TSTP Solution File: SEU592^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU592^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 03:28:25 EDT 2024

% Result   : Timeout 0.82s 300.03s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  292
% Syntax   : Number of formulae    :  341 (  28 unt; 179 typ;   0 def)
%            Number of atoms       : 1287 ( 336 equ;   0 cnn)
%            Maximal formula atoms :  386 (   7 avg)
%            Number of connectives : 4944 ( 425   ~; 479   |; 298   &;2940   @)
%                                         ( 173 <=>; 629  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  473 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  319 ( 319   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  182 ( 179 usr; 115 con; 0-4 aty)
%            Number of variables   : 1102 (  73   ^ 925   !; 104   ?;1102   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_90,type,
    set2prop: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_147,type,
    epred1_0: $o ).

thf(decl_148,type,
    esk1_2: $i > $i > $i ).

thf(decl_149,type,
    esk2_2: $i > $i > $i ).

thf(decl_150,type,
    esk3_2: $i > $i > $i ).

thf(decl_151,type,
    esk4_1: $i > $i ).

thf(decl_152,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_153,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_154,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_155,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_156,type,
    esk9_1: $i > $i ).

thf(decl_157,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_158,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_159,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_160,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_161,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_162,type,
    esk15_2: $i > $i > $i ).

thf(decl_163,type,
    esk16_2: $i > $i > $i ).

thf(decl_164,type,
    esk17_1: $i > $i ).

thf(decl_165,type,
    esk18_1: $i > $i ).

thf(decl_166,type,
    esk19_1: $i > $i ).

thf(decl_167,type,
    esk20_2: $i > $i > $i ).

thf(decl_168,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_169,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_170,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_171,type,
    esk24_1: $i > $i ).

thf(decl_172,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_173,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_174,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_175,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_176,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_177,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_178,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_179,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_180,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_181,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_182,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_183,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_184,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_185,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_186,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_187,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_188,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_189,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_190,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_191,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_192,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_193,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_194,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_195,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_196,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_197,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_198,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_199,type,
    esk52_2: $i > $i > $i ).

thf(decl_200,type,
    esk53_2: $i > $i > $i ).

thf(decl_201,type,
    esk54_0: $i ).

thf(decl_202,type,
    esk55_0: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_0_112,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_113,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_114,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_115,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_116,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_117,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X312: $i] :
                  ( ( X6 @ X2 @ X312 )
                  & ! [X313: $i] :
                      ( ( X6 @ X2 @ X313 )
                     => ( X312 = X313 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_112,c_0_113]) ).

thf(c_0_128,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X314: $i] :
              ( ( X1 @ X314 )
              & ! [X315: $i] :
                  ( ( X1 @ X315 )
                 => ( X314 = X315 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_114,c_0_113]) ).

thf(c_0_129,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_130,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_131,plain,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
       => ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrER]) ).

thf(c_0_132,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X316: $i] :
              ( ( X1 @ X316 )
              & ! [X317: $i] :
                  ( ( X1 @ X317 )
                 => ( X316 = X317 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_115,c_0_113]) ).

thf(c_0_133,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X318: $i] :
              ( ( X1 @ X318 )
              & ! [X319: $i] :
                  ( ( X1 @ X319 )
                 => ( X318 = X319 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_116,c_0_113]) ).

thf(c_0_134,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_135,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_117]) ).

thf(c_0_136,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_118,c_0_117]) ).

thf(c_0_137,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_117]) ).

thf(c_0_138,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_139,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X320: $i] :
              ( ( X1 @ X320 )
              & ! [X321: $i] :
                  ( ( X1 @ X321 )
                 => ( X320 = X321 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_119,c_0_113]) ).

thf(c_0_140,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_117]) ).

thf(c_0_141,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_142,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X322: $i] :
              ( ( X1 @ X322 )
              & ! [X323: $i] :
                  ( ( X1 @ X323 )
                 => ( X322 = X323 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_120,c_0_113]) ).

thf(c_0_143,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X324: $i] :
                ( ( X1 @ X324 )
                & ! [X325: $i] :
                    ( ( X1 @ X325 )
                   => ( X324 = X325 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_121,c_0_113]) ).

thf(c_0_144,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X326: $i] :
              ( ( X1 @ X326 )
              & ! [X327: $i] :
                  ( ( X1 @ X327 )
                 => ( X326 = X327 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_122,c_0_113]) ).

thf(c_0_145,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X328: $i] :
              ( ( X1 @ X328 )
              & ! [X329: $i] :
                  ( ( X1 @ X329 )
                 => ( X328 = X329 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_123,c_0_113]) ).

thf(c_0_146,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X330: $i] :
                ( ( X1 @ X330 )
                & ! [X331: $i] :
                    ( ( X1 @ X331 )
                   => ( X330 = X331 ) ) )
          <=> ? [X332: $i] :
                ( ( X17 @ X332 )
                & ! [X333: $i] :
                    ( ( X17 @ X333 )
                   => ( X332 = X333 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_124,c_0_113]) ).

thf(c_0_147,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X334: $i] :
              ( ( X1 @ X334 )
              & ! [X335: $i] :
                  ( ( X1 @ X335 )
                 => ( X334 = X335 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_125,c_0_113]) ).

thf(c_0_148,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X336: $i] :
                ( ( X1 @ X336 )
                & ! [X337: $i] :
                    ( ( X1 @ X337 )
                   => ( X336 = X337 ) ) )
           => ( ? [X338: $i] :
                  ( ( X17 @ X338 )
                  & ! [X339: $i] :
                      ( ( X17 @ X339 )
                     => ( X338 = X339 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_126,c_0_113]) ).

thf(c_0_149,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_150,plain,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ ( powerset @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[sepInPowerset]) ).

thf(c_0_151,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_152,plain,
    ( epred1_0
  <=> ! [X369: $i] :
      ? [X370: $i] :
        ( ! [X371: $i] :
            ( ( in @ X371 @ X370 )
           => ! [X372: $i] :
                ( ( in @ X372 @ X371 )
               => ( in @ X372 @ X369 ) ) )
        & ! [X373: $i,X374: $i] :
            ( ( ( in @ X373 @ X369 )
              & ( in @ X374 @ X369 ) )
           => ( ! [X375: $i] :
                  ( ( in @ X375 @ X370 )
                 => ( ( in @ X373 @ X375 )
                  <=> ( in @ X374 @ X375 ) ) )
             => ( X373 = X374 ) ) )
        & ! [X376: $i,X377: $i] :
            ( ( ( in @ X376 @ X370 )
              & ( in @ X377 @ X370 ) )
           => ( ! [X378: $i] :
                  ( ( in @ X378 @ X376 )
                 => ( in @ X378 @ X377 ) )
              | ! [X379: $i] :
                  ( ( in @ X379 @ X377 )
                 => ( in @ X379 @ X376 ) ) ) )
        & ! [X380: $i] :
            ( ( ! [X381: $i] :
                  ( ( in @ X381 @ X380 )
                 => ( in @ X381 @ X369 ) )
              & ? [X382: $i] : ( in @ X382 @ X380 ) )
           => ? [X383: $i,X384: $i] :
                ( ( in @ X383 @ X370 )
                & ( in @ X384 @ X380 )
                & ~ ? [X385: $i] :
                      ( ( in @ X385 @ X383 )
                      & ( in @ X385 @ X380 ) )
                & ! [X386: $i] :
                    ( ( in @ X386 @ X370 )
                   => ( ! [X387: $i] :
                          ( ( in @ X387 @ X386 )
                         => ( in @ X387 @ X383 ) )
                      | ( in @ X384 @ X386 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_153,negated_conjecture,
    ~ ( ! [X340: $i,X341: $i] :
          ( ! [X342: $i] :
              ( ( in @ X342 @ X340 )
            <=> ( in @ X342 @ X341 ) )
         => ( X340 = X341 ) )
     => ( ! [X343: $i] :
            ~ ( in @ X343 @ emptyset )
       => ( ! [X344: $i,X345: $i,X346: $i] :
              ( ( in @ X346 @ ( setadjoin @ X344 @ X345 ) )
            <=> ( ( X346 = X344 )
                | ( in @ X346 @ X345 ) ) )
         => ( ! [X347: $i,X348: $i] :
                ( ( in @ X348 @ ( powerset @ X347 ) )
              <=> ! [X349: $i] :
                    ( ( in @ X349 @ X348 )
                   => ( in @ X349 @ X347 ) ) )
           => ( ! [X350: $i,X351: $i] :
                  ( ( in @ X351 @ ( setunion @ X350 ) )
                <=> ? [X352: $i] :
                      ( ( in @ X351 @ X352 )
                      & ( in @ X352 @ X350 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X353: $i] :
                      ( ( in @ X353 @ omega )
                     => ( in @ ( setadjoin @ X353 @ X353 ) @ omega ) )
                 => ( ! [X354: $i] :
                        ( ( ( in @ emptyset @ X354 )
                          & ! [X355: $i] :
                              ( ( ( in @ X355 @ omega )
                                & ( in @ X355 @ X354 ) )
                             => ( in @ ( setadjoin @ X355 @ X355 ) @ X354 ) ) )
                       => ! [X356: $i] :
                            ( ( in @ X356 @ omega )
                           => ( in @ X356 @ X354 ) ) )
                   => ( ! [X357: $i > $i > $o,X358: $i] :
                          ( ! [X359: $i] :
                              ( ( in @ X359 @ X358 )
                             => ? [X360: $i] :
                                  ( ( X357 @ X359 @ X360 )
                                  & ! [X361: $i] :
                                      ( ( X357 @ X359 @ X361 )
                                     => ( X360 = X361 ) ) ) )
                         => ? [X362: $i] :
                            ! [X363: $i] :
                              ( ( in @ X363 @ X362 )
                            <=> ? [X364: $i] :
                                  ( ( in @ X364 @ X358 )
                                  & ( X357 @ X364 @ X363 ) ) ) )
                     => ( ! [X365: $i] :
                            ( ? [X366: $i] : ( in @ X366 @ X365 )
                           => ? [X367: $i] :
                                ( ( in @ X367 @ X365 )
                                & ~ ? [X368: $i] :
                                      ( ( in @ X368 @ X367 )
                                      & ( in @ X368 @ X365 ) ) ) )
                       => ( epred1_0
                         => ( ! [X388: $i > $o] :
                                ( ? [X389: $i] :
                                    ( ( X388 @ X389 )
                                    & ! [X390: $i] :
                                        ( ( X388 @ X390 )
                                       => ( X389 = X390 ) ) )
                               => ( X388
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X388 @ Z0 ) ) ) )
                           => ( ! [X391: $i,X392: $i > $o,X393: $i] :
                                  ( ( in @ X393 @ X391 )
                                 => ( ( X392 @ X393 )
                                   => ( in @ X393 @ ( dsetconstr @ X391 @ X392 ) ) ) )
                             => ( ! [X394: $i,X395: $i > $o,X396: $i] :
                                    ( ( in @ X396 @ ( dsetconstr @ X394 @ X395 ) )
                                   => ( in @ X396 @ X394 ) )
                               => ( ! [X397: $i,X398: $i > $o,X399: $i] :
                                      ( ( in @ X399 @ ( dsetconstr @ X397 @ X398 ) )
                                     => ( X398 @ X399 ) )
                                 => ( ! [X400: $i > $o] :
                                        ( ? [X401: $i] :
                                            ( ( X400 @ X401 )
                                            & ! [X402: $i] :
                                                ( ( X400 @ X402 )
                                               => ( X401 = X402 ) ) )
                                       => ? [X403: $i] :
                                            ( ( X400 @ X403 )
                                            & ! [X404: $i] :
                                                ( ( X400 @ X404 )
                                               => ( X403 = X404 ) ) ) )
                                   => ( ! [X405: $o,X406: $i] :
                                          ( ( in @ X406 @ ( prop2set @ X405 ) )
                                         => X405 )
                                     => ( ! [X407: $i] :
                                            ( ( in @ X407 @ emptyset )
                                           => ! [X408: $o] : X408 )
                                       => ( ! [X409: $i] :
                                              ( ( in @ X409 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X410: $i] :
                                                ~ ( in @ X410 @ emptyset )
                                           => ( ! [X411: $i > $o] :
                                                  ( ? [X412: $i] :
                                                      ( ( X411 @ X412 )
                                                      & ! [X413: $i] :
                                                          ( ( X411 @ X413 )
                                                         => ( X412 = X413 ) ) )
                                                 => ? [X414: $i] : ( X411 @ X414 ) )
                                             => ( ! [X415: $i,X416: $i] :
                                                    ( ! [X417: $i] :
                                                        ( ( in @ X417 @ X415 )
                                                       => ( in @ X417 @ X416 ) )
                                                   => ( ! [X418: $i] :
                                                          ( ( in @ X418 @ X416 )
                                                         => ( in @ X418 @ X415 ) )
                                                     => ( X415 = X416 ) ) )
                                               => ( ! [X419: $i] :
                                                      ( ! [X420: $i] :
                                                          ~ ( in @ X420 @ X419 )
                                                     => ( X419 = emptyset ) )
                                                 => ( ! [X421: $i] :
                                                        ( ! [X422: $i] :
                                                            ~ ( in @ X422 @ X421 )
                                                       => ( X421 = emptyset ) )
                                                   => ( ! [X423: $i,X424: $i > $o,X425: $i] :
                                                          ( ( in @ X425 @ X423 )
                                                         => ( ( in @ X425 @ ( dsetconstr @ X423 @ X424 ) )
                                                          <=> ( X424 @ X425 ) ) )
                                                     => ( ! [X426: $i] :
                                                            ( ( X426 != emptyset )
                                                           => ? [X427: $i] : ( in @ X427 @ X426 ) )
                                                       => ( ! [X428: $i,X429: $i > $o,X430: $i] :
                                                              ( ( in @ X430 @ X428 )
                                                             => ( ( X429 @ X430 )
                                                               => ( ( dsetconstr @ X428 @ X429 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X431: $i] :
                                                                ( ? [X432: $i] : ( in @ X432 @ X431 )
                                                               => ( X431 != emptyset ) )
                                                           => ( ! [X433: $i,X434: $i] : ( in @ X433 @ ( setadjoin @ X433 @ X434 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X435: $i,X436: $i,X437: $i] :
                                                                      ( ( in @ X437 @ X436 )
                                                                     => ( in @ X437 @ ( setadjoin @ X435 @ X436 ) ) )
                                                                 => ( ! [X438: $i,X439: $i,X440: $i] :
                                                                        ( ( in @ X440 @ ( setadjoin @ X438 @ X439 ) )
                                                                       => ! [X441: $o] :
                                                                            ( ( ( X440 = X438 )
                                                                             => X441 )
                                                                           => ( ( ( in @ X440 @ X439 )
                                                                               => X441 )
                                                                             => X441 ) ) )
                                                                   => ( ! [X442: $i,X443: $i,X444: $i] :
                                                                          ( ( in @ X444 @ ( setadjoin @ X442 @ X443 ) )
                                                                         => ( ( X444 = X442 )
                                                                            | ( in @ X444 @ X443 ) ) )
                                                                     => ( ! [X445: $i] :
                                                                            ( ( dsetconstr @ X445
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X445 )
                                                                       => ( ! [X446: $i,X447: $i] :
                                                                              ( ! [X448: $i] :
                                                                                  ( ( in @ X448 @ X447 )
                                                                                 => ( in @ X448 @ X446 ) )
                                                                             => ( in @ X447 @ ( powerset @ X446 ) ) )
                                                                         => ( ! [X449: $i] : ( in @ emptyset @ ( powerset @ X449 ) )
                                                                           => ( ! [X450: $i] : ( in @ emptyset @ ( powerset @ X450 ) )
                                                                             => ( ! [X451: $i,X452: $i,X453: $i] :
                                                                                    ( ( in @ X452 @ ( powerset @ X451 ) )
                                                                                   => ( ( in @ X453 @ X452 )
                                                                                     => ( in @ X453 @ X451 ) ) )
                                                                               => ( ! [X454: $i,X455: $i,X456: $i] :
                                                                                      ( ( in @ X455 @ X456 )
                                                                                     => ( ( in @ X456 @ X454 )
                                                                                       => ( in @ X455 @ ( setunion @ X454 ) ) ) )
                                                                                 => ( ! [X457: $i,X458: $i] :
                                                                                        ( ( in @ X458 @ ( setunion @ X457 ) )
                                                                                       => ! [X459: $o] :
                                                                                            ( ! [X460: $i] :
                                                                                                ( ( in @ X458 @ X460 )
                                                                                               => ( ( in @ X460 @ X457 )
                                                                                                 => X459 ) )
                                                                                           => X459 ) )
                                                                                   => ( ! [X461: $i,X462: $i] :
                                                                                          ( ( in @ X462 @ X461 )
                                                                                         => ( in @ X462 @ ( powerset @ ( setunion @ X461 ) ) ) )
                                                                                     => ( ! [X463: $i > $o] :
                                                                                            ( ? [X464: $i] :
                                                                                                ( ( X463 @ X464 )
                                                                                                & ! [X465: $i] :
                                                                                                    ( ( X463 @ X465 )
                                                                                                   => ( X464 = X465 ) ) )
                                                                                           => ? [X466: $i] :
                                                                                              ! [X467: $i] :
                                                                                                ( ( X463 @ X467 )
                                                                                              <=> ( X467 = X466 ) ) )
                                                                                       => ( ! [X468: $i] :
                                                                                              ( ( X468 != emptyset )
                                                                                             => ? [X469: $i] :
                                                                                                  ( ( in @ X469 @ X468 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X470: $i,X471: $i] :
                                                                                                ( ( in @ X470 @ ( setadjoin @ X471 @ emptyset ) )
                                                                                               => ( X470 = X471 ) )
                                                                                           => ( ! [X472: $i,X473: $i] :
                                                                                                  ( ( X472 != X473 )
                                                                                                 => ~ ( in @ X473 @ ( setadjoin @ X472 @ emptyset ) ) )
                                                                                             => ( ! [X474: $i,X475: $i] :
                                                                                                    ( ( X474 = X475 )
                                                                                                   => ( in @ X474 @ ( setadjoin @ X475 @ emptyset ) ) )
                                                                                               => ( ! [X476: $i,X477: $i] :
                                                                                                      ( ( in @ X476 @ ( setadjoin @ X477 @ emptyset ) )
                                                                                                     => ( in @ X477 @ ( setadjoin @ X476 @ emptyset ) ) )
                                                                                                 => ( ! [X478: $i,X479: $i,X480: $i] :
                                                                                                        ( ( in @ X480 @ ( setadjoin @ X478 @ ( setadjoin @ X479 @ emptyset ) ) )
                                                                                                       => ( ( X480 = X478 )
                                                                                                          | ( X480 = X479 ) ) )
                                                                                                   => ( ! [X481: $i,X482: $i] : ( in @ X481 @ ( setadjoin @ X481 @ ( setadjoin @ X482 @ emptyset ) ) )
                                                                                                     => ( ! [X483: $i,X484: $i] : ( in @ X484 @ ( setadjoin @ X483 @ ( setadjoin @ X484 @ emptyset ) ) )
                                                                                                       => ( ! [X485: $i,X486: $i > $o] :
                                                                                                              ( ? [X487: $i] :
                                                                                                                  ( ( in @ X487 @ X485 )
                                                                                                                  & ( X486 @ X487 ) )
                                                                                                             => ( ( ( dsetconstr @ X485 @ X486 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X488: $i > $o,X489: $i] :
                                                                                                                ( ( in @ X489 @ emptyset )
                                                                                                               => ( X488 @ X489 ) )
                                                                                                           => ( ! [X490: $i,X491: $i > $o] :
                                                                                                                  ( ~ ! [X492: $i] :
                                                                                                                        ( ( in @ X492 @ X490 )
                                                                                                                       => ( X491 @ X492 ) )
                                                                                                                 => ? [X493: $i] :
                                                                                                                      ( ( in @ X493 @ X490 )
                                                                                                                      & ~ ( X491 @ X493 ) ) )
                                                                                                             => ( ! [X494: $i,X495: $i > $o] :
                                                                                                                    ( ! [X496: $i] :
                                                                                                                        ( ( in @ X496 @ X494 )
                                                                                                                       => ~ ( X495 @ X496 ) )
                                                                                                                   => ~ ? [X497: $i] :
                                                                                                                          ( ( in @ X497 @ X494 )
                                                                                                                          & ( X495 @ X497 ) ) )
                                                                                                               => ( ! [X498: $i,X499: $i > $o] :
                                                                                                                      ( ~ ? [X500: $i] :
                                                                                                                            ( ( in @ X500 @ X498 )
                                                                                                                            & ( X499 @ X500 ) )
                                                                                                                     => ! [X501: $i] :
                                                                                                                          ( ( in @ X501 @ X498 )
                                                                                                                         => ~ ( X499 @ X501 ) ) )
                                                                                                                 => ( ! [X502: $i,X503: $i > $o] :
                                                                                                                        ( ? [X504: $i] :
                                                                                                                            ( ( in @ X504 @ X502 )
                                                                                                                            & ~ ( X503 @ X504 ) )
                                                                                                                       => ~ ! [X505: $i] :
                                                                                                                              ( ( in @ X505 @ X502 )
                                                                                                                             => ( X503 @ X505 ) ) )
                                                                                                                   => ( ! [X506: $o] :
                                                                                                                          ( X506
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X506 ) ) )
                                                                                                                     => ( ! [X507: $o] :
                                                                                                                            ( X507
                                                                                                                           => ( set2prop @ ( prop2set @ X507 ) ) )
                                                                                                                       => ( ! [X508: $i,X509: $i > $o] :
                                                                                                                              ( ~ ? [X510: $i] :
                                                                                                                                    ( ( in @ X510 @ X508 )
                                                                                                                                    & ( X509 @ X510 ) )
                                                                                                                             => ! [X511: $i] :
                                                                                                                                  ( ( in @ X511 @ X508 )
                                                                                                                                 => ~ ( X509 @ X511 ) ) )
                                                                                                                         => ( ! [X512: $i,X513: $i > $o] :
                                                                                                                                ( ~ ! [X514: $i] :
                                                                                                                                      ( ( in @ X514 @ X512 )
                                                                                                                                     => ( X513 @ X514 ) )
                                                                                                                               => ? [X515: $i] :
                                                                                                                                    ( ( in @ X515 @ X512 )
                                                                                                                                    & ~ ( X513 @ X515 ) ) )
                                                                                                                           => ( ! [X516: $i > $o] :
                                                                                                                                  ( ? [X517: $i] :
                                                                                                                                      ( ( X516 @ X517 )
                                                                                                                                      & ! [X518: $i] :
                                                                                                                                          ( ( X516 @ X518 )
                                                                                                                                         => ( X517 = X518 ) ) )
                                                                                                                                 => ? [X519: $i] :
                                                                                                                                      ( ( X516 @ X519 )
                                                                                                                                      & ! [X520: $i] :
                                                                                                                                          ( ( X516 @ X520 )
                                                                                                                                         => ( X519 = X520 ) ) ) )
                                                                                                                             => ( ! [X521: $i > $o] :
                                                                                                                                    ( ? [X522: $i] : ( X521 @ X522 )
                                                                                                                                   => ( ! [X523: $i,X524: $i] :
                                                                                                                                          ( ( X521 @ X523 )
                                                                                                                                         => ( ( X521 @ X524 )
                                                                                                                                           => ( X523 = X524 ) ) )
                                                                                                                                     => ? [X525: $i] :
                                                                                                                                          ( ( X521 @ X525 )
                                                                                                                                          & ! [X526: $i] :
                                                                                                                                              ( ( X521 @ X526 )
                                                                                                                                             => ( X525 = X526 ) ) ) ) )
                                                                                                                               => ( ! [X527: $i > $o] :
                                                                                                                                      ( ? [X528: $i] :
                                                                                                                                        ! [X529: $i] :
                                                                                                                                          ( ( X527 @ X529 )
                                                                                                                                        <=> ( X529 = X528 ) )
                                                                                                                                     => ? [X530: $i] :
                                                                                                                                          ( ( X527 @ X530 )
                                                                                                                                          & ! [X531: $i] :
                                                                                                                                              ( ( X527 @ X531 )
                                                                                                                                             => ( X530 = X531 ) ) ) )
                                                                                                                                 => ( ! [X532: $i,X533: $i] :
                                                                                                                                        ( ( X532 = X533 )
                                                                                                                                       => ! [X534: $i,X535: $i] :
                                                                                                                                            ( ( X534 = X535 )
                                                                                                                                           => ( ( in @ X534 @ X532 )
                                                                                                                                             => ( in @ X535 @ X533 ) ) ) )
                                                                                                                                   => ( ! [X536: $i,X537: $i] :
                                                                                                                                          ( ( X536 = X537 )
                                                                                                                                         => ! [X538: $i,X539: $i] :
                                                                                                                                              ( ( X538 = X539 )
                                                                                                                                             => ( ( in @ X538 @ X536 )
                                                                                                                                              <=> ( in @ X539 @ X537 ) ) ) )
                                                                                                                                     => ( ! [X540: $i > $o] :
                                                                                                                                            ( ? [X541: $i] :
                                                                                                                                                ( ( X540 @ X541 )
                                                                                                                                                & ! [X542: $i] :
                                                                                                                                                    ( ( X540 @ X542 )
                                                                                                                                                   => ( X541 = X542 ) ) )
                                                                                                                                           => ! [X543: $i,X544: $i] :
                                                                                                                                                ( ( X540 @ X543 )
                                                                                                                                               => ( ( X540 @ X544 )
                                                                                                                                                 => ( X543 = X544 ) ) ) )
                                                                                                                                       => ( ! [X545: $i > $o,X546: $i > $o] :
                                                                                                                                              ( ! [X547: $i,X548: $i] :
                                                                                                                                                  ( ( X547 = X548 )
                                                                                                                                                 => ( ( X545 @ X547 )
                                                                                                                                                  <=> ( X546 @ X548 ) ) )
                                                                                                                                             => ( ? [X549: $i] :
                                                                                                                                                    ( ( X545 @ X549 )
                                                                                                                                                    & ! [X550: $i] :
                                                                                                                                                        ( ( X545 @ X550 )
                                                                                                                                                       => ( X549 = X550 ) ) )
                                                                                                                                              <=> ? [X551: $i] :
                                                                                                                                                    ( ( X546 @ X551 )
                                                                                                                                                    & ! [X552: $i] :
                                                                                                                                                        ( ( X546 @ X552 )
                                                                                                                                                       => ( X551 = X552 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X553: $i,X554: $i] :
                                                                                                                                                  ( ( X553 = X554 )
                                                                                                                                                 => ! [X555: $i,X556: $i] :
                                                                                                                                                      ( ( X555 = X556 )
                                                                                                                                                     => ( ( setadjoin @ X553 @ X555 )
                                                                                                                                                        = ( setadjoin @ X554 @ X556 ) ) ) )
                                                                                                                                             => ( ! [X557: $i,X558: $i] :
                                                                                                                                                    ( ( X557 = X558 )
                                                                                                                                                   => ( ( powerset @ X557 )
                                                                                                                                                      = ( powerset @ X558 ) ) )
                                                                                                                                               => ( ! [X559: $i,X560: $i] :
                                                                                                                                                      ( ( X559 = X560 )
                                                                                                                                                     => ( ( setunion @ X559 )
                                                                                                                                                        = ( setunion @ X560 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X561: $i > $o] :
                                                                                                                                                          ( ? [X562: $i] :
                                                                                                                                                              ( ( X561 @ X562 )
                                                                                                                                                              & ! [X563: $i] :
                                                                                                                                                                  ( ( X561 @ X563 )
                                                                                                                                                                 => ( X562 = X563 ) ) )
                                                                                                                                                         => ! [X564: $i,X565: $i] :
                                                                                                                                                              ( ( X561 @ X564 )
                                                                                                                                                             => ( ( X561 @ X565 )
                                                                                                                                                               => ( X564 = X565 ) ) ) )
                                                                                                                                                     => ( ! [X566: $i > $o,X567: $i > $o] :
                                                                                                                                                            ( ! [X568: $i,X569: $i] :
                                                                                                                                                                ( ( X568 = X569 )
                                                                                                                                                               => ( ( X566 @ X568 )
                                                                                                                                                                <=> ( X567 @ X569 ) ) )
                                                                                                                                                           => ( ? [X570: $i] :
                                                                                                                                                                  ( ( X566 @ X570 )
                                                                                                                                                                  & ! [X571: $i] :
                                                                                                                                                                      ( ( X566 @ X571 )
                                                                                                                                                                     => ( X570 = X571 ) ) )
                                                                                                                                                             => ( ? [X572: $i] :
                                                                                                                                                                    ( ( X567 @ X572 )
                                                                                                                                                                    & ! [X573: $i] :
                                                                                                                                                                        ( ( X567 @ X573 )
                                                                                                                                                                       => ( X572 = X573 ) ) )
                                                                                                                                                               => ( ( descr @ X566 )
                                                                                                                                                                  = ( descr @ X567 ) ) ) ) )
                                                                                                                                                       => ( ! [X574: $i,X575: $i] :
                                                                                                                                                              ( ( X574 = X575 )
                                                                                                                                                             => ! [X576: $i > $o,X577: $i > $o] :
                                                                                                                                                                  ( ! [X578: $i] :
                                                                                                                                                                      ( ( in @ X578 @ X574 )
                                                                                                                                                                     => ! [X579: $i] :
                                                                                                                                                                          ( ( in @ X579 @ X575 )
                                                                                                                                                                         => ( ( X578 = X579 )
                                                                                                                                                                           => ( ( X576 @ X578 )
                                                                                                                                                                            <=> ( X577 @ X579 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X574 @ X576 )
                                                                                                                                                                    = ( dsetconstr @ X575 @ X577 ) ) ) )
                                                                                                                                                         => ( ! [X580: $i,X581: $i] :
                                                                                                                                                                ( ! [X582: $i] :
                                                                                                                                                                    ( ( in @ X582 @ X580 )
                                                                                                                                                                   => ( in @ X582 @ X581 ) )
                                                                                                                                                               => ( subset @ X580 @ X581 ) )
                                                                                                                                                           => ( ! [X583: $i,X584: $i] :
                                                                                                                                                                  ( ( X583 = X584 )
                                                                                                                                                                 => ( subset @ X584 @ X583 ) )
                                                                                                                                                             => ( ! [X585: $i,X586: $i] :
                                                                                                                                                                    ( ( X585 = X586 )
                                                                                                                                                                   => ( subset @ X585 @ X586 ) )
                                                                                                                                                               => ( ! [X587: $i,X588: $i] :
                                                                                                                                                                      ( ! [X589: $i] :
                                                                                                                                                                          ( ( in @ X589 @ X587 )
                                                                                                                                                                         => ( in @ X589 @ X588 ) )
                                                                                                                                                                     => ( subset @ X587 @ X588 ) )
                                                                                                                                                                 => ( ! [X590: $i] : ( subset @ emptyset @ X590 )
                                                                                                                                                                   => ( ! [X591: $i,X592: $i,X593: $i] :
                                                                                                                                                                          ( ( subset @ X591 @ X592 )
                                                                                                                                                                         => ( ( in @ X593 @ X591 )
                                                                                                                                                                           => ( in @ X593 @ X592 ) ) )
                                                                                                                                                                     => ( ! [X594: $i,X595: $i,X596: $i] :
                                                                                                                                                                            ( ( subset @ X594 @ X595 )
                                                                                                                                                                           => ( ~ ( in @ X596 @ X595 )
                                                                                                                                                                             => ~ ( in @ X596 @ X594 ) ) )
                                                                                                                                                                       => ( ! [X597: $i,X598: $i,X599: $i] :
                                                                                                                                                                              ( ( in @ X599 @ X597 )
                                                                                                                                                                             => ( ~ ( in @ X599 @ X598 )
                                                                                                                                                                               => ~ ( subset @ X597 @ X598 ) ) )
                                                                                                                                                                         => ( ! [X600: $i,X601: $i] :
                                                                                                                                                                                ( ~ ( subset @ X600 @ X601 )
                                                                                                                                                                               => ( X600 != X601 ) )
                                                                                                                                                                           => ( ! [X602: $i,X603: $i,X604: $i] :
                                                                                                                                                                                  ( ( in @ X604 @ X602 )
                                                                                                                                                                                 => ( ~ ( in @ X604 @ X603 )
                                                                                                                                                                                   => ( X602 != X603 ) ) )
                                                                                                                                                                             => ( ! [X605: $i] : ( subset @ X605 @ X605 )
                                                                                                                                                                               => ( ! [X606: $i,X607: $i,X608: $i] :
                                                                                                                                                                                      ( ( subset @ X606 @ X607 )
                                                                                                                                                                                     => ( ( subset @ X607 @ X608 )
                                                                                                                                                                                       => ( subset @ X606 @ X608 ) ) )
                                                                                                                                                                                 => ( ! [X609: $i,X610: $i] : ( subset @ X610 @ ( setadjoin @ X609 @ X610 ) )
                                                                                                                                                                                   => ( ! [X611: $i,X612: $i,X613: $i] :
                                                                                                                                                                                          ( ( subset @ X611 @ X613 )
                                                                                                                                                                                         => ( subset @ X611 @ ( setadjoin @ X612 @ X613 ) ) )
                                                                                                                                                                                     => ( ! [X614: $i,X615: $i] :
                                                                                                                                                                                            ( ( subset @ X614 @ X615 )
                                                                                                                                                                                           => ( in @ X614 @ ( powerset @ X615 ) ) )
                                                                                                                                                                                       => ( ! [X616: $i,X617: $i] :
                                                                                                                                                                                              ( ( subset @ X616 @ X617 )
                                                                                                                                                                                             => ( ( subset @ X617 @ X616 )
                                                                                                                                                                                               => ( X616 = X617 ) ) )
                                                                                                                                                                                         => ( ! [X618: $i] :
                                                                                                                                                                                                ( ( subset @ X618 @ emptyset )
                                                                                                                                                                                               => ( X618 = emptyset ) )
                                                                                                                                                                                           => ( ! [X619: $i,X620: $i] :
                                                                                                                                                                                                  ( ( subset @ X620 @ X619 )
                                                                                                                                                                                                 => ( in @ X620 @ ( powerset @ X619 ) ) )
                                                                                                                                                                                             => ( ! [X621: $i,X622: $i] :
                                                                                                                                                                                                    ( ( in @ X622 @ ( powerset @ X621 ) )
                                                                                                                                                                                                   => ( subset @ X622 @ X621 ) )
                                                                                                                                                                                               => ( ! [X623: $i] : ( in @ X623 @ ( powerset @ X623 ) )
                                                                                                                                                                                                 => ( ! [X624: $i,X625: $i] :
                                                                                                                                                                                                        ( ( subset @ X624 @ X625 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X624 ) @ ( powerset @ X625 ) ) )
                                                                                                                                                                                                   => ( ! [X626: $i,X627: $i > $o] : ( in @ ( dsetconstr @ X626 @ X627 ) @ ( powerset @ X626 ) )
                                                                                                                                                                                                     => ( ! [X628: $i,X629: $i > $o] : ( subset @ ( dsetconstr @ X628 @ X629 ) @ X628 )
                                                                                                                                                                                                       => ( ! [X630: $i,X631: $i,X632: $i] :
                                                                                                                                                                                                              ( ( in @ X632 @ X630 )
                                                                                                                                                                                                             => ( in @ X632 @ ( binunion @ X630 @ X631 ) ) )
                                                                                                                                                                                                         => ( ! [X633: $i,X634: $i] : ( in @ X634 @ ( setadjoin @ X633 @ ( setadjoin @ X634 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X635: $i,X636: $i,X637: $i] :
                                                                                                                                                                                                                  ( ( in @ X637 @ X636 )
                                                                                                                                                                                                                 => ( in @ X637 @ ( binunion @ X635 @ X636 ) ) )
                                                                                                                                                                                                             => ( ! [X638: $i,X639: $i,X640: $i,X641: $o] :
                                                                                                                                                                                                                    ( ( in @ X640 @ ( binunion @ X638 @ X639 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X640 @ X638 )
                                                                                                                                                                                                                       => X641 )
                                                                                                                                                                                                                     => ( ( ( in @ X640 @ X639 )
                                                                                                                                                                                                                         => X641 )
                                                                                                                                                                                                                       => X641 ) ) )
                                                                                                                                                                                                               => ( ! [X642: $i,X643: $i,X644: $i] :
                                                                                                                                                                                                                      ( ( in @ X644 @ ( binunion @ X642 @ X643 ) )
                                                                                                                                                                                                                     => ( ( in @ X644 @ X642 )
                                                                                                                                                                                                                        | ( in @ X644 @ X643 ) ) )
                                                                                                                                                                                                                 => ( ! [X645: $i,X646: $i] : ( subset @ X645 @ ( binunion @ X645 @ X646 ) )
                                                                                                                                                                                                                   => ( ! [X647: $i,X648: $i] : ( subset @ X648 @ ( binunion @ X647 @ X648 ) )
                                                                                                                                                                                                                     => ( ! [X649: $i,X650: $i,X651: $i] :
                                                                                                                                                                                                                            ( ( in @ X651 @ X649 )
                                                                                                                                                                                                                           => ( ( in @ X651 @ X650 )
                                                                                                                                                                                                                             => ( in @ X651 @ ( binintersect @ X649 @ X650 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X652: $i,X653: $i,X654: $i] :
                                                                                                                                                                                                                              ( ( subset @ X654 @ X652 )
                                                                                                                                                                                                                             => ( ( subset @ X654 @ X653 )
                                                                                                                                                                                                                               => ( subset @ X654 @ ( binintersect @ X652 @ X653 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X655: $i,X656: $i,X657: $i] :
                                                                                                                                                                                                                                ( ( in @ X657 @ ( binintersect @ X655 @ X656 ) )
                                                                                                                                                                                                                               => ( in @ X657 @ X655 ) )
                                                                                                                                                                                                                           => ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[binintersectLsub]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_127]),foundationAx]),wellorderingAx]),c_0_128]),c_0_129]),c_0_130]),c_0_131]),c_0_132]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_133]),setext]),emptyI]),noeltsimpempty]),c_0_134]),c_0_135]),c_0_136]),c_0_137]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_138]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_139]),c_0_140]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_141]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_142]),c_0_143]),c_0_144]),inCongP]),in__Cong]),c_0_145]),c_0_146]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_147]),c_0_148]),c_0_149]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_150]),c_0_151]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL])])]),c_0_152]) ).

thf(c_0_154,plain,
    ! [X658: $i,X659: $i] :
      ( ( binintersect @ X658 @ X659 )
      = ( dsetconstr @ X658
        @ ^ [Z0: $i] : ( in @ Z0 @ X659 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])]) ).

thf(c_0_155,negated_conjecture,
    ! [X662: $i,X663: $i,X665: $i,X666: $i,X667: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $i,X675: $i,X676: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X684: $i,X685: $i > $i > $o,X686: $i,X688: $i,X691: $i,X693: $i,X694: $i,X695: $i,X696: $i,X698: $i,X699: $i > $o,X700: $i,X702: $i,X703: $i > $o,X704: $i,X705: $i,X706: $i > $o,X707: $i,X708: $i,X709: $i > $o,X710: $i,X711: $i > $o,X712: $i,X715: $i,X716: $o,X717: $i,X718: $i,X719: $o,X720: $i,X721: $i,X722: $i > $o,X723: $i,X726: $i,X727: $i,X730: $i,X732: $i,X734: $i,X735: $i > $o,X736: $i,X737: $i,X739: $i,X740: $i > $o,X741: $i,X742: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i,X752: $o,X753: $i,X754: $i,X755: $i,X756: $i,X757: $i,X758: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X770: $o,X772: $i,X773: $i,X774: $i > $o,X775: $i,X778: $i,X779: $i,X780: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i,X787: $i,X788: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i > $o,X799: $i,X800: $i > $o,X801: $i,X802: $i,X803: $i > $o,X804: $i,X806: $i,X807: $i > $o,X809: $i,X810: $i,X811: $i > $o,X813: $i,X814: $i,X815: $i > $o,X816: $i,X818: $o,X819: $o,X820: $i,X821: $i > $o,X823: $i,X824: $i,X825: $i > $o,X826: $i,X828: $i > $o,X829: $i,X832: $i,X833: $i > $o,X834: $i,X838: $i,X839: $i > $o,X840: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i > $o,X853: $i,X855: $i,X856: $i,X857: $i > $o,X858: $i > $o,X861: $i,X864: $i,X865: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i > $o,X878: $i,X880: $i,X881: $i,X882: $i > $o,X883: $i > $o,X886: $i,X888: $i,X890: $i,X891: $i,X892: $i > $o,X893: $i > $o,X896: $i,X897: $i,X899: $i,X900: $i,X901: $i,X902: $i,X903: $i,X904: $i,X906: $i,X907: $i,X908: $i,X909: $i,X910: $i,X911: $i,X912: $i,X913: $i,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $i,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $i > $o,X944: $i,X945: $i > $o,X946: $i,X947: $i,X948: $i,X949: $i,X950: $i,X951: $i,X952: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $o,X958: $i,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X662 @ X663 ) @ X662 )
        | ~ ( in @ ( esk1_2 @ X662 @ X663 ) @ X663 )
        | ( X662 = X663 ) )
      & ( ( in @ ( esk1_2 @ X662 @ X663 ) @ X662 )
        | ( in @ ( esk1_2 @ X662 @ X663 ) @ X663 )
        | ( X662 = X663 ) )
      & ~ ( in @ X665 @ emptyset )
      & ( ~ ( in @ X668 @ ( setadjoin @ X666 @ X667 ) )
        | ( X668 = X666 )
        | ( in @ X668 @ X667 ) )
      & ( ( X668 != X666 )
        | ( in @ X668 @ ( setadjoin @ X666 @ X667 ) ) )
      & ( ~ ( in @ X668 @ X667 )
        | ( in @ X668 @ ( setadjoin @ X666 @ X667 ) ) )
      & ( ~ ( in @ X670 @ ( powerset @ X669 ) )
        | ~ ( in @ X671 @ X670 )
        | ( in @ X671 @ X669 ) )
      & ( ( in @ ( esk2_2 @ X672 @ X673 ) @ X673 )
        | ( in @ X673 @ ( powerset @ X672 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X672 @ X673 ) @ X672 )
        | ( in @ X673 @ ( powerset @ X672 ) ) )
      & ( ( in @ X676 @ ( esk3_2 @ X675 @ X676 ) )
        | ~ ( in @ X676 @ ( setunion @ X675 ) ) )
      & ( ( in @ ( esk3_2 @ X675 @ X676 ) @ X675 )
        | ~ ( in @ X676 @ ( setunion @ X675 ) ) )
      & ( ~ ( in @ X679 @ X680 )
        | ~ ( in @ X680 @ X678 )
        | ( in @ X679 @ ( setunion @ X678 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X681 @ omega )
        | ( in @ ( setadjoin @ X681 @ X681 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X682 ) @ omega )
        | ~ ( in @ emptyset @ X682 )
        | ~ ( in @ X684 @ omega )
        | ( in @ X684 @ X682 ) )
      & ( ( in @ ( esk4_1 @ X682 ) @ X682 )
        | ~ ( in @ emptyset @ X682 )
        | ~ ( in @ X684 @ omega )
        | ( in @ X684 @ X682 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X682 ) @ ( esk4_1 @ X682 ) ) @ X682 )
        | ~ ( in @ emptyset @ X682 )
        | ~ ( in @ X684 @ omega )
        | ( in @ X684 @ X682 ) )
      & ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
      & ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
      & ( ~ ( in @ X694 @ X686 )
        | ~ ( X685 @ X694 @ X693 )
        | ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
        | ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
      & ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ~ ( in @ X694 @ X686 )
        | ~ ( X685 @ X694 @ X693 )
        | ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X688
         != ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
        | ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X688
         != ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ~ ( in @ X694 @ X686 )
        | ~ ( X685 @ X694 @ X693 )
        | ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
        | ( X688
         != ( esk6_3 @ X685 @ X686 @ X688 ) )
        | ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
      & ( ( in @ ( esk9_1 @ X695 ) @ X695 )
        | ~ ( in @ X696 @ X695 ) )
      & ( ~ ( in @ X698 @ ( esk9_1 @ X695 ) )
        | ~ ( in @ X698 @ X695 )
        | ~ ( in @ X696 @ X695 ) )
      & epred1_0
      & ( ( X699 @ ( esk10_2 @ X699 @ X700 ) )
        | ~ ( X699 @ X700 )
        | ( X699 @ ( descr @ X699 ) ) )
      & ( ( X700
         != ( esk10_2 @ X699 @ X700 ) )
        | ~ ( X699 @ X700 )
        | ( X699 @ ( descr @ X699 ) ) )
      & ( ~ ( in @ X704 @ X702 )
        | ~ ( X703 @ X704 )
        | ( in @ X704 @ ( dsetconstr @ X702 @ X703 ) ) )
      & ( ~ ( in @ X707 @ ( dsetconstr @ X705 @ X706 ) )
        | ( in @ X707 @ X705 ) )
      & ( ~ ( in @ X710 @ ( dsetconstr @ X708 @ X709 ) )
        | ( X709 @ X710 ) )
      & ( ( X711 @ ( esk12_1 @ X711 ) )
        | ( X711 @ ( esk11_2 @ X711 @ X712 ) )
        | ~ ( X711 @ X712 ) )
      & ( ~ ( X711 @ X715 )
        | ( ( esk12_1 @ X711 )
          = X715 )
        | ( X711 @ ( esk11_2 @ X711 @ X712 ) )
        | ~ ( X711 @ X712 ) )
      & ( ( X711 @ ( esk12_1 @ X711 ) )
        | ( X712
         != ( esk11_2 @ X711 @ X712 ) )
        | ~ ( X711 @ X712 ) )
      & ( ~ ( X711 @ X715 )
        | ( ( esk12_1 @ X711 )
          = X715 )
        | ( X712
         != ( esk11_2 @ X711 @ X712 ) )
        | ~ ( X711 @ X712 ) )
      & ( ~ ( in @ X717 @ ( prop2set @ X716 ) )
        | X716 )
      & ( ~ ( in @ X718 @ emptyset )
        | X719 )
      & ( ~ ( in @ X720 @ emptyset )
        | ~ $true )
      & ~ ( in @ X721 @ emptyset )
      & ( ( X722 @ ( esk13_2 @ X722 @ X723 ) )
        | ~ ( X722 @ X723 )
        | ( X722 @ ( esk14_1 @ X722 ) ) )
      & ( ( X723
         != ( esk13_2 @ X722 @ X723 ) )
        | ~ ( X722 @ X723 )
        | ( X722 @ ( esk14_1 @ X722 ) ) )
      & ( ( in @ ( esk16_2 @ X726 @ X727 ) @ X727 )
        | ( X726 = X727 )
        | ( in @ ( esk15_2 @ X726 @ X727 ) @ X726 ) )
      & ( ~ ( in @ ( esk16_2 @ X726 @ X727 ) @ X726 )
        | ( X726 = X727 )
        | ( in @ ( esk15_2 @ X726 @ X727 ) @ X726 ) )
      & ( ( in @ ( esk16_2 @ X726 @ X727 ) @ X727 )
        | ( X726 = X727 )
        | ~ ( in @ ( esk15_2 @ X726 @ X727 ) @ X727 ) )
      & ( ~ ( in @ ( esk16_2 @ X726 @ X727 ) @ X726 )
        | ( X726 = X727 )
        | ~ ( in @ ( esk15_2 @ X726 @ X727 ) @ X727 ) )
      & ( ( in @ ( esk17_1 @ X730 ) @ X730 )
        | ( X730 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X732 ) @ X732 )
        | ( X732 = emptyset ) )
      & ( ~ ( in @ X736 @ ( dsetconstr @ X734 @ X735 ) )
        | ( X735 @ X736 )
        | ~ ( in @ X736 @ X734 ) )
      & ( ~ ( X735 @ X736 )
        | ( in @ X736 @ ( dsetconstr @ X734 @ X735 ) )
        | ~ ( in @ X736 @ X734 ) )
      & ( ( X737 = emptyset )
        | ( in @ ( esk19_1 @ X737 ) @ X737 ) )
      & ( ~ ( in @ X741 @ X739 )
        | ~ ( X740 @ X741 )
        | ( ( dsetconstr @ X739 @ X740 )
         != emptyset ) )
      & ( ~ ( in @ X743 @ X742 )
        | ( X742 != emptyset ) )
      & ( in @ X744 @ ( setadjoin @ X744 @ X745 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X748 @ X747 )
        | ( in @ X748 @ ( setadjoin @ X746 @ X747 ) ) )
      & ( ( in @ X751 @ X750 )
        | X752
        | ( X751 = X749 )
        | ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
      & ( ~ X752
        | X752
        | ( X751 = X749 )
        | ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
      & ( ( in @ X751 @ X750 )
        | X752
        | ~ X752
        | ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
      & ( ~ X752
        | X752
        | ~ X752
        | ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
      & ( ~ ( in @ X755 @ ( setadjoin @ X753 @ X754 ) )
        | ( X755 = X753 )
        | ( in @ X755 @ X754 ) )
      & ( ( dsetconstr @ X756
          @ ^ [Z0: $i] : $true )
        = X756 )
      & ( ( in @ ( esk20_2 @ X757 @ X758 ) @ X758 )
        | ( in @ X758 @ ( powerset @ X757 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X757 @ X758 ) @ X757 )
        | ( in @ X758 @ ( powerset @ X757 ) ) )
      & ( in @ emptyset @ ( powerset @ X760 ) )
      & ( in @ emptyset @ ( powerset @ X761 ) )
      & ( ~ ( in @ X763 @ ( powerset @ X762 ) )
        | ~ ( in @ X764 @ X763 )
        | ( in @ X764 @ X762 ) )
      & ( ~ ( in @ X766 @ X767 )
        | ~ ( in @ X767 @ X765 )
        | ( in @ X766 @ ( setunion @ X765 ) ) )
      & ( ( in @ X769 @ ( esk21_3 @ X768 @ X769 @ X770 ) )
        | X770
        | ~ ( in @ X769 @ ( setunion @ X768 ) ) )
      & ( ( in @ ( esk21_3 @ X768 @ X769 @ X770 ) @ X768 )
        | X770
        | ~ ( in @ X769 @ ( setunion @ X768 ) ) )
      & ( ~ X770
        | X770
        | ~ ( in @ X769 @ ( setunion @ X768 ) ) )
      & ( ~ ( in @ X773 @ X772 )
        | ( in @ X773 @ ( powerset @ ( setunion @ X772 ) ) ) )
      & ( ~ ( X774 @ X778 )
        | ( X778
          = ( esk23_1 @ X774 ) )
        | ( X774 @ ( esk22_2 @ X774 @ X775 ) )
        | ~ ( X774 @ X775 ) )
      & ( ( X779
         != ( esk23_1 @ X774 ) )
        | ( X774 @ X779 )
        | ( X774 @ ( esk22_2 @ X774 @ X775 ) )
        | ~ ( X774 @ X775 ) )
      & ( ~ ( X774 @ X778 )
        | ( X778
          = ( esk23_1 @ X774 ) )
        | ( X775
         != ( esk22_2 @ X774 @ X775 ) )
        | ~ ( X774 @ X775 ) )
      & ( ( X779
         != ( esk23_1 @ X774 ) )
        | ( X774 @ X779 )
        | ( X775
         != ( esk22_2 @ X774 @ X775 ) )
        | ~ ( X774 @ X775 ) )
      & ( ( in @ ( esk24_1 @ X780 ) @ X780 )
        | ( X780 = emptyset ) )
      & ( $true
        | ( X780 = emptyset ) )
      & ( ~ ( in @ X782 @ ( setadjoin @ X783 @ emptyset ) )
        | ( X782 = X783 ) )
      & ( ( X784 = X785 )
        | ~ ( in @ X785 @ ( setadjoin @ X784 @ emptyset ) ) )
      & ( ( X786 != X787 )
        | ( in @ X786 @ ( setadjoin @ X787 @ emptyset ) ) )
      & ( ~ ( in @ X788 @ ( setadjoin @ X789 @ emptyset ) )
        | ( in @ X789 @ ( setadjoin @ X788 @ emptyset ) ) )
      & ( ~ ( in @ X792 @ ( setadjoin @ X790 @ ( setadjoin @ X791 @ emptyset ) ) )
        | ( X792 = X790 )
        | ( X792 = X791 ) )
      & ( in @ X793 @ ( setadjoin @ X793 @ ( setadjoin @ X794 @ emptyset ) ) )
      & ( in @ X796 @ ( setadjoin @ X795 @ ( setadjoin @ X796 @ emptyset ) ) )
      & ( ~ ( in @ X799 @ X797 )
        | ~ ( X798 @ X799 )
        | ( ( dsetconstr @ X797 @ X798 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X801 @ emptyset )
        | ( X800 @ X801 ) )
      & ( ( in @ ( esk25_2 @ X802 @ X803 ) @ X802 )
        | ~ ( in @ X804 @ X802 )
        | ( X803 @ X804 ) )
      & ( ~ ( X803 @ ( esk25_2 @ X802 @ X803 ) )
        | ~ ( in @ X804 @ X802 )
        | ( X803 @ X804 ) )
      & ( ( in @ ( esk26_2 @ X806 @ X807 ) @ X806 )
        | ~ ( in @ X809 @ X806 )
        | ~ ( X807 @ X809 ) )
      & ( ( X807 @ ( esk26_2 @ X806 @ X807 ) )
        | ~ ( in @ X809 @ X806 )
        | ~ ( X807 @ X809 ) )
      & ( ( in @ ( esk27_2 @ X810 @ X811 ) @ X810 )
        | ~ ( in @ X813 @ X810 )
        | ~ ( X811 @ X813 ) )
      & ( ( X811 @ ( esk27_2 @ X810 @ X811 ) )
        | ~ ( in @ X813 @ X810 )
        | ~ ( X811 @ X813 ) )
      & ( ( in @ ( esk28_2 @ X814 @ X815 ) @ X814 )
        | ~ ( in @ X816 @ X814 )
        | ( X815 @ X816 ) )
      & ( ~ ( X815 @ ( esk28_2 @ X814 @ X815 ) )
        | ~ ( in @ X816 @ X814 )
        | ( X815 @ X816 ) )
      & ( ~ X818
        | ( in @ emptyset @ ( prop2set @ X818 ) ) )
      & ( ~ X819
        | ( set2prop @ ( prop2set @ X819 ) ) )
      & ( ( in @ ( esk29_2 @ X820 @ X821 ) @ X820 )
        | ~ ( in @ X823 @ X820 )
        | ~ ( X821 @ X823 ) )
      & ( ( X821 @ ( esk29_2 @ X820 @ X821 ) )
        | ~ ( in @ X823 @ X820 )
        | ~ ( X821 @ X823 ) )
      & ( ( in @ ( esk30_2 @ X824 @ X825 ) @ X824 )
        | ~ ( in @ X826 @ X824 )
        | ( X825 @ X826 ) )
      & ( ~ ( X825 @ ( esk30_2 @ X824 @ X825 ) )
        | ~ ( in @ X826 @ X824 )
        | ( X825 @ X826 ) )
      & ( ( X828 @ ( esk32_1 @ X828 ) )
        | ( X828 @ ( esk31_2 @ X828 @ X829 ) )
        | ~ ( X828 @ X829 ) )
      & ( ~ ( X828 @ X832 )
        | ( ( esk32_1 @ X828 )
          = X832 )
        | ( X828 @ ( esk31_2 @ X828 @ X829 ) )
        | ~ ( X828 @ X829 ) )
      & ( ( X828 @ ( esk32_1 @ X828 ) )
        | ( X829
         != ( esk31_2 @ X828 @ X829 ) )
        | ~ ( X828 @ X829 ) )
      & ( ~ ( X828 @ X832 )
        | ( ( esk32_1 @ X828 )
          = X832 )
        | ( X829
         != ( esk31_2 @ X828 @ X829 ) )
        | ~ ( X828 @ X829 ) )
      & ( ( X833 @ ( esk35_1 @ X833 ) )
        | ( X833 @ ( esk33_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ~ ( X833 @ X838 )
        | ( ( esk35_1 @ X833 )
          = X838 )
        | ( X833 @ ( esk33_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ( X833 @ ( esk35_1 @ X833 ) )
        | ( X833 @ ( esk34_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ~ ( X833 @ X838 )
        | ( ( esk35_1 @ X833 )
          = X838 )
        | ( X833 @ ( esk34_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ( X833 @ ( esk35_1 @ X833 ) )
        | ( ( esk33_1 @ X833 )
         != ( esk34_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ~ ( X833 @ X838 )
        | ( ( esk35_1 @ X833 )
          = X838 )
        | ( ( esk33_1 @ X833 )
         != ( esk34_1 @ X833 ) )
        | ~ ( X833 @ X834 ) )
      & ( ( X839 @ ( esk37_1 @ X839 ) )
        | ~ ( X839 @ ( esk36_2 @ X839 @ X840 ) )
        | ( ( esk36_2 @ X839 @ X840 )
         != X840 ) )
      & ( ~ ( X839 @ X843 )
        | ( ( esk37_1 @ X839 )
          = X843 )
        | ~ ( X839 @ ( esk36_2 @ X839 @ X840 ) )
        | ( ( esk36_2 @ X839 @ X840 )
         != X840 ) )
      & ( ( X839 @ ( esk37_1 @ X839 ) )
        | ( X839 @ ( esk36_2 @ X839 @ X840 ) )
        | ( ( esk36_2 @ X839 @ X840 )
          = X840 ) )
      & ( ~ ( X839 @ X843 )
        | ( ( esk37_1 @ X839 )
          = X843 )
        | ( X839 @ ( esk36_2 @ X839 @ X840 ) )
        | ( ( esk36_2 @ X839 @ X840 )
          = X840 ) )
      & ( ( X844 != X845 )
        | ( X846 != X847 )
        | ~ ( in @ X846 @ X844 )
        | ( in @ X847 @ X845 ) )
      & ( ~ ( