TSTP Solution File: SEU560^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU560^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 03:28:11 EDT 2024

% Result   : Timeout 0.35s 300.10s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  224
% Syntax   : Number of formulae    :  270 (  27 unt; 144 typ;   0 def)
%            Number of atoms       : 1020 ( 320 equ;   0 cnn)
%            Maximal formula atoms :  314 (   8 avg)
%            Number of connectives : 4170 ( 370   ~; 431   |; 262   &;2471   @)
%                                         ( 138 <=>; 498  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  363 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  303 ( 303   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  147 ( 144 usr;  84 con; 0-4 aty)
%            Number of variables   :  917 ( 120   ^ 693   !; 104   ?; 917   :)

% 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,
    epred1_0: $o ).

thf(decl_114,type,
    esk1_2: $i > $i > $i ).

thf(decl_115,type,
    esk2_2: $i > $i > $i ).

thf(decl_116,type,
    esk3_2: $i > $i > $i ).

thf(decl_117,type,
    esk4_1: $i > $i ).

thf(decl_118,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_119,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_120,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_121,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_122,type,
    esk9_1: $i > $i ).

thf(decl_123,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_124,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_125,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_126,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_127,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_128,type,
    esk15_2: $i > $i > $i ).

thf(decl_129,type,
    esk16_2: $i > $i > $i ).

thf(decl_130,type,
    esk17_1: $i > $i ).

thf(decl_131,type,
    esk18_1: $i > $i ).

thf(decl_132,type,
    esk19_1: $i > $i ).

thf(decl_133,type,
    esk20_2: $i > $i > $i ).

thf(decl_134,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_135,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_136,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_137,type,
    esk24_1: $i > $i ).

thf(decl_138,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_139,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_140,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_141,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_142,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_143,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_144,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_145,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_146,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_147,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_148,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_149,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_150,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_151,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_152,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_153,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_154,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_155,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_156,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_157,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_158,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_159,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_160,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_161,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_162,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_163,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_164,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_165,type,
    esk52_2: $i > $i > $i ).

thf(decl_166,type,
    esk53_0: $i ).

thf(decl_167,type,
    esk54_0: $i ).

thf(decl_168,type,
    esk55_0: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(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(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_79,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_80,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_81,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_82,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_83,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_84,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_85,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_86,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_87,plain,
    ( subset
    = ( ^ [Z0: $i,Z1: $i] :
        ! [X2: $i] :
          ( ( in @ X2 @ Z0 )
         => ( in @ X2 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subset]) ).

thf(c_0_88,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_89,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_90,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_91,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_92,plain,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE1]) ).

thf(c_0_93,plain,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ( X1
          @ ( descr
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descrp]) ).

thf(c_0_94,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_95,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X249: $i] :
              ( ( X1 @ X249 )
              & ! [X250: $i] :
                  ( ( X1 @ X250 )
                 => ( X249 = X250 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_79,c_0_80]) ).

thf(c_0_96,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X251: $i] :
              ( ( X1 @ X251 )
              & ! [X252: $i] :
                  ( ( X1 @ X252 )
                 => ( X251 = X252 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_81,c_0_80]) ).

thf(c_0_97,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_98,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X253: $i] :
                ( ( X1 @ X253 )
                & ! [X254: $i] :
                    ( ( X1 @ X254 )
                   => ( X253 = X254 ) ) )
          <=> ? [X255: $i] :
                ( ( X17 @ X255 )
                & ! [X256: $i] :
                    ( ( X17 @ X256 )
                   => ( X255 = X256 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_82,c_0_80]) ).

thf(c_0_99,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_83]) ).

thf(c_0_100,plain,
    ( nonemptyI
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
             != emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_84,c_0_83]) ).

thf(c_0_101,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_83]) ).

thf(c_0_102,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X257: $i] :
              ( ( X1 @ X257 )
              & ! [X258: $i] :
                  ( ( X1 @ X258 )
                 => ( X257 = X258 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_85,c_0_80]) ).

thf(c_0_103,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X259: $i] :
                ( ( X1 @ X259 )
                & ! [X260: $i] :
                    ( ( X1 @ X260 )
                   => ( X259 = X260 ) ) )
           => ( ? [X261: $i] :
                  ( ( X17 @ X261 )
                  & ! [X262: $i] :
                      ( ( X17 @ X262 )
                     => ( X261 = X262 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_86,c_0_80]) ).

thf(c_0_104,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_105,axiom,
    ( subsetI1
    = ( ! [X4: $i,X5: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( in @ X2 @ X5 ) )
         => ! [X263: $i] :
              ( ( in @ X263 @ X4 )
             => ( in @ X263 @ X5 ) ) ) ) ),
    inference(apply_def,[status(thm)],[subsetI1,c_0_87]) ).

thf(c_0_106,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_107,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_108,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X243: $i] :
              ( ( X1 @ X243 )
              & ! [X244: $i] :
                  ( ( X1 @ X244 )
                 => ( X243 = X244 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_88,c_0_80]) ).

thf(c_0_109,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_83]) ).

thf(c_0_110,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X245: $i] :
              ( ( X1 @ X245 )
              & ! [X246: $i] :
                  ( ( X1 @ X246 )
                 => ( X245 = X246 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_89,c_0_80]) ).

thf(c_0_111,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X247: $i] :
                ( ( X1 @ X247 )
                & ! [X248: $i] :
                    ( ( X1 @ X248 )
                   => ( X247 = X248 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_90,c_0_80]) ).

thf(c_0_112,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X241: $i] :
              ( ( X1 @ X241 )
              & ! [X242: $i] :
                  ( ( X1 @ X242 )
                 => ( X241 = X242 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_91,c_0_80]) ).

thf(c_0_113,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X239: $i] :
              ( ( X1 @ X239 )
              & ! [X240: $i] :
                  ( ( X1 @ X240 )
                 => ( X239 = X240 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_92,c_0_80]) ).

thf(c_0_114,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_115,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_116,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_117,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X237: $i] :
              ( ( X1 @ X237 )
              & ! [X238: $i] :
                  ( ( X1 @ X238 )
                 => ( X237 = X238 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_93,c_0_80]) ).

thf(c_0_118,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X235: $i] :
                  ( ( X6 @ X2 @ X235 )
                  & ! [X236: $i] :
                      ( ( X6 @ X2 @ X236 )
                     => ( X235 = X236 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_94,c_0_80]) ).

