $i,X827: $i,X828: $i > $o,X829: $i,X830: $i,X831: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X838: $i,X839: $i,X840: $o,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $o,X860: $i,X861: $i,X862: $i > $o,X864: $i,X865: $i,X866: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i,X878: $i,X879: $i,X880: $i,X881: $i,X882: $i,X883: $i,X884: $i > $o,X885: $i,X886: $i > $o,X887: $i,X888: $i,X889: $i > $o,X890: $i,X892: $i,X893: $i > $o,X895: $i,X896: $i,X897: $i > $o,X899: $i,X900: $i,X901: $i > $o,X902: $i,X904: $o,X905: $i,X906: $i > $o,X908: $i,X909: $i,X910: $i > $o,X911: $i,X913: $i > $o,X914: $i,X916: $i > $o,X917: $i,X920: $i > $o,X921: $i,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i > $o,X932: $i,X933: $i,X934: $i > $o,X935: $i > $o,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $i,X944: $i,X945: $i,X946: $i > $o,X947: $i,X948: $i,X949: $i > $o,X950: $i > $o,X953: $i,X954: $i,X955: $i > $o,X956: $i > $o,X959: $i,X960: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i,X979: $i,X980: $i,X981: $i,X982: $i,X983: $i,X984: $i,X985: $i,X986: $i,X987: $i,X988: $i,X989: $i,X990: $i,X991: $i,X992: $i,X993: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $i > $o,X1007: $i,X1008: $i > $o,X1009: $i,X1010: $i,X1011: $i,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $o,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1025: $i,X1026: $i,X1027: $i,X1028: $i,X1029: $i,X1030: $i,X1031: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1053: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1059: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $o,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X758 @ X759 ) @ X758 )
        | ~ ( in @ ( esk1_2 @ X758 @ X759 ) @ X759 )
        | ( X758 = X759 ) )
      & ( ( in @ ( esk1_2 @ X758 @ X759 ) @ X758 )
        | ( in @ ( esk1_2 @ X758 @ X759 ) @ X759 )
        | ( X758 = X759 ) )
      & ~ ( in @ X761 @ emptyset )
      & ( ~ ( in @ X764 @ ( setadjoin @ X762 @ X763 ) )
        | ( X764 = X762 )
        | ( in @ X764 @ X763 ) )
      & ( ( X764 != X762 )
        | ( in @ X764 @ ( setadjoin @ X762 @ X763 ) ) )
      & ( ~ ( in @ X764 @ X763 )
        | ( in @ X764 @ ( setadjoin @ X762 @ X763 ) ) )
      & ( ~ ( in @ X766 @ ( powerset @ X765 ) )
        | ~ ( in @ X767 @ X766 )
        | ( in @ X767 @ X765 ) )
      & ( ( in @ ( esk2_2 @ X768 @ X769 ) @ X769 )
        | ( in @ X769 @ ( powerset @ X768 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X768 @ X769 ) @ X768 )
        | ( in @ X769 @ ( powerset @ X768 ) ) )
      & ( ( in @ X772 @ ( esk3_2 @ X771 @ X772 ) )
        | ~ ( in @ X772 @ ( setunion @ X771 ) ) )
      & ( ( in @ ( esk3_2 @ X771 @ X772 ) @ X771 )
        | ~ ( in @ X772 @ ( setunion @ X771 ) ) )
      & ( ~ ( in @ X775 @ X776 )
        | ~ ( in @ X776 @ X774 )
        | ( in @ X775 @ ( setunion @ X774 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X777 @ omega )
        | ( in @ ( setadjoin @ X777 @ X777 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X778 ) @ omega )
        | ~ ( in @ emptyset @ X778 )
        | ~ ( in @ X780 @ omega )
        | ( in @ X780 @ X778 ) )
      & ( ( in @ ( esk4_1 @ X778 ) @ X778 )
        | ~ ( in @ emptyset @ X778 )
        | ~ ( in @ X780 @ omega )
        | ( in @ X780 @ X778 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X778 ) @ ( esk4_1 @ X778 ) ) @ X778 )
        | ~ ( in @ emptyset @ X778 )
        | ~ ( in @ X780 @ omega )
        | ( in @ X780 @ X778 ) )
      & ( ( in @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X782 )
        | ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
        | ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
      & ( ( X781 @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X785 )
        | ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
        | ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
      & ( ~ ( in @ X788 @ X782 )
        | ~ ( X781 @ X788 @ X787 )
        | ( in @ X787 @ ( esk6_2 @ X781 @ X782 ) )
        | ( in @ ( esk5_2 @ X781 @ X782 ) @ X782 ) )
      & ( ( in @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X782 )
        | ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
        | ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
      & ( ( X781 @ ( esk7_3 @ X781 @ X782 @ X785 ) @ X785 )
        | ~ ( in @ X785 @ ( esk6_2 @ X781 @ X782 ) )
        | ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
      & ( ~ ( in @ X788 @ X782 )
        | ~ ( X781 @ X788 @ X787 )
        | ( in @ X787 @ ( esk6_2 @ X781 @ X782 ) )
        | ~ ( exu @ ( X781 @ ( esk5_2 @ X781 @ X782 ) ) ) )
      & ( ( in @ ( esk8_1 @ X789 ) @ X789 )
        | ~ ( in @ X790 @ X789 ) )
      & ( ~ ( in @ X792 @ ( esk8_1 @ X789 ) )
        | ~ ( in @ X792 @ X789 )
        | ~ ( in @ X790 @ X789 ) )
      & epred1_0
      & ( ~ ( exu @ X793 )
        | ( X793 @ ( descr @ X793 ) ) )
      & ( ~ ( in @ X796 @ X794 )
        | ~ ( X795 @ X796 )
        | ( in @ X796 @ ( dsetconstr @ X794 @ X795 ) ) )
      & ( ~ ( in @ X799 @ ( dsetconstr @ X797 @ X798 ) )
        | ( in @ X799 @ X797 ) )
      & ( ~ ( in @ X802 @ ( dsetconstr @ X800 @ X801 ) )
        | ( X801 @ X802 ) )
      & ( ( X803 @ ( esk9_1 @ X803 ) )
        | ~ ( exu @ X803 ) )
      & ( ~ ( X803 @ X805 )
        | ( ( esk9_1 @ X803 )
          = X805 )
        | ~ ( exu @ X803 ) )
      & ( ~ ( in @ X807 @ ( prop2set @ X806 ) )
        | X806 )
      & ( ~ ( in @ X808 @ emptyset )
        | X809 )
      & ( ~ ( in @ X810 @ emptyset )
        | ~ $true )
      & ~ ( in @ X811 @ emptyset )
      & ( ~ ( exu @ X812 )
        | ( X812 @ ( esk10_1 @ X812 ) ) )
      & ( ( in @ ( esk12_2 @ X814 @ X815 ) @ X815 )
        | ( X814 = X815 )
        | ( in @ ( esk11_2 @ X814 @ X815 ) @ X814 ) )
      & ( ~ ( in @ ( esk12_2 @ X814 @ X815 ) @ X814 )
        | ( X814 = X815 )
        | ( in @ ( esk11_2 @ X814 @ X815 ) @ X814 ) )
      & ( ( in @ ( esk12_2 @ X814 @ X815 ) @ X815 )
        | ( X814 = X815 )
        | ~ ( in @ ( esk11_2 @ X814 @ X815 ) @ X815 ) )
      & ( ~ ( in @ ( esk12_2 @ X814 @ X815 ) @ X814 )
        | ( X814 = X815 )
        | ~ ( in @ ( esk11_2 @ X814 @ X815 ) @ X815 ) )
      & ( ( in @ ( esk13_1 @ X818 ) @ X818 )
        | ( X818 = emptyset ) )
      & ( ( in @ ( esk14_1 @ X820 ) @ X820 )
        | ( X820 = emptyset ) )
      & ( ~ ( in @ X824 @ ( dsetconstr @ X822 @ X823 ) )
        | ( X823 @ X824 )
        | ~ ( in @ X824 @ X822 ) )
      & ( ~ ( X823 @ X824 )
        | ( in @ X824 @ ( dsetconstr @ X822 @ X823 ) )
        | ~ ( in @ X824 @ X822 ) )
      & ( ~ ( nonempty @ X825 )
        | ( in @ ( esk15_1 @ X825 ) @ X825 ) )
      & ( ~ ( in @ X829 @ X827 )
        | ~ ( X828 @ X829 )
        | ( nonempty @ ( dsetconstr @ X827 @ X828 ) ) )
      & ( ~ ( in @ X831 @ X830 )
        | ( nonempty @ X830 ) )
      & ( in @ X832 @ ( setadjoin @ X832 @ X833 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X836 @ X835 )
        | ( in @ X836 @ ( setadjoin @ X834 @ X835 ) ) )
      & ( ( in @ X839 @ X838 )
        | X840
        | ( X839 = X837 )
        | ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
      & ( ~ X840
        | X840
        | ( X839 = X837 )
        | ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
      & ( ( in @ X839 @ X838 )
        | X840
        | ~ X840
        | ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
      & ( ~ X840
        | X840
        | ~ X840
        | ~ ( in @ X839 @ ( setadjoin @ X837 @ X838 ) ) )
      & ( ~ ( in @ X843 @ ( setadjoin @ X841 @ X842 ) )
        | ( X843 = X841 )
        | ( in @ X843 @ X842 ) )
      & ( ( dsetconstr @ X844
          @ ^ [Z0: $i] : $true )
        = X844 )
      & ( ( in @ ( esk16_2 @ X845 @ X846 ) @ X846 )
        | ( in @ X846 @ ( powerset @ X845 ) ) )
      & ( ~ ( in @ ( esk16_2 @ X845 @ X846 ) @ X845 )
        | ( in @ X846 @ ( powerset @ X845 ) ) )
      & ( in @ emptyset @ ( powerset @ X848 ) )
      & ( in @ emptyset @ ( powerset @ X849 ) )
      & ( ~ ( in @ X851 @ ( powerset @ X850 ) )
        | ~ ( in @ X852 @ X851 )
        | ( in @ X852 @ X850 ) )
      & ( ~ ( in @ X854 @ X855 )
        | ~ ( in @ X855 @ X853 )
        | ( in @ X854 @ ( setunion @ X853 ) ) )
      & ( ( in @ X857 @ ( esk17_3 @ X856 @ X857 @ X858 ) )
        | X858
        | ~ ( in @ X857 @ ( setunion @ X856 ) ) )
      & ( ( in @ ( esk17_3 @ X856 @ X857 @ X858 ) @ X856 )
        | X858
        | ~ ( in @ X857 @ ( setunion @ X856 ) ) )
      & ( ~ X858
        | X858
        | ~ ( in @ X857 @ ( setunion @ X856 ) ) )
      & ( ~ ( in @ X861 @ X860 )
        | ( in @ X861 @ ( powerset @ ( setunion @ X860 ) ) ) )
      & ( ~ ( X862 @ X864 )
        | ( X864
          = ( esk18_1 @ X862 ) )
        | ~ ( exu @ X862 ) )
      & ( ( X865
         != ( esk18_1 @ X862 ) )
        | ( X862 @ X865 )
        | ~ ( exu @ X862 ) )
      & ( ( in @ ( esk19_1 @ X866 ) @ X866 )
        | ~ ( nonempty @ X866 ) )
      & ( $true
        | ~ ( nonempty @ X866 ) )
      & ( ~ ( in @ X868 @ ( setadjoin @ X869 @ emptyset ) )
        | ( X868 = X869 ) )
      & ( ( X870 = X871 )
        | ~ ( in @ X871 @ ( setadjoin @ X870 @ emptyset ) ) )
      & ( ( X872 != X873 )
        | ( in @ X872 @ ( setadjoin @ X873 @ emptyset ) ) )
      & ( ~ ( in @ X874 @ ( setadjoin @ X875 @ emptyset ) )
        | ( in @ X875 @ ( setadjoin @ X874 @ emptyset ) ) )
      & ( ~ ( in @ X878 @ ( setadjoin @ X876 @ ( setadjoin @ X877 @ emptyset ) ) )
        | ( X878 = X876 )
        | ( X878 = X877 ) )
      & ( in @ X879 @ ( setadjoin @ X879 @ ( setadjoin @ X880 @ emptyset ) ) )
      & ( in @ X882 @ ( setadjoin @ X881 @ ( setadjoin @ X882 @ emptyset ) ) )
      & ( ~ ( in @ X885 @ X883 )
        | ~ ( X884 @ X885 )
        | ( ( dsetconstr @ X883 @ X884 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X887 @ emptyset )
        | ( X886 @ X887 ) )
      & ( ( in @ ( esk20_2 @ X888 @ X889 ) @ X888 )
        | ~ ( in @ X890 @ X888 )
        | ( X889 @ X890 ) )
      & ( ~ ( X889 @ ( esk20_2 @ X888 @ X889 ) )
        | ~ ( in @ X890 @ X888 )
        | ( X889 @ X890 ) )
      & ( ( in @ ( esk21_2 @ X892 @ X893 ) @ X892 )
        | ~ ( in @ X895 @ X892 )
        | ~ ( X893 @ X895 ) )
      & ( ( X893 @ ( esk21_2 @ X892 @ X893 ) )
        | ~ ( in @ X895 @ X892 )
        | ~ ( X893 @ X895 ) )
      & ( ( in @ ( esk22_2 @ X896 @ X897 ) @ X896 )
        | ~ ( in @ X899 @ X896 )
        | ~ ( X897 @ X899 ) )
      & ( ( X897 @ ( esk22_2 @ X896 @ X897 ) )
        | ~ ( in @ X899 @ X896 )
        | ~ ( X897 @ X899 ) )
      & ( ( in @ ( esk23_2 @ X900 @ X901 ) @ X900 )
        | ~ ( in @ X902 @ X900 )
        | ( X901 @ X902 ) )
      & ( ~ ( X901 @ ( esk23_2 @ X900 @ X901 ) )
        | ~ ( in @ X902 @ X900 )
        | ( X901 @ X902 ) )
      & ( ~ X904
        | ( in @ emptyset @ ( prop2set @ X904 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk24_2 @ X905 @ X906 ) @ X905 )
        | ~ ( in @ X908 @ X905 )
        | ~ ( X906 @ X908 ) )
      & ( ( X906 @ ( esk24_2 @ X905 @ X906 ) )
        | ~ ( in @ X908 @ X905 )
        | ~ ( X906 @ X908 ) )
      & ( ( in @ ( esk25_2 @ X909 @ X910 ) @ X909 )
        | ~ ( in @ X911 @ X909 )
        | ( X910 @ X911 ) )
      & ( ~ ( X910 @ ( esk25_2 @ X909 @ X910 ) )
        | ~ ( in @ X911 @ X909 )
        | ( X910 @ X911 ) )
      & ( ( X913 @ ( esk26_2 @ X913 @ X914 ) )
        | ~ ( X913 @ X914 )
        | ( exu @ X913 ) )
      & ( ( X914
         != ( esk26_2 @ X913 @ X914 ) )
        | ~ ( X913 @ X914 )
        | ( exu @ X913 ) )
      & ( ( X916 @ ( esk27_1 @ X916 ) )
        | ( exu @ X916 )
        | ~ ( X916 @ X917 ) )
      & ( ( X916 @ ( esk28_1 @ X916 ) )
        | ( exu @ X916 )
        | ~ ( X916 @ X917 ) )
      & ( ( ( esk27_1 @ X916 )
         != ( esk28_1 @ X916 ) )
        | ( exu @ X916 )
        | ~ ( X916 @ X917 ) )
      & ( ~ ( X920 @ ( esk29_2 @ X920 @ X921 ) )
        | ( ( esk29_2 @ X920 @ X921 )
         != X921 )
        | ( exu @ X920 ) )
      & ( ( X920 @ ( esk29_2 @ X920 @ X921 ) )
        | ( ( esk29_2 @ X920 @ X921 )
          = X921 )
        | ( exu @ X920 ) )
      & ( ( X923 != X924 )
        | ( X925 != X926 )
        | ~ ( in @ X925 @ X923 )
        | ( in @ X926 @ X924 ) )
      & ( ~ ( in @ X929 @ X927 )
        | ( in @ X930 @ X928 )
        | ( X929 != X930 )
        | ( X927 != X928 ) )
      & ( ~ ( in @ X930 @ X928 )
        | ( in @ X929 @ X927 )
        | ( X929 != X930 )
        | ( X927 != X928 ) )
      & ( ~ ( exu @ X931 )
        | ~ ( X931 @ X932 )
        | ~ ( X931 @ X933 )
        | ( X932 = X933 ) )
      & ( ~ ( exu @ X934 )
        | ( exu @ X935 )
        | ( ( esk30_2 @ X934 @ X935 )
          = ( esk31_2 @ X934 @ X935 ) ) )
      & ( ~ ( exu @ X935 )
        | ( exu @ X934 )
        | ( ( esk30_2 @ X934 @ X935 )
          = ( esk31_2 @ X934 @ X935 ) ) )
      & ( ~ ( exu @ X934 )
        | ( exu @ X935 )
        | ~ ( X934 @ ( esk30_2 @ X934 @ X935 ) )
        | ~ ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
      & ( ~ ( exu @ X935 )
        | ( exu @ X934 )
        | ~ ( X934 @ ( esk30_2 @ X934 @ X935 ) )
        | ~ ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
      & ( ~ ( exu @ X934 )
        | ( exu @ X935 )
        | ( X934 @ ( esk30_2 @ X934 @ X935 ) )
        | ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
      & ( ~ ( exu @ X935 )
        | ( exu @ X934 )
        | ( X934 @ ( esk30_2 @ X934 @ X935 ) )
        | ( X935 @ ( esk31_2 @ X934 @ X935 ) ) )
      & ( emptyset = emptyset )
      & ( ( X938 != X939 )
        | ( X940 != X941 )
        | ( ( setadjoin @ X938 @ X940 )
          = ( setadjoin @ X939 @ X941 ) ) )
      & ( ( X942 != X943 )
        | ( ( powerset @ X942 )
          = ( powerset @ X943 ) ) )
      & ( ( X944 != X945 )
        | ( ( setunion @ X944 )
          = ( setunion @ X945 ) ) )
      & ( omega = omega )
      & ( ~ ( exu @ X946 )
        | ~ ( X946 @ X947 )
        | ~ ( X946 @ X948 )
        | ( X947 = X948 ) )
      & ( ( ( esk32_2 @ X949 @ X950 )
          = ( esk33_2 @ X949 @ X950 ) )
        | ~ ( exu @ X949 )
        | ~ ( exu @ X950 )
        | ( ( descr @ X949 )
          = ( descr @ X950 ) ) )
      & ( ~ ( X949 @ ( esk32_2 @ X949 @ X950 ) )
        | ~ ( X950 @ ( esk33_2 @ X949 @ X950 ) )
        | ~ ( exu @ X949 )
        | ~ ( exu @ X950 )
        | ( ( descr @ X949 )
          = ( descr @ X950 ) ) )
      & ( ( X949 @ ( esk32_2 @ X949 @ X950 ) )
        | ( X950 @ ( esk33_2 @ X949 @ X950 ) )
        | ~ ( exu @ X949 )
        | ~ ( exu @ X950 )
        | ( ( descr @ X949 )
          = ( descr @ X950 ) ) )
      & ( ( in @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) @ X953 )
        | ( ( dsetconstr @ X953 @ X955 )
          = ( dsetconstr @ X954 @ X956 ) )
        | ( X953 != X954 ) )
      & ( ( in @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) @ X954 )
        | ( ( dsetconstr @ X953 @ X955 )
          = ( dsetconstr @ X954 @ X956 ) )
        | ( X953 != X954 ) )
      & ( ( ( esk34_4 @ X953 @ X954 @ X955 @ X956 )
          = ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
        | ( ( dsetconstr @ X953 @ X955 )
          = ( dsetconstr @ X954 @ X956 ) )
        | ( X953 != X954 ) )
      & ( ~ ( X955 @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) )
        | ~ ( X956 @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
        | ( ( dsetconstr @ X953 @ X955 )
          = ( dsetconstr @ X954 @ X956 ) )
        | ( X953 != X954 ) )
      & ( ( X955 @ ( esk34_4 @ X953 @ X954 @ X955 @ X956 ) )
        | ( X956 @ ( esk35_4 @ X953 @ X954 @ X955 @ X956 ) )
        | ( ( dsetconstr @ X953 @ X955 )
          = ( dsetconstr @ X954 @ X956 ) )
        | ( X953 != X954 ) )
      & ( ( in @ ( esk36_2 @ X959 @ X960 ) @ X959 )
        | ( subset @ X959 @ X960 ) )
      & ( ~ ( in @ ( esk36_2 @ X959 @ X960 ) @ X960 )
        | ( subset @ X959 @ X960 ) )
      & ( ( X962 != X963 )
        | ( subset @ X963 @ X962 ) )
      & ( ( X964 != X965 )
        | ( subset @ X964 @ X965 ) )
      & ( ( in @ ( esk37_2 @ X966 @ X967 ) @ X966 )
        | ( subset @ X966 @ X967 ) )
      & ( ~ ( in @ ( esk37_2 @ X966 @ X967 ) @ X967 )
        | ( subset @ X966 @ X967 ) )
      & ( subset @ emptyset @ X969 )
      & ( ~ ( subset @ X970 @ X971 )
        | ~ ( in @ X972 @ X970 )
        | ( in @ X972 @ X971 ) )
      & ( ~ ( subset @ X973 @ X974 )
        | ( in @ X975 @ X974 )
        | ~ ( in @ X975 @ X973 ) )
      & ( ~ ( in @ X978 @ X976 )
        | ( in @ X978 @ X977 )
        | ~ ( subset @ X976 @ X977 ) )
      & ( ( subset @ X979 @ X980 )
        | ( X979 != X980 ) )
      & ( ~ ( in @ X983 @ X981 )
        | ( in @ X983 @ X982 )
        | ( X981 != X982 ) )
      & ( subset @ X984 @ X984 )
      & ( ~ ( subset @ X985 @ X986 )
        | ~ ( subset @ X986 @ X987 )
        | ( subset @ X985 @ X987 ) )
      & ( subset @ X989 @ ( setadjoin @ X988 @ X989 ) )
      & ( ~ ( subset @ X990 @ X992 )
        | ( subset @ X990 @ ( setadjoin @ X991 @ X992 ) ) )
      & ( ~ ( subset @ X993 @ X994 )
        | ( in @ X993 @ ( powerset @ X994 ) ) )
      & ( ~ ( subset @ X995 @ X996 )
        | ~ ( subset @ X996 @ X995 )
        | ( X995 = X996 ) )
      & ( ~ ( subset @ X997 @ emptyset )
        | ( X997 = emptyset ) )
      & ( ~ ( subset @ X999 @ X998 )
        | ( in @ X999 @ ( powerset @ X998 ) ) )
      & ( ~ ( in @ X1001 @ ( powerset @ X1000 ) )
        | ( subset @ X1001 @ X1000 ) )
      & ( in @ X1002 @ ( powerset @ X1002 ) )
      & ( ~ ( subset @ X1003 @ X1004 )
        | ( subset @ ( powerset @ X1003 ) @ ( powerset @ X1004 ) ) )
      & ( in @ ( dsetconstr @ X1005 @ X1006 ) @ ( powerset @ X1005 ) )
      & ( subset @ ( dsetconstr @ X1007 @ X1008 ) @ X1007 )
      & ( ~ ( in @ X1011 @ X1009 )
        | ( in @ X1011 @ ( binunion @ X1009 @ X1010 ) ) )
      & ( in @ X1013 @ ( setadjoin @ X1012 @ ( setadjoin @ X1013 @ emptyset ) ) )
      & ( ~ ( in @ X1016 @ X1015 )
        | ( in @ X1016 @ ( binunion @ X1014 @ X1015 ) ) )
      & ( ( in @ X1019 @ X1018 )
        | X1020
        | ( in @ X1019 @ X1017 )
        | ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
      & ( ~ X1020
        | X1020
        | ( in @ X1019 @ X1017 )
        | ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
      & ( ( in @ X1019 @ X1018 )
        | X1020
        | ~ X1020
        | ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
      & ( ~ X1020
        | X1020
        | ~ X1020
        | ~ ( in @ X1019 @ ( binunion @ X1017 @ X1018 ) ) )
      & ( ~ ( in @ X1023 @ ( binunion @ X1021 @ X1022 ) )
        | ( in @ X1023 @ X1021 )
        | ( in @ X1023 @ X1022 ) )
      & ( subset @ X1024 @ ( binunion @ X1024 @ X1025 ) )
      & ( subset @ X1027 @ ( binunion @ X1026 @ X1027 ) )
      & ( ~ ( in @ X1030 @ X1028 )
        | ~ ( in @ X1030 @ X1029 )
        | ( in @ X1030 @ ( binintersect @ X1028 @ X1029 ) ) )
      & ( ~ ( subset @ X1033 @ X1031 )
        | ~ ( subset @ X1033 @ X1032 )
        | ( subset @ X1033 @ ( binintersect @ X1031 @ X1032 ) ) )
      & ( ~ ( in @ X1036 @ ( binintersect @ X1034 @ X1035 ) )
        | ( in @ X1036 @ X1034 ) )
      & ( subset @ ( binintersect @ X1037 @ X1038 ) @ X1037 )
      & ( ~ ( subset @ X1039 @ X1040 )
        | ( ( binintersect @ X1039 @ X1040 )
          = X1039 ) )
      & ( ( ( binintersect @ X1041 @ X1042 )
         != X1042 )
        | ( subset @ X1042 @ X1041 ) )
      & ( ~ ( in @ X1045 @ ( binintersect @ X1043 @ X1044 ) )
        | ( in @ X1045 @ X1044 ) )
      & ( ( in @ ( esk38_2 @ X1046 @ X1047 ) @ X1046 )
        | ( ( binintersect @ X1046 @ X1047 )
          = emptyset ) )
      & ( ( in @ ( esk38_2 @ X1046 @ X1047 ) @ X1047 )
        | ( ( binintersect @ X1046 @ X1047 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X1049 @ X1050 ) @ X1050 )
      & ( ~ ( subset @ X1052 @ X1051 )
        | ( ( binintersect @ X1051 @ X1052 )
          = X1052 ) )
      & ( ( ( binintersect @ X1053 @ X1054 )
         != X1053 )
        | ( subset @ X1053 @ X1054 ) )
      & ( ( binintersect @ X1055 @ ( binunion @ X1056 @ X1057 ) )
        = ( binunion @ ( binintersect @ X1055 @ X1056 ) @ ( binintersect @ X1055 @ X1057 ) ) )
      & ( ~ ( in @ X1060 @ X1058 )
        | ( in @ X1060 @ X1059 )
        | ( in @ X1060 @ ( setminus @ X1058 @ X1059 ) ) )
      & ( ~ ( in @ X1063 @ ( setminus @ X1061 @ X1062 ) )
        | ( in @ X1063 @ X1061 ) )
      & ( ~ ( in @ X1066 @ ( setminus @ X1064 @ X1065 ) )
        | ~ ( in @ X1066 @ X1065 ) )
      & ( ~ ( subset @ X1067 @ X1068 )
        | ( ( setminus @ X1067 @ X1068 )
          = emptyset ) )
      & ( ( in @ X1071 @ ( setminus @ X1069 @ X1070 ) )
        | ~ ( in @ X1071 @ X1069 )
        | ( in @ X1071 @ X1070 ) )
      & ( ( in @ X1074 @ ( setminus @ X1072 @ X1073 ) )
        | ( in @ X1074 @ X1073 )
        | ~ ( in @ X1074 @ X1072 ) )
      & ( ( in @ X1077 @ X1075 )
        | ~ ( in @ X1077 @ ( setminus @ X1075 @ X1076 ) ) )
      & ( ~ ( in @ X1080 @ X1079 )
        | ~ ( in @ X1080 @ ( setminus @ X1078 @ X1079 ) ) )
      & ( subset @ ( setminus @ X1081 @ X1082 ) @ X1081 )
      & ( ( ( setminus @ X1083 @ X1084 )
         != emptyset )
        | ( subset @ X1083 @ X1084 ) )
      & ( ~ ( in @ X1087 @ X1085 )
        | X1088
        | ( in @ X1087 @ X1085 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ( in @ X1087 @ X1086 )
        | X1088
        | ( in @ X1087 @ X1085 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ X1088
        | X1088
        | ( in @ X1087 @ X1085 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ ( in @ X1087 @ X1085 )
        | X1088
        | ~ ( in @ X1087 @ X1086 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ( in @ X1087 @ X1086 )
        | X1088
        | ~ ( in @ X1087 @ X1086 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ X1088
        | X1088
        | ~ ( in @ X1087 @ X1086 )
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ ( in @ X1087 @ X1085 )
        | X1088
        | ~ X1088
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ( in @ X1087 @ X1086 )
        | X1088
        | ~ X1088
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ X1088
        | X1088
        | ~ X1088
        | ~ ( in @ X1087 @ ( symdiff @ X1085 @ X1086 ) ) )
      & ( ~ ( in @ X1091 @ X1089 )
        | ( in @ X1091 @ X1090 )
        | ( in @ X1091 @ ( symdiff @ X1089 @ X1090 ) ) )
      & ( ( in @ X1094 @ X1092 )
        | ~ ( in @ X1094 @ X1093 )
        | ( in @ X1094 @ ( symdiff @ X1092 @ X1093 ) ) )
      & ( ~ ( in @ X1097 @ X1095 )
        | ~ ( in @ X1097 @ X1096 )
        | ~ ( in @ X1097 @ ( symdiff @ X1095 @ X1096 ) ) )
      & ( ( in @ X1100 @ X1098 )
        | ( in @ X1100 @ X1099 )
        | ~ ( in @ X1100 @ ( symdiff @ X1098 @ X1099 ) ) )
      & ( in @ X1102 @ ( setadjoin @ X1101 @ ( setadjoin @ X1102 @ emptyset ) ) )
      & ( in @ X1103 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1103 @ ( setadjoin @ X1104 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ X1106 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1105 @ ( setadjoin @ X1106 @ emptyset ) ) @ emptyset ) ) ) )
      & ( iskpair @ ( setadjoin @ ( setadjoin @ X1107 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1107 @ ( setadjoin @ X1108 @ emptyset ) ) @ emptyset ) ) )
      & ( iskpair @ ( kpair @ X1109 @ X1110 ) )
      & ( ~ ( in @ X1112 @ X1111 )
        | ( subset @ ( setadjoin @ X1112 @ emptyset ) @ X1111 ) )
      & ( ~ ( in @ X1114 @ X1113 )
        | ( in @ ( setadjoin @ X1114 @ emptyset ) @ ( powerset @ X1113 ) ) )
      & ( in @ esk41_0 @ esk39_0 )
      & ~ ( in @ ( setadjoin @ esk41_0 @ emptyset ) @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])])])])])]) ).

thf(c_0_164,negated_conjecture,
    ~ ( in @ ( setadjoin @ esk41_0 @ emptyset ) @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

thf(c_0_165,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ X2 @ ( powerset @ X3 ) )
      | ~ ( subset @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

thf(c_0_166,negated_conjecture,
    ~ ( subset @ ( setadjoin @ esk41_0 @ emptyset ) @ ( binunion @ esk39_0 @ esk40_0 ) ),
    inference(spm,[status(thm)],[c_0_164,c_0_165]) ).

thf(c_0_167,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
      | ~ ( in @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

thf(c_0_168,negated_conjecture,
    ~ ( in @ esk41_0 @ ( binunion @ esk39_0 @ esk40_0 ) ),
    inference(spm,[status(thm)],[c_0_166,c_0_167]) ).

thf(c_0_169,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
      | ~ ( in @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

thf(c_0_170,negated_conjecture,
    in @ esk41_0 @ esk39_0,
    inference(split_conjunct,[status(thm)],[c_0_163]) ).

thf(c_0_171,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU623^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 16:01:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.59  # Version: 3.1.0-ho
% 0.57/0.59  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59  # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59  # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59  # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59  # Starting pre_casc_3 with 300s (1) cores
% 0.57/0.59  # Starting ho_unfolding_8 with 300s (1) cores
% 0.57/0.59  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.57/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.57/0.59  # Starting new_ho_5 with 300s (1) cores
% 0.57/0.59  # new_bool_5 with pid 20149 completed with status 0
% 0.57/0.59  # Result found by new_bool_5
% 0.57/0.59  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59  # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59  # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59  # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.57/0.59  # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.57/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.59  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.57/0.59  # new_ho_10_cnf2 with pid 20175 completed with status 0
% 0.57/0.59  # Result found by new_ho_10_cnf2
% 0.57/0.59  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.59  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.59  # Starting ehoh_best5 with 300s (1) cores
% 0.57/0.59  # Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.59  # Starting new_bool_5 with 300s (1) cores
% 0.57/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.57/0.59  # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.57/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.59  # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.57/0.59  # Preprocessing time       : 0.005 s
% 0.57/0.59  # Presaturation interreduction done
% 0.57/0.59  
% 0.57/0.59  # Proof found!
% 0.57/0.59  # SZS status Theorem
% 0.57/0.59  # SZS output start CNFRefutation
% See solution above
% 0.57/0.59  # Parsed axioms                        : 307
% 0.57/0.59  # Removed by relevancy pruning/SinE    : 168
% 0.57/0.59  # Initial clauses                      : 220
% 0.57/0.59  # Removed in clause preprocessing      : 25
% 0.57/0.59  # Initial clauses in saturation        : 195
% 0.57/0.59  # Processed clauses                    : 316
% 0.57/0.59  # ...of these trivial                  : 6
% 0.57/0.59  # ...subsumed                          : 36
% 0.57/0.59  # ...remaining for further processing  : 274
% 0.57/0.59  # Other redundant clauses eliminated   : 16
% 0.57/0.59  # Clauses deleted for lack of memory   : 0
% 0.57/0.59  # Backward-subsumed                    : 0
% 0.57/0.59  # Backward-rewritten                   : 3
% 0.57/0.59  # Generated clauses                    : 353
% 0.57/0.59  # ...of the previous two non-redundant : 278
% 0.57/0.59  # ...aggressively subsumed             : 0
% 0.57/0.59  # Contextual simplify-reflections      : 0
% 0.57/0.59  # Paramodulations                      : 337
% 0.57/0.59  # Factorizations                       : 0
% 0.57/0.59  # NegExts                              : 0
% 0.57/0.59  # Equation resolutions                 : 16
% 0.57/0.59  # Disequality decompositions           : 0
% 0.57/0.59  # Total rewrite steps                  : 75
% 0.57/0.59  # ...of those cached                   : 43
% 0.57/0.59  # Propositional unsat checks           : 0
% 0.57/0.59  #    Propositional check models        : 0
% 0.57/0.59  #    Propositional check unsatisfiable : 0
% 0.57/0.59  #    Propositional clauses             : 0
% 0.57/0.59  #    Propositional clauses after purity: 0
% 0.57/0.59  #    Propositional unsat core size     : 0
% 0.57/0.59  #    Propositional preprocessing time  : 0.000
% 0.57/0.59  #    Propositional encoding time       : 0.000
% 0.57/0.59  #    Propositional solver time         : 0.000
% 0.57/0.59  #    Success case prop preproc time    : 0.000
% 0.57/0.59  #    Success case prop encoding time   : 0.000
% 0.57/0.59  #    Success case prop solver time     : 0.000
% 0.57/0.59  # Current number of processed clauses  : 98
% 0.57/0.59  #    Positive orientable unit clauses  : 40
% 0.57/0.59  #    Positive unorientable unit clauses: 0
% 0.57/0.59  #    Negative unit clauses             : 5
% 0.57/0.59  #    Non-unit-clauses                  : 53
% 0.57/0.59  # Current number of unprocessed clauses: 316
% 0.57/0.59  # ...number of literals in the above   : 757
% 0.57/0.59  # Current number of archived formulas  : 0
% 0.57/0.59  # Current number of archived clauses   : 165
% 0.57/0.59  # Clause-clause subsumption calls (NU) : 3484
% 0.57/0.59  # Rec. Clause-clause subsumption calls : 1815
% 0.57/0.59  # Non-unit clause-clause subsumptions  : 23
% 0.57/0.59  # Unit Clause-clause subsumption calls : 39
% 0.57/0.59  # Rewrite failures with RHS unbound    : 0
% 0.57/0.59  # BW rewrite match attempts            : 16
% 0.57/0.59  # BW rewrite match successes           : 2
% 0.57/0.59  # Condensation attempts                : 316
% 0.57/0.59  # Condensation successes               : 4
% 0.57/0.59  # Termbank termtop insertions          : 34972
% 0.57/0.59  # Search garbage collected termcells   : 12061
% 0.57/0.59  
% 0.57/0.59  # -------------------------------------------------
% 0.57/0.59  # User time                : 0.056 s
% 0.57/0.59  # System time              : 0.013 s
% 0.57/0.59  # Total time               : 0.070 s
% 0.57/0.59  # Maximum resident set size: 4864 pages
% 0.57/0.59  
% 0.57/0.59  # -------------------------------------------------
% 0.57/0.59  # User time                : 0.065 s
% 0.57/0.59  # System time              : 0.016 s
% 0.57/0.59  # Total time               : 0.081 s
% 0.57/0.59  # Maximum resident set size: 2068 pages
% 0.57/0.59  % E---3.1 exiting
% 0.57/0.59  % E exiting
%------------------------------------------------------------------------------