thf(c_0_119,plain,
    ( epred1_0
  <=> ! [X293: $i] :
      ? [X294: $i] :
        ( ! [X295: $i] :
            ( ( in @ X295 @ X294 )
           => ! [X296: $i] :
                ( ( in @ X296 @ X295 )
               => ( in @ X296 @ X293 ) ) )
        & ! [X297: $i,X298: $i] :
            ( ( ( in @ X297 @ X293 )
              & ( in @ X298 @ X293 ) )
           => ( ! [X299: $i] :
                  ( ( in @ X299 @ X294 )
                 => ( ( in @ X297 @ X299 )
                  <=> ( in @ X298 @ X299 ) ) )
             => ( X297 = X298 ) ) )
        & ! [X300: $i,X301: $i] :
            ( ( ( in @ X300 @ X294 )
              & ( in @ X301 @ X294 ) )
           => ( ! [X302: $i] :
                  ( ( in @ X302 @ X300 )
                 => ( in @ X302 @ X301 ) )
              | ! [X303: $i] :
                  ( ( in @ X303 @ X301 )
                 => ( in @ X303 @ X300 ) ) ) )
        & ! [X304: $i] :
            ( ( ! [X305: $i] :
                  ( ( in @ X305 @ X304 )
                 => ( in @ X305 @ X293 ) )
              & ? [X306: $i] : ( in @ X306 @ X304 ) )
           => ? [X307: $i,X308: $i] :
                ( ( in @ X307 @ X294 )
                & ( in @ X308 @ X304 )
                & ~ ? [X309: $i] :
                      ( ( in @ X309 @ X307 )
                      & ( in @ X309 @ X304 ) )
                & ! [X310: $i] :
                    ( ( in @ X310 @ X294 )
                   => ( ! [X311: $i] :
                          ( ( in @ X311 @ X310 )
                         => ( in @ X311 @ X307 ) )
                      | ( in @ X308 @ X310 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_120,negated_conjecture,
    ~ ( ! [X264: $i,X265: $i] :
          ( ! [X266: $i] :
              ( ( in @ X266 @ X264 )
            <=> ( in @ X266 @ X265 ) )
         => ( X264 = X265 ) )
     => ( ! [X267: $i] :
            ~ ( in @ X267 @ emptyset )
       => ( ! [X268: $i,X269: $i,X270: $i] :
              ( ( in @ X270 @ ( setadjoin @ X268 @ X269 ) )
            <=> ( ( X270 = X268 )
                | ( in @ X270 @ X269 ) ) )
         => ( ! [X271: $i,X272: $i] :
                ( ( in @ X272 @ ( powerset @ X271 ) )
              <=> ! [X273: $i] :
                    ( ( in @ X273 @ X272 )
                   => ( in @ X273 @ X271 ) ) )
           => ( ! [X274: $i,X275: $i] :
                  ( ( in @ X275 @ ( setunion @ X274 ) )
                <=> ? [X276: $i] :
                      ( ( in @ X275 @ X276 )
                      & ( in @ X276 @ X274 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X277: $i] :
                      ( ( in @ X277 @ omega )
                     => ( in @ ( setadjoin @ X277 @ X277 ) @ omega ) )
                 => ( ! [X278: $i] :
                        ( ( ( in @ emptyset @ X278 )
                          & ! [X279: $i] :
                              ( ( ( in @ X279 @ omega )
                                & ( in @ X279 @ X278 ) )
                             => ( in @ ( setadjoin @ X279 @ X279 ) @ X278 ) ) )
                       => ! [X280: $i] :
                            ( ( in @ X280 @ omega )
                           => ( in @ X280 @ X278 ) ) )
                   => ( ! [X281: $i > $i > $o,X282: $i] :
                          ( ! [X283: $i] :
                              ( ( in @ X283 @ X282 )
                             => ? [X284: $i] :
                                  ( ( X281 @ X283 @ X284 )
                                  & ! [X285: $i] :
                                      ( ( X281 @ X283 @ X285 )
                                     => ( X284 = X285 ) ) ) )
                         => ? [X286: $i] :
                            ! [X287: $i] :
                              ( ( in @ X287 @ X286 )
                            <=> ? [X288: $i] :
                                  ( ( in @ X288 @ X282 )
                                  & ( X281 @ X288 @ X287 ) ) ) )
                     => ( ! [X289: $i] :
                            ( ? [X290: $i] : ( in @ X290 @ X289 )
                           => ? [X291: $i] :
                                ( ( in @ X291 @ X289 )
                                & ~ ? [X292: $i] :
                                      ( ( in @ X292 @ X291 )
                                      & ( in @ X292 @ X289 ) ) ) )
                       => ( epred1_0
                         => ( ! [X312: $i > $o] :
                                ( ? [X313: $i] :
                                    ( ( X312 @ X313 )
                                    & ! [X314: $i] :
                                        ( ( X312 @ X314 )
                                       => ( X313 = X314 ) ) )
                               => ( X312
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X312 @ Z0 ) ) ) )
                           => ( ! [X315: $i,X316: $i > $o,X317: $i] :
                                  ( ( in @ X317 @ X315 )
                                 => ( ( X316 @ X317 )
                                   => ( in @ X317
                                      @ ( dsetconstr @ X315
                                        @ ^ [Z0: $i] : ( X316 @ Z0 ) ) ) ) )
                             => ( ! [X318: $i,X319: $i > $o,X320: $i] :
                                    ( ( in @ X320
                                      @ ( dsetconstr @ X318
                                        @ ^ [Z0: $i] : ( X319 @ Z0 ) ) )
                                   => ( in @ X320 @ X318 ) )
                               => ( ! [X321: $i,X322: $i > $o,X323: $i] :
                                      ( ( in @ X323
                                        @ ( dsetconstr @ X321
                                          @ ^ [Z0: $i] : ( X322 @ Z0 ) ) )
                                     => ( X322 @ X323 ) )
                                 => ( ! [X324: $i > $o] :
                                        ( ? [X325: $i] :
                                            ( ( X324 @ X325 )
                                            & ! [X326: $i] :
                                                ( ( X324 @ X326 )
                                               => ( X325 = X326 ) ) )
                                       => ? [X327: $i] :
                                            ( ( X324 @ X327 )
                                            & ! [X328: $i] :
                                                ( ( X324 @ X328 )
                                               => ( X327 = X328 ) ) ) )
                                   => ( ! [X329: $o,X330: $i] :
                                          ( ( in @ X330 @ ( prop2set @ X329 ) )
                                         => X329 )
                                     => ( ! [X331: $i] :
                                            ( ( in @ X331 @ emptyset )
                                           => ! [X332: $o] : X332 )
                                       => ( ! [X333: $i] :
                                              ~ ( in @ X333 @ emptyset )
                                         => ( ! [X334: $i] :
                                                ~ ( in @ X334 @ emptyset )
                                           => ( ! [X335: $i > $o] :
                                                  ( ? [X336: $i] :
                                                      ( ( X335 @ X336 )
                                                      & ! [X337: $i] :
                                                          ( ( X335 @ X337 )
                                                         => ( X336 = X337 ) ) )
                                                 => ? [X338: $i] : ( X335 @ X338 ) )
                                             => ( ! [X339: $i,X340: $i] :
                                                    ( ! [X341: $i] :
                                                        ( ( in @ X341 @ X339 )
                                                       => ( in @ X341 @ X340 ) )
                                                   => ( ! [X342: $i] :
                                                          ( ( in @ X342 @ X340 )
                                                         => ( in @ X342 @ X339 ) )
                                                     => ( X339 = X340 ) ) )
                                               => ( ! [X343: $i] :
                                                      ( ! [X344: $i] :
                                                          ~ ( in @ X344 @ X343 )
                                                     => ( X343 = emptyset ) )
                                                 => ( ! [X345: $i] :
                                                        ( ! [X346: $i] :
                                                            ~ ( in @ X346 @ X345 )
                                                       => ( X345 = emptyset ) )
                                                   => ( ! [X347: $i,X348: $i > $o,X349: $i] :
                                                          ( ( in @ X349 @ X347 )
                                                         => ( ( in @ X349
                                                              @ ( dsetconstr @ X347
                                                                @ ^ [Z0: $i] : ( X348 @ Z0 ) ) )
                                                          <=> ( X348 @ X349 ) ) )
                                                     => ( ! [X350: $i] :
                                                            ( ( X350 != emptyset )
                                                           => ? [X351: $i] : ( in @ X351 @ X350 ) )
                                                       => ( ! [X352: $i,X353: $i > $o,X354: $i] :
                                                              ( ( in @ X354 @ X352 )
                                                             => ( ( X353 @ X354 )
                                                               => ( ( dsetconstr @ X352
                                                                    @ ^ [Z0: $i] : ( X353 @ Z0 ) )
                                                                 != emptyset ) ) )
                                                         => ( ! [X355: $i] :
                                                                ( ? [X356: $i] : ( in @ X356 @ X355 )
                                                               => ( X355 != emptyset ) )
                                                           => ( ! [X357: $i,X358: $i] : ( in @ X357 @ ( setadjoin @ X357 @ X358 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X359: $i,X360: $i,X361: $i] :
                                                                      ( ( in @ X361 @ X360 )
                                                                     => ( in @ X361 @ ( setadjoin @ X359 @ X360 ) ) )
                                                                 => ( ! [X362: $i,X363: $i,X364: $i] :
                                                                        ( ( in @ X364 @ ( setadjoin @ X362 @ X363 ) )
                                                                       => ! [X365: $o] :
                                                                            ( ( ( X364 = X362 )
                                                                             => X365 )
                                                                           => ( ( ( in @ X364 @ X363 )
                                                                               => X365 )
                                                                             => X365 ) ) )
                                                                   => ( ! [X366: $i,X367: $i,X368: $i] :
                                                                          ( ( in @ X368 @ ( setadjoin @ X366 @ X367 ) )
                                                                         => ( ( X368 = X366 )
                                                                            | ( in @ X368 @ X367 ) ) )
                                                                     => ( ! [X369: $i] :
                                                                            ( ( dsetconstr @ X369
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X369 )
                                                                       => ( ! [X370: $i,X371: $i] :
                                                                              ( ! [X372: $i] :
                                                                                  ( ( in @ X372 @ X371 )
                                                                                 => ( in @ X372 @ X370 ) )
                                                                             => ( in @ X371 @ ( powerset @ X370 ) ) )
                                                                         => ( ! [X373: $i] : ( in @ emptyset @ ( powerset @ X373 ) )
                                                                           => ( ! [X374: $i] : ( in @ emptyset @ ( powerset @ X374 ) )
                                                                             => ( ! [X375: $i,X376: $i,X377: $i] :
                                                                                    ( ( in @ X376 @ ( powerset @ X375 ) )
                                                                                   => ( ( in @ X377 @ X376 )
                                                                                     => ( in @ X377 @ X375 ) ) )
                                                                               => ( ! [X378: $i,X379: $i,X380: $i] :
                                                                                      ( ( in @ X379 @ X380 )
                                                                                     => ( ( in @ X380 @ X378 )
                                                                                       => ( in @ X379 @ ( setunion @ X378 ) ) ) )
                                                                                 => ( ! [X381: $i,X382: $i] :
                                                                                        ( ( in @ X382 @ ( setunion @ X381 ) )
                                                                                       => ! [X383: $o] :
                                                                                            ( ! [X384: $i] :
                                                                                                ( ( in @ X382 @ X384 )
                                                                                               => ( ( in @ X384 @ X381 )
                                                                                                 => X383 ) )
                                                                                           => X383 ) )
                                                                                   => ( ! [X385: $i,X386: $i] :
                                                                                          ( ( in @ X386 @ X385 )
                                                                                         => ( in @ X386 @ ( powerset @ ( setunion @ X385 ) ) ) )
                                                                                     => ( ! [X387: $i > $o] :
                                                                                            ( ? [X388: $i] :
                                                                                                ( ( X387 @ X388 )
                                                                                                & ! [X389: $i] :
                                                                                                    ( ( X387 @ X389 )
                                                                                                   => ( X388 = X389 ) ) )
                                                                                           => ? [X390: $i] :
                                                                                              ! [X391: $i] :
                                                                                                ( ( X387 @ X391 )
                                                                                              <=> ( X391 = X390 ) ) )
                                                                                       => ( ! [X392: $i] :
                                                                                              ( ( X392 != emptyset )
                                                                                             => ? [X393: $i] : ( in @ X393 @ X392 ) )
                                                                                         => ( ! [X394: $i,X395: $i] :
                                                                                                ( ( in @ X394 @ ( setadjoin @ X395 @ emptyset ) )
                                                                                               => ( X394 = X395 ) )
                                                                                           => ( ! [X396: $i,X397: $i] :
                                                                                                  ( ( X396 != X397 )
                                                                                                 => ~ ( in @ X397 @ ( setadjoin @ X396 @ emptyset ) ) )
                                                                                             => ( ! [X398: $i,X399: $i] :
                                                                                                    ( ( X398 = X399 )
                                                                                                   => ( in @ X398 @ ( setadjoin @ X399 @ emptyset ) ) )
                                                                                               => ( ! [X400: $i,X401: $i] :
                                                                                                      ( ( in @ X400 @ ( setadjoin @ X401 @ emptyset ) )
                                                                                                     => ( in @ X401 @ ( setadjoin @ X400 @ emptyset ) ) )
                                                                                                 => ( ! [X402: $i,X403: $i,X404: $i] :
                                                                                                        ( ( in @ X404 @ ( setadjoin @ X402 @ ( setadjoin @ X403 @ emptyset ) ) )
                                                                                                       => ( ( X404 = X402 )
                                                                                                          | ( X404 = X403 ) ) )
                                                                                                   => ( ! [X405: $i,X406: $i] : ( in @ X405 @ ( setadjoin @ X405 @ ( setadjoin @ X406 @ emptyset ) ) )
                                                                                                     => ( ! [X407: $i,X408: $i] : ( in @ X408 @ ( setadjoin @ X407 @ ( setadjoin @ X408 @ emptyset ) ) )
                                                                                                       => ( ! [X409: $i,X410: $i > $o] :
                                                                                                              ( ? [X411: $i] :
                                                                                                                  ( ( in @ X411 @ X409 )
                                                                                                                  & ( X410 @ X411 ) )
                                                                                                             => ( ( dsetconstr @ X409
                                                                                                                  @ ^ [Z0: $i] : ( X410 @ Z0 ) )
                                                                                                               != emptyset ) )
                                                                                                         => ( ! [X412: $i > $o,X413: $i] :
                                                                                                                ( ( in @ X413 @ emptyset )
                                                                                                               => ( X412 @ X413 ) )
                                                                                                           => ( ! [X414: $i,X415: $i > $o] :
                                                                                                                  ( ~ ! [X416: $i] :
                                                                                                                        ( ( in @ X416 @ X414 )
                                                                                                                       => ( X415 @ X416 ) )
                                                                                                                 => ? [X417: $i] :
                                                                                                                      ( ( in @ X417 @ X414 )
                                                                                                                      & ~ ( X415 @ X417 ) ) )
                                                                                                             => ( ! [X418: $i,X419: $i > $o] :
                                                                                                                    ( ! [X420: $i] :
                                                                                                                        ( ( in @ X420 @ X418 )
                                                                                                                       => ~ ( X419 @ X420 ) )
                                                                                                                   => ~ ? [X421: $i] :
                                                                                                                          ( ( in @ X421 @ X418 )
                                                                                                                          & ( X419 @ X421 ) ) )
                                                                                                               => ( ! [X422: $i,X423: $i > $o] :
                                                                                                                      ( ~ ? [X424: $i] :
                                                                                                                            ( ( in @ X424 @ X422 )
                                                                                                                            & ( X423 @ X424 ) )
                                                                                                                     => ! [X425: $i] :
                                                                                                                          ( ( in @ X425 @ X422 )
                                                                                                                         => ~ ( X423 @ X425 ) ) )
                                                                                                                 => ( ! [X426: $i,X427: $i > $o] :
                                                                                                                        ( ? [X428: $i] :
                                                                                                                            ( ( in @ X428 @ X426 )
                                                                                                                            & ~ ( X427 @ X428 ) )
                                                                                                                       => ~ ! [X429: $i] :
                                                                                                                              ( ( in @ X429 @ X426 )
                                                                                                                             => ( X427 @ X429 ) ) )
                                                                                                                   => ( ! [X430: $o] :
                                                                                                                          ( X430
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X430 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X431: $i,X432: $i > $o] :
                                                                                                                              ( ~ ? [X433: $i] :
                                                                                                                                    ( ( in @ X433 @ X431 )
                                                                                                                                    & ( X432 @ X433 ) )
                                                                                                                             => ! [X434: $i] :
                                                                                                                                  ( ( in @ X434 @ X431 )
                                                                                                                                 => ~ ( X432 @ X434 ) ) )
                                                                                                                         => ( ! [X435: $i,X436: $i > $o] :
                                                                                                                                ( ~ ! [X437: $i] :
                                                                                                                                      ( ( in @ X437 @ X435 )
                                                                                                                                     => ( X436 @ X437 ) )
                                                                                                                               => ? [X438: $i] :
                                                                                                                                    ( ( in @ X438 @ X435 )
                                                                                                                                    & ~ ( X436 @ X438 ) ) )
                                                                                                                           => ( ! [X439: $i > $o] :
                                                                                                                                  ( ? [X440: $i] :
                                                                                                                                      ( ( X439 @ X440 )
                                                                                                                                      & ! [X441: $i] :
                                                                                                                                          ( ( X439 @ X441 )
                                                                                                                                         => ( X440 = X441 ) ) )
                                                                                                                                 => ? [X442: $i] :
                                                                                                                                      ( ( X439 @ X442 )
                                                                                                                                      & ! [X443: $i] :
                                                                                                                                          ( ( X439 @ X443 )
                                                                                                                                         => ( X442 = X443 ) ) ) )
                                                                                                                             => ( ! [X444: $i > $o] :
                                                                                                                                    ( ? [X445: $i] : ( X444 @ X445 )
                                                                                                                                   => ( ! [X446: $i,X447: $i] :
                                                                                                                                          ( ( X444 @ X446 )
                                                                                                                                         => ( ( X444 @ X447 )
                                                                                                                                           => ( X446 = X447 ) ) )
                                                                                                                                     => ? [X448: $i] :
                                                                                                                                          ( ( X444 @ X448 )
                                                                                                                                          & ! [X449: $i] :
                                                                                                                                              ( ( X444 @ X449 )
                                                                                                                                             => ( X448 = X449 ) ) ) ) )
                                                                                                                               => ( ! [X450: $i > $o] :
                                                                                                                                      ( ? [X451: $i] :
                                                                                                                                        ! [X452: $i] :
                                                                                                                                          ( ( X450 @ X452 )
                                                                                                                                        <=> ( X452 = X451 ) )
                                                                                                                                     => ? [X453: $i] :
                                                                                                                                          ( ( X450 @ X453 )
                                                                                                                                          & ! [X454: $i] :
                                                                                                                                              ( ( X450 @ X454 )
                                                                                                                                             => ( X453 = X454 ) ) ) )
                                                                                                                                 => ( ! [X455: $i,X456: $i] :
                                                                                                                                        ( ( X455 = X456 )
                                                                                                                                       => ! [X457: $i,X458: $i] :
                                                                                                                                            ( ( X457 = X458 )
                                                                                                                                           => ( ( in @ X457 @ X455 )
                                                                                                                                             => ( in @ X458 @ X456 ) ) ) )
                                                                                                                                   => ( ! [X459: $i,X460: $i] :
                                                                                                                                          ( ( X459 = X460 )
                                                                                                                                         => ! [X461: $i,X462: $i] :
                                                                                                                                              ( ( X461 = X462 )
                                                                                                                                             => ( ( in @ X461 @ X459 )
                                                                                                                                              <=> ( in @ X462 @ X460 ) ) ) )
                                                                                                                                     => ( ! [X463: $i > $o] :
                                                                                                                                            ( ? [X464: $i] :
                                                                                                                                                ( ( X463 @ X464 )
                                                                                                                                                & ! [X465: $i] :
                                                                                                                                                    ( ( X463 @ X465 )
                                                                                                                                                   => ( X464 = X465 ) ) )
                                                                                                                                           => ! [X466: $i,X467: $i] :
                                                                                                                                                ( ( X463 @ X466 )
                                                                                                                                               => ( ( X463 @ X467 )
                                                                                                                                                 => ( X466 = X467 ) ) ) )
                                                                                                                                       => ( ! [X468: $i > $o,X469: $i > $o] :
                                                                                                                                              ( ! [X470: $i,X471: $i] :
                                                                                                                                                  ( ( X470 = X471 )
                                                                                                                                                 => ( ( X468 @ X470 )
                                                                                                                                                  <=> ( X469 @ X471 ) ) )
                                                                                                                                             => ( ? [X472: $i] :
                                                                                                                                                    ( ( X468 @ X472 )
                                                                                                                                                    & ! [X473: $i] :
                                                                                                                                                        ( ( X468 @ X473 )
                                                                                                                                                       => ( X472 = X473 ) ) )
                                                                                                                                              <=> ? [X474: $i] :
                                                                                                                                                    ( ( X469 @ X474 )
                                                                                                                                                    & ! [X475: $i] :
                                                                                                                                                        ( ( X469 @ X475 )
                                                                                                                                                       => ( X474 = X475 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X476: $i,X477: $i] :
                                                                                                                                                  ( ( X476 = X477 )
                                                                                                                                                 => ! [X478: $i,X479: $i] :
                                                                                                                                                      ( ( X478 = X479 )
                                                                                                                                                     => ( ( setadjoin @ X476 @ X478 )
                                                                                                                                                        = ( setadjoin @ X477 @ X479 ) ) ) )
                                                                                                                                             => ( ! [X480: $i,X481: $i] :
                                                                                                                                                    ( ( X480 = X481 )
                                                                                                                                                   => ( ( powerset @ X480 )
                                                                                                                                                      = ( powerset @ X481 ) ) )
                                                                                                                                               => ( ! [X482: $i,X483: $i] :
                                                                                                                                                      ( ( X482 = X483 )
                                                                                                                                                     => ( ( setunion @ X482 )
                                                                                                                                                        = ( setunion @ X483 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X484: $i > $o] :
                                                                                                                                                          ( ? [X485: $i] :
                                                                                                                                                              ( ( X484 @ X485 )
                                                                                                                                                              & ! [X486: $i] :
                                                                                                                                                                  ( ( X484 @ X486 )
                                                                                                                                                                 => ( X485 = X486 ) ) )
                                                                                                                                                         => ! [X487: $i,X488: $i] :
                                                                                                                                                              ( ( X484 @ X487 )
                                                                                                                                                             => ( ( X484 @ X488 )
                                                                                                                                                               => ( X487 = X488 ) ) ) )
                                                                                                                                                     => ( ! [X489: $i > $o,X490: $i > $o] :
                                                                                                                                                            ( ! [X491: $i,X492: $i] :
                                                                                                                                                                ( ( X491 = X492 )
                                                                                                                                                               => ( ( X489 @ X491 )
                                                                                                                                                                <=> ( X490 @ X492 ) ) )
                                                                                                                                                           => ( ? [X493: $i] :
                                                                                                                                                                  ( ( X489 @ X493 )
                                                                                                                                                                  & ! [X494: $i] :
                                                                                                                                                                      ( ( X489 @ X494 )
                                                                                                                                                                     => ( X493 = X494 ) ) )
                                                                                                                                                             => ( ? [X495: $i] :
                                                                                                                                                                    ( ( X490 @ X495 )
                                                                                                                                                                    & ! [X496: $i] :
                                                                                                                                                                        ( ( X490 @ X496 )
                                                                                                                                                                       => ( X495 = X496 ) ) )
                                                                                                                                                               => ( ( descr
                                                                                                                                                                    @ ^ [Z0: $i] : ( X489 @ Z0 ) )
                                                                                                                                                                  = ( descr
                                                                                                                                                                    @ ^ [Z0: $i] : ( X490 @ Z0 ) ) ) ) ) )
                                                                                                                                                       => ( ! [X497: $i,X498: $i] :
                                                                                                                                                              ( ( X497 = X498 )
                                                                                                                                                             => ! [X499: $i > $o,X500: $i > $o] :
                                                                                                                                                                  ( ! [X501: $i] :
                                                                                                                                                                      ( ( in @ X501 @ X497 )
                                                                                                                                                                     => ! [X502: $i] :
                                                                                                                                                                          ( ( in @ X502 @ X498 )
                                                                                                                                                                         => ( ( X501 = X502 )
                                                                                                                                                                           => ( ( X499 @ X501 )
                                                                                                                                                                            <=> ( X500 @ X502 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X497
                                                                                                                                                                      @ ^ [Z0: $i] : ( X499 @ Z0 ) )
                                                                                                                                                                    = ( dsetconstr @ X498
                                                                                                                                                                      @ ^ [Z0: $i] : ( X500 @ Z0 ) ) ) ) )
                                                                                                                                                         => ( ! [X503: $i,X504: $i] :
                                                                                                                                                                ( ! [X505: $i] :
                                                                                                                                                                    ( ( in @ X505 @ X503 )
                                                                                                                                                                   => ( in @ X505 @ X504 ) )
                                                                                                                                                               => ! [X506: $i] :
                                                                                                                                                                    ( ( in @ X506 @ X503 )
                                                                                                                                                                   => ( in @ X506 @ X504 ) ) )
                                                                                                                                                           => ! [X4: $i,X5: $i] :
                                                                                                                                                                ( ( X4 = X5 )
                                                                                                                                                               => ! [X507: $i] :
                                                                                                                                                                    ( ( in @ X507 @ X5 )
                                                                                                                                                                   => ( in @ X507 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[eqimpsubset2]),setadjoinOr]),c_0_87]),c_0_95]),noeltsimpempty]),inCongP]),in__Cong]),c_0_96]),c_0_97]),c_0_98]),emptyset__Cong]),c_0_99]),setadjoin__Cong]),powerset__Cong]),c_0_100]),setunion__Cong]),omega__Cong]),c_0_101]),c_0_102]),c_0_103]),setadjoinIL]),c_0_104]),c_0_105]),emptyinunitempty]),setadjoinIR]),setadjoinE]),c_0_106]),c_0_107]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_108]),c_0_109]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_110]),c_0_111]),emptyI]),setext]),c_0_112]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_113]),c_0_114]),c_0_115]),c_0_116]),c_0_117]),wellorderingAx]),foundationAx]),c_0_118]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_119]) ).

thf(c_0_121,negated_conjecture,
    ! [X508: $i,X509: $i,X511: $i,X512: $i,X513: $i,X514: $i,X515: $i,X516: $i,X517: $i,X518: $i,X519: $i,X521: $i,X522: $i,X524: $i,X525: $i,X526: $i,X527: $i,X528: $i,X530: $i,X531: $i > $i > $o,X532: $i,X534: $i,X537: $i,X539: $i,X540: $i,X541: $i,X542: $i,X544: $i,X545: $i > $o,X546: $i,X548: $i,X549: $i > $o,X550: $i,X551: $i,X552: $i > $o,X553: $i,X554: $i,X555: $i > $o,X556: $i,X557: $i > $o,X558: $i,X561: $i,X562: $o,X563: $i,X564: $i,X565: $o,X566: $i,X567: $i,X568: $i > $o,X569: $i,X572: $i,X573: $i,X576: $i,X578: $i,X580: $i,X581: $i > $o,X582: $i,X583: $i,X585: $i,X586: $i > $o,X587: $i,X588: $i,X589: $i,X590: $i,X591: $i,X592: $i,X593: $i,X594: $i,X595: $i,X596: $i,X597: $i,X598: $o,X599: $i,X600: $i,X601: $i,X602: $i,X603: $i,X604: $i,X606: $i,X607: $i,X608: $i,X609: $i,X610: $i,X611: $i,X612: $i,X613: $i,X614: $i,X615: $i,X616: $o,X618: $i,X619: $i,X620: $i > $o,X621: $i,X624: $i,X625: $i,X626: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X641: $i,X642: $i,X643: $i,X644: $i > $o,X645: $i,X646: $i > $o,X647: $i,X648: $i,X649: $i > $o,X650: $i,X652: $i,X653: $i > $o,X655: $i,X656: $i,X657: $i > $o,X659: $i,X660: $i,X661: $i > $o,X662: $i,X664: $o,X665: $i,X666: $i > $o,X668: $i,X669: $i,X670: $i > $o,X671: $i,X673: $i > $o,X674: $i,X677: $i,X678: $i > $o,X679: $i,X683: $i,X684: $i > $o,X685: $i,X688: $i,X689: $i,X690: $i,X691: $i,X692: $i,X693: $i,X694: $i,X695: $i,X696: $i,X697: $i > $o,X698: $i,X700: $i,X701: $i,X702: $i > $o,X703: $i > $o,X706: $i,X709: $i,X710: $i,X713: $i,X714: $i,X715: $i,X716: $i,X717: $i,X718: $i,X719: $i,X720: $i,X721: $i,X722: $i > $o,X723: $i,X725: $i,X726: $i,X727: $i > $o,X728: $i > $o,X731: $i,X733: $i,X735: $i,X736: $i,X737: $i > $o,X738: $i > $o,X741: $i,X742: $i,X744: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X508 @ X509 ) @ X508 )
        | ~ ( in @ ( esk1_2 @ X508 @ X509 ) @ X509 )
        | ( X508 = X509 ) )
      & ( ( in @ ( esk1_2 @ X508 @ X509 ) @ X508 )
        | ( in @ ( esk1_2 @ X508 @ X509 ) @ X509 )
        | ( X508 = X509 ) )
      & ~ ( in @ X511 @ emptyset )
      & ( ~ ( in @ X514 @ ( setadjoin @ X512 @ X513 ) )
        | ( X514 = X512 )
        | ( in @ X514 @ X513 ) )
      & ( ( X514 != X512 )
        | ( in @ X514 @ ( setadjoin @ X512 @ X513 ) ) )
      & ( ~ ( in @ X514 @ X513 )
        | ( in @ X514 @ ( setadjoin @ X512 @ X513 ) ) )
      & ( ~ ( in @ X516 @ ( powerset @ X515 ) )
        | ~ ( in @ X517 @ X516 )
        | ( in @ X517 @ X515 ) )
      & ( ( in @ ( esk2_2 @ X518 @ X519 ) @ X519 )
        | ( in @ X519 @ ( powerset @ X518 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X518 @ X519 ) @ X518 )
        | ( in @ X519 @ ( powerset @ X518 ) ) )
      & ( ( in @ X522 @ ( esk3_2 @ X521 @ X522 ) )
        | ~ ( in @ X522 @ ( setunion @ X521 ) ) )
      & ( ( in @ ( esk3_2 @ X521 @ X522 ) @ X521 )
        | ~ ( in @ X522 @ ( setunion @ X521 ) ) )
      & ( ~ ( in @ X525 @ X526 )
        | ~ ( in @ X526 @ X524 )
        | ( in @ X525 @ ( setunion @ X524 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X527 @ omega )
        | ( in @ ( setadjoin @ X527 @ X527 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X528 ) @ omega )
        | ~ ( in @ emptyset @ X528 )
        | ~ ( in @ X530 @ omega )
        | ( in @ X530 @ X528 ) )
      & ( ( in @ ( esk4_1 @ X528 ) @ X528 )
        | ~ ( in @ emptyset @ X528 )
        | ~ ( in @ X530 @ omega )
        | ( in @ X530 @ X528 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X528 ) @ ( esk4_1 @ X528 ) ) @ X528 )
        | ~ ( in @ emptyset @ X528 )
        | ~ ( in @ X530 @ omega )
        | ( in @ X530 @ X528 ) )
      & ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
      & ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
      & ( ~ ( in @ X540 @ X532 )
        | ~ ( X531 @ X540 @ X539 )
        | ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
        | ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
      & ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ~ ( in @ X540 @ X532 )
        | ~ ( X531 @ X540 @ X539 )
        | ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X534
         != ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
        | ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X534
         != ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ~ ( in @ X540 @ X532 )
        | ~ ( X531 @ X540 @ X539 )
        | ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
        | ( X534
         != ( esk6_3 @ X531 @ X532 @ X534 ) )
        | ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
      & ( ( in @ ( esk9_1 @ X541 ) @ X541 )
        | ~ ( in @ X542 @ X541 ) )
      & ( ~ ( in @ X544 @ ( esk9_1 @ X541 ) )
        | ~ ( in @ X544 @ X541 )
        | ~ ( in @ X542 @ X541 ) )
      & epred1_0
      & ( ( X545 @ ( esk10_2 @ X545 @ X546 ) )
        | ~ ( X545 @ X546 )
        | ( X545
          @ ( descr
            @ ^ [Z0: $i] : ( X545 @ Z0 ) ) ) )
      & ( ( X546
         != ( esk10_2 @ X545 @ X546 ) )
        | ~ ( X545 @ X546 )
        | ( X545
          @ ( descr
            @ ^ [Z0: $i] : ( X545 @ Z0 ) ) ) )
      & ( ~ ( in @ X550 @ X548 )
        | ~ ( X549 @ X550 )
        | ( in @ X550
          @ ( dsetconstr @ X548
            @ ^ [Z0: $i] : ( X549 @ Z0 ) ) ) )
      & ( ~ ( in @ X553
            @ ( dsetconstr @ X551
              @ ^ [Z0: $i] : ( X552 @ Z0 ) ) )
        | ( in @ X553 @ X551 ) )
      & ( ~ ( in @ X556
            @ ( dsetconstr @ X554
              @ ^ [Z0: $i] : ( X555 @ Z0 ) ) )
        | ( X555 @ X556 ) )
      & ( ( X557 @ ( esk12_1 @ X557 ) )
        | ( X557 @ ( esk11_2 @ X557 @ X558 ) )
        | ~ ( X557 @ X558 ) )
      & ( ~ ( X557 @ X561 )
        | ( ( esk12_1 @ X557 )
          = X561 )
        | ( X557 @ ( esk11_2 @ X557 @ X558 ) )
        | ~ ( X557 @ X558 ) )
      & ( ( X557 @ ( esk12_1 @ X557 ) )
        | ( X558
         != ( esk11_2 @ X557 @ X558 ) )
        | ~ ( X557 @ X558 ) )
      & ( ~ ( X557 @ X561 )
        | ( ( esk12_1 @ X557 )
          = X561 )
        | ( X558
         != ( esk11_2 @ X557 @ X558 ) )
        | ~ ( X557 @ X558 ) )
      & ( ~ ( in @ X563 @ ( prop2set @ X562 ) )
        | X562 )
      & ( ~ ( in @ X564 @ emptyset )
        | X565 )
      & ~ ( in @ X566 @ emptyset )
      & ~ ( in @ X567 @ emptyset )
      & ( ( X568 @ ( esk13_2 @ X568 @ X569 ) )
        | ~ ( X568 @ X569 )
        | ( X568 @ ( esk14_1 @ X568 ) ) )
      & ( ( X569
         != ( esk13_2 @ X568 @ X569 ) )
        | ~ ( X568 @ X569 )
        | ( X568 @ ( esk14_1 @ X568 ) ) )
      & ( ( in @ ( esk16_2 @ X572 @ X573 ) @ X573 )
        | ( X572 = X573 )
        | ( in @ ( esk15_2 @ X572 @ X573 ) @ X572 ) )
      & ( ~ ( in @ ( esk16_2 @ X572 @ X573 ) @ X572 )
        | ( X572 = X573 )
        | ( in @ ( esk15_2 @ X572 @ X573 ) @ X572 ) )
      & ( ( in @ ( esk16_2 @ X572 @ X573 ) @ X573 )
        | ( X572 = X573 )
        | ~ ( in @ ( esk15_2 @ X572 @ X573 ) @ X573 ) )
      & ( ~ ( in @ ( esk16_2 @ X572 @ X573 ) @ X572 )
        | ( X572 = X573 )
        | ~ ( in @ ( esk15_2 @ X572 @ X573 ) @ X573 ) )
      & ( ( in @ ( esk17_1 @ X576 ) @ X576 )
        | ( X576 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X578 ) @ X578 )
        | ( X578 = emptyset ) )
      & ( ~ ( in @ X582
            @ ( dsetconstr @ X580
              @ ^ [Z0: $i] : ( X581 @ Z0 ) ) )
        | ( X581 @ X582 )
        | ~ ( in @ X582 @ X580 ) )
      & ( ~ ( X581 @ X582 )
        | ( in @ X582
          @ ( dsetconstr @ X580
            @ ^ [Z0: $i] : ( X581 @ Z0 ) ) )
        | ~ ( in @ X582 @ X580 ) )
      & ( ( X583 = emptyset )
        | ( in @ ( esk19_1 @ X583 ) @ X583 ) )
      & ( ~ ( in @ X587 @ X585 )
        | ~ ( X586 @ X587 )
        | ( ( dsetconstr @ X585
            @ ^ [Z0: $i] : ( X586 @ Z0 ) )
         != emptyset ) )
      & ( ~ ( in @ X589 @ X588 )
        | ( X588 != emptyset ) )
      & ( in @ X590 @ ( setadjoin @ X590 @ X591 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X594 @ X593 )
        | ( in @ X594 @ ( setadjoin @ X592 @ X593 ) ) )
      & ( ( in @ X597 @ X596 )
        | X598
        | ( X597 = X595 )
        | ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
      & ( ~ X598
        | X598
        | ( X597 = X595 )
        | ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
      & ( ( in @ X597 @ X596 )
        | X598
        | ~ X598
        | ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
      & ( ~ X598
        | X598
        | ~ X598
        | ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
      & ( ~ ( in @ X601 @ ( setadjoin @ X599 @ X600 ) )
        | ( X601 = X599 )
        | ( in @ X601 @ X600 ) )
      & ( ( dsetconstr @ X602
          @ ^ [Z0: $i] : $true )
        = X602 )
      & ( ( in @ ( esk20_2 @ X603 @ X604 ) @ X604 )
        | ( in @ X604 @ ( powerset @ X603 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X603 @ X604 ) @ X603 )
        | ( in @ X604 @ ( powerset @ X603 ) ) )
      & ( in @ emptyset @ ( powerset @ X606 ) )
      & ( in @ emptyset @ ( powerset @ X607 ) )
      & ( ~ ( in @ X609 @ ( powerset @ X608 ) )
        | ~ ( in @ X610 @ X609 )
        | ( in @ X610 @ X608 ) )
      & ( ~ ( in @ X612 @ X613 )
        | ~ ( in @ X613 @ X611 )
        | ( in @ X612 @ ( setunion @ X611 ) ) )
      & ( ( in @ X615 @ ( esk21_3 @ X614 @ X615 @ X616 ) )
        | X616
        | ~ ( in @ X615 @ ( setunion @ X614 ) ) )
      & ( ( in @ ( esk21_3 @ X614 @ X615 @ X616 ) @ X614 )
        | X616
        | ~ ( in @ X615 @ ( setunion @ X614 ) ) )
      & ( ~ X616
        | X616
        | ~ ( in @ X615 @ ( setunion @ X614 ) ) )
      & ( ~ ( in @ X619 @ X618 )
        | ( in @ X619 @ ( powerset @ ( setunion @ X618 ) ) ) )
      & ( ~ ( X620 @ X624 )
        | ( X624
          = ( esk23_1 @ X620 ) )
        | ( X620 @ ( esk22_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 ) )
      & ( ( X625
         != ( esk23_1 @ X620 ) )
        | ( X620 @ X625 )
        | ( X620 @ ( esk22_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 ) )
      & ( ~ ( X620 @ X624 )
        | ( X624
          = ( esk23_1 @ X620 ) )
        | ( X621
         != ( esk22_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 ) )
      & ( ( X625
         != ( esk23_1 @ X620 ) )
        | ( X620 @ X625 )
        | ( X621
         != ( esk22_2 @ X620 @ X621 ) )
        | ~ ( X620 @ X621 ) )
      & ( ( X626 = emptyset )
        | ( in @ ( esk24_1 @ X626 ) @ X626 ) )
      & ( ~ ( in @ X628 @ ( setadjoin @ X629 @ emptyset ) )
        | ( X628 = X629 ) )
      & ( ( X630 = X631 )
        | ~ ( in @ X631 @ ( setadjoin @ X630 @ emptyset ) ) )
      & ( ( X632 != X633 )
        | ( in @ X632 @ ( setadjoin @ X633 @ emptyset ) ) )
      & ( ~ ( in @ X634 @ ( setadjoin @ X635 @ emptyset ) )
        | ( in @ X635 @ ( setadjoin @ X634 @ emptyset ) ) )
      & ( ~ ( in @ X638 @ ( setadjoin @ X636 @ ( setadjoin @ X637 @ emptyset ) ) )
        | ( X638 = X636 )
        | ( X638 = X637 ) )
      & ( in @ X639 @ ( setadjoin @ X639 @ ( setadjoin @ X640 @ emptyset ) ) )
      & ( in @ X642 @ ( setadjoin @ X641 @ ( setadjoin @ X642 @ emptyset ) ) )
      & ( ~ ( in @ X645 @ X643 )
        | ~ ( X644 @ X645 )
        | ( ( dsetconstr @ X643
            @ ^ [Z0: $i] : ( X644 @ Z0 ) )
         != emptyset ) )
      & ( ~ ( in @ X647 @ emptyset )
        | ( X646 @ X647 ) )
      & ( ( in @ ( esk25_2 @ X648 @ X649 ) @ X648 )
        | ~ ( in @ X650 @ X648 )
        | ( X649 @ X650 ) )
      & ( ~ ( X649 @ ( esk25_2 @ X648 @ X649 ) )
        | ~ ( in @ X650 @ X648 )
        | ( X649 @ X650 ) )
      & ( ( in @ ( esk26_2 @ X652 @ X653 ) @ X652 )
        | ~ ( in @ X655 @ X652 )
        | ~ ( X653 @ X655 ) )
      & ( ( X653 @ ( esk26_2 @ X652 @ X653 ) )
        | ~ ( in @ X655 @ X652 )
        | ~ ( X653 @ X655 ) )
      & ( ( in @ ( esk27_2 @ X656 @ X657 ) @ X656 )
        | ~ ( in @ X659 @ X656 )
        | ~ ( X657 @ X659 ) )
      & ( ( X657 @ ( esk27_2 @ X656 @ X657 ) )
        | ~ ( in @ X659 @ X656 )
        | ~ ( X657 @ X659 ) )
      & ( ( in @ ( esk28_2 @ X660 @ X661 ) @ X660 )
        | ~ ( in @ X662 @ X660 )
        | ( X661 @ X662 ) )
      & ( ~ ( X661 @ ( esk28_2 @ X660 @ X661 ) )
        | ~ ( in @ X662 @ X660 )
        | ( X661 @ X662 ) )
      & ( ~ X664
        | ( in @ emptyset @ ( prop2set @ X664 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk29_2 @ X665 @ X666 ) @ X665 )
        | ~ ( in @ X668 @ X665 )
        | ~ ( X666 @ X668 ) )
      & ( ( X666 @ ( esk29_2 @ X665 @ X666 ) )
        | ~ ( in @ X668 @ X665 )
        | ~ ( X666 @ X668 ) )
      & ( ( in @ ( esk30_2 @ X669 @ X670 ) @ X669 )
        | ~ ( in @ X671 @ X669 )
        | ( X670 @ X671 ) )
      & ( ~ ( X670 @ ( esk30_2 @ X669 @ X670 ) )
        | ~ ( in @ X671 @ X669 )
        | ( X670 @ X671 ) )
      & ( ( X673 @ ( esk32_1 @ X673 ) )
        | ( X673 @ ( esk31_2 @ X673 @ X674 ) )
        | ~ ( X673 @ X674 ) )
      & ( ~ ( X673 @ X677 )
        | ( ( esk32_1 @ X673 )
          = X677 )
        | ( X673 @ ( esk31_2 @ X673 @ X674 ) )
        | ~ ( X673 @ X674 ) )
      & ( ( X673 @ ( esk32_1 @ X673 ) )
        | ( X674
         != ( esk31_2 @ X673 @ X674 ) )
        | ~ ( X673 @ X674 ) )
      & ( ~ ( X673 @ X677 )
        | ( ( esk32_1 @ X673 )
          = X677 )
        | ( X674
         != ( esk31_2 @ X673 @ X674 ) )
        | ~ ( X673 @ X674 ) )
      & ( ( X678 @ ( esk35_1 @ X678 ) )
        | ( X678 @ ( esk33_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ~ ( X678 @ X683 )
        | ( ( esk35_1 @ X678 )
          = X683 )
        | ( X678 @ ( esk33_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ( X678 @ ( esk35_1 @ X678 ) )
        | ( X678 @ ( esk34_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ~ ( X678 @ X683 )
        | ( ( esk35_1 @ X678 )
          = X683 )
        | ( X678 @ ( esk34_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ( X678 @ ( esk35_1 @ X678 ) )
        | ( ( esk33_1 @ X678 )
         != ( esk34_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ~ ( X678 @ X683 )
        | ( ( esk35_1 @ X678 )
          = X683 )
        | ( ( esk33_1 @ X678 )
         != ( esk34_1 @ X678 ) )
        | ~ ( X678 @ X679 ) )
      & ( ( X684 @ ( esk37_1 @ X684 ) )
        | ~ ( X684 @ ( esk36_2 @ X684 @ X685 ) )
        | ( ( esk36_2 @ X684 @ X685 )
         != X685 ) )
      & ( ~ ( X684 @ X688 )
        | ( ( esk37_1 @ X684 )
          = X688 )
        | ~ ( X684 @ ( esk36_2 @ X684 @ X685 ) )
        | ( ( esk36_2 @ X684 @ X685 )
         != X685 ) )
      & ( ( X684 @ ( esk37_1 @ X684 ) )
        | ( X684 @ ( esk36_2 @ X684 @ X685 ) )
        | ( ( esk36_2 @ X684 @ X685 )
          = X685 ) )
      & ( ~ ( X684 @ X688 )
        | ( ( esk37_1 @ X684 )
          = X688 )
        | ( X684 @ ( esk36_2 @ X684 @ X685 ) )
        | ( ( esk36_2 @ X684 @ X685 )
          = X685 ) )
      & ( ( X689 != X690 )
        | ( X691 != X692 )
        | ~ ( in @ X691 @ X689 )
        | ( in @ X692 @ X690 ) )
      & ( ~ ( in @ X695 @ X693 )
        | ( in @ X696 @ X694 )
        | ( X695 != X696 )
        | ( X693 != X694 ) )
      & ( ~ ( in @ X696 @ X694 )
        | ( in @ X695 @ X693 )
        | ( X695 != X696 )
        | ( X693 != X694 ) )
      & ( ( X697 @ ( esk38_2 @ X697 @ X698 ) )
        | ~ ( X697 @ X698 )
        | ~ ( X697 @ X700 )
        | ~ ( X697 @ X701 )
        | ( X700 = X701 ) )
      & ( ( X698
         != ( esk38_2 @ X697 @ X698 ) )
        | ~ ( X697 @ X698 )
        | ~ ( X697 @ X700 )
        | ~ ( X697 @ X701 )
        | ( X700 = X701 ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( ( esk39_2 @ X702 @ X703 )
          = ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X703 @ X709 )
        | ( ( esk42_2 @ X702 @ X703 )
          = X709 )
        | ( X706
         != ( esk41_3 @ X702 @ X703 @ X706 ) )
        | ~ ( X702 @ X706 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( ~ ( X702 @ X713 )
        | ( ( esk44_2 @ X702 @ X703 )
          = X713 )
        | ( X710
         != ( esk43_3 @ X702 @ X703 @ X710 ) )
        | ~ ( X703 @ X710 )
        | ( X702 @ ( esk39_2 @ X702 @ X703 ) )
        | ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
      & ( emptyset = emptyset )
      & ( ( X714 != X715 )
        | ( X716 != X717 )
        | ( ( setadjoin @ X714 @ X716 )
          = ( setadjoin @ X715 @ X717 ) ) )
      & ( ( X718 != X719 )
        | ( ( powerset @ X718 )
          = ( powerset @ X719 ) ) )
      & ( ( X720 != X721 )
        | ( ( setunion @ X720 )
          = ( setunion @ X721 ) ) )
      & ( omega = omega )
      & ( ( X722 @ ( esk45_2 @ X722 @ X723 ) )
        | ~ ( X722 @ X723 )
        | ~ ( X722 @ X725 )
        | ~ ( X722 @ X726 )
        | ( X725 = X726 ) )
      & ( ( X723
         != ( esk45_2 @ X722 @ X723 ) )
        | ~ ( X722 @ X723 )
        | ~ ( X722 @ X725 )
        | ~ ( X722 @ X726 )
        | ( X725 = X726 ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( ( esk46_2 @ X727 @ X728 )
          = ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( ( esk46_2 @ X727 @ X728 )
          = ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( ( esk46_2 @ X727 @ X728 )
          = ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( ( esk46_2 @ X727 @ X728 )
          = ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( X733
         != ( esk49_3 @ X727 @ X728 @ X733 ) )
        | ~ ( X728 @ X733 )
        | ( ( descr
            @ ^ [Z0: $i] : ( X727 @ Z0 ) )
          = ( descr
            @ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
        | ( X731
         != ( esk48_3 @ X727 @ X728 @ X731 ) )
        | ~ ( X727 @ X731 )
        | ( X727 @ ( esk46_2 @ X727 @ X728 ) )
        | ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
      & ( ( in @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) @ X735 )
        | ( ( dsetconstr @ X735
            @ ^ [Z0: $i] : ( X737 @ Z0 ) )
          = ( dsetconstr @ X736
            @ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
        | ( X735 != X736 ) )
      & ( ( in @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) @ X736 )
        | ( ( dsetconstr @ X735
            @ ^ [Z0: $i] : ( X737 @ Z0 ) )
          = ( dsetconstr @ X736
            @ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
        | ( X735 != X736 ) )
      & ( ( ( esk50_4 @ X735 @ X736 @ X737 @ X738 )
          = ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
        | ( ( dsetconstr @ X735
            @ ^ [Z0: $i] : ( X737 @ Z0 ) )
          = ( dsetconstr @ X736
            @ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
        | ( X735 != X736 ) )
      & ( ~ ( X737 @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) )
        | ~ ( X738 @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
        | ( ( dsetconstr @ X735
            @ ^ [Z0: $i] : ( X737 @ Z0 ) )
          = ( dsetconstr @ X736
            @ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
        | ( X735 != X736 ) )
      & ( ( X737 @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) )
        | ( X738 @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
        | ( ( dsetconstr @ X735
            @ ^ [Z0: $i] : ( X737 @ Z0 ) )
          = ( dsetconstr @ X736
            @ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
        | ( X735 != X736 ) )
      & ( ( in @ ( esk52_2 @ X741 @ X742 ) @ X741 )
        | ~ ( in @ X744 @ X741 )
        | ( in @ X744 @ X742 ) )
      & ( ~ ( in @ ( esk52_2 @ X741 @ X742 ) @ X742 )
        | ~ ( in @ X744 @ X741 )
        | ( in @ X744 @ X742 ) )
      & ( esk53_0 = esk54_0 )
      & ( in @ esk55_0 @ esk54_0 )
      & ~ ( in @ esk55_0 @ esk53_0 ) ),
    inference(distribute,[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_120])])])])])]) ).

thf(c_0_122,negated_conjecture,
    in @ esk55_0 @ esk54_0,
    inference(split_conjunct,[status(thm)],[c_0_121]) ).

thf(c_0_123,negated_conjecture,
    esk53_0 = esk54_0,
    inference(split_conjunct,[status(thm)],[c_0_121]) ).

thf(c_0_124,negated_conjecture,
    ~ ( in @ esk55_0 @ esk53_0 ),
    inference(split_conjunct,[status(thm)],[c_0_121]) ).

thf(c_0_125,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_124]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SEU560^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n019.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sun May 19 17:41:37 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.17/0.45  Running higher-order theorem proving
% 0.17/0.45  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
% 0.35/300.10  # Version: 3.1.0-ho
% 0.35/300.10  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10  # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10  # Starting sh5l with 300s (1) cores
% 0.35/300.10  # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10  # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10  # new_bool_2 with pid 16939 completed with status 0
% 0.35/300.10  # Result found by new_bool_2
% 0.35/300.10  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10  # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10  # Starting sh5l with 300s (1) cores
% 0.35/300.10  # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10  # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.35/300.10  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.35/300.10  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/300.10  # Starting ho_unfolding_3 with 163s (1) cores
% 0.35/300.10  # ho_unfolding_3 with pid 16940 completed with status 0
% 0.35/300.10  # Result found by ho_unfolding_3
% 0.35/300.10  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10  # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10  # Starting sh5l with 300s (1) cores
% 0.35/300.10  # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10  # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.35/300.10  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.35/300.10  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/300.10  # Starting ho_unfolding_3 with 163s (1) cores
% 0.35/300.10  # Preprocessing time       : 0.005 s
% 0.35/300.10  # Presaturation interreduction done
% 0.35/300.10  
% 0.35/300.10  # Proof found!
% 0.35/300.10  # SZS status Theorem
% 0.35/300.10  # SZS output start CNFRefutation
% See solution above
% 0.35/300.10  # Parsed axioms                        : 171
% 0.35/300.10  # Removed by relevancy pruning/SinE    : 92
% 0.35/300.10  # Initial clauses                      : 187
% 0.35/300.10  # Removed in clause preprocessing      : 12
% 0.35/300.10  # Initial clauses in saturation        : 175
% 0.35/300.10  # Processed clauses                    : 6
% 0.35/300.10  # ...of these trivial                  : 0
% 0.35/300.10  # ...subsumed                          : 0
% 0.35/300.10  # ...remaining for further processing  : 5
% 0.35/300.10  # Other redundant clauses eliminated   : 0
% 0.35/300.10  # Clauses deleted for lack of memory   : 0
% 0.35/300.10  # Backward-subsumed                    : 0
% 0.35/300.10  # Backward-rewritten                   : 0
% 0.35/300.10  # Generated clauses                    : 0
% 0.35/300.10  # ...of the previous two non-redundant : 0
% 0.35/300.10  # ...aggressively subsumed             : 0
% 0.35/300.10  # Contextual simplify-reflections      : 0
% 0.35/300.10  # Paramodulations                      : 0
% 0.35/300.10  # Factorizations                       : 0
% 0.35/300.10  # NegExts                              : 0
% 0.35/300.10  # Equation resolutions                 : 0
% 0.35/300.10  # Disequality decompositions           : 0
% 0.35/300.10  # Total rewrite steps                  : 1
% 0.35/300.10  # ...of those cached                   : 0
% 0.35/300.10  # Propositional unsat checks           : 0
% 0.35/300.10  #    Propositional check models        : 0
% 0.35/300.10  #    Propositional check unsatisfiable : 0
% 0.35/300.10  #    Propositional clauses             : 0
% 0.35/300.10  #    Propositional clauses after purity: 0
% 0.35/300.10  #    Propositional unsat core size     : 0
% 0.35/300.10  #    Propositional preprocessing time  : 0.000
% 0.35/300.10  #    Propositional encoding time       : 0.000
% 0.35/300.10  #    Propositional solver time         : 0.000
% 0.35/300.10  #    Success case prop preproc time    : 0.000
% 0.35/300.10  #    Success case prop encoding time   : 0.000
% 0.35/300.10  #    Success case prop solver time     : 0.000
% 0.35/300.10  # Current number of processed clauses  : 5
% 0.35/300.10  #    Positive orientable unit clauses  : 4
% 0.35/300.10  #    Positive unorientable unit clauses: 0
% 0.35/300.10  #    Negative unit clauses             : 1
% 0.35/300.10  #    Non-unit-clauses                  : 0
% 0.35/300.10  # Current number of unprocessed clauses: 169
% 0.35/300.10  # ...number of literals in the above   : 615
% 0.35/300.10  # Current number of archived formulas  : 0
% 0.35/300.10  # Current number of archived clauses   : 0
% 0.35/300.10  # Clause-clause subsumption calls (NU) : 0
% 0.35/300.10  # Rec. Clause-clause subsumption calls : 0
% 0.35/300.10  # Non-unit clause-clause subsumptions  : 0
% 0.35/300.10  # Unit Clause-clause subsumption calls : 0
% 0.35/300.10  # Rewrite failures with RHS unbound    : 0
% 0.35/300.10  # BW rewrite match attempts            : 0
% 0.35/300.10  # BW rewrite match successes           : 0
% 0.35/300.10  # Condensation attempts                : 6
% 0.35/300.10  # Condensation successes               : 0
% 0.35/300.10  # Termbank termtop insertions          : 21365
% 0.35/300.10  # Search garbage collected termcells   : 7642
% 0.35/300.10  
% 0.35/300.10  # -------------------------------------------------
% 0.35/300.10  # User time                : 0.013 s
% 0.35/300.10  # System time              : 0.010 s
% 0.35/300.10  # Total time               : 0.023 s
% 0.35/300.10  # Maximum resident set size: 4288 pages
% 0.35/300.10  
% 0.35/300.10  # -------------------------------------------------
% 0.35/300.10  # User time                : 0.017 s
% 0.35/300.10  # System time              : 0.013 s
% 0.35/300.10  # Total time               : 0.030 s
% 0.35/300.10  # Maximum resident set size: 1920 pages
% 0.35/300.10  % E---3.1 exiting
% 0.35/300.10  % E exiting
%------------------------------------------------------------------------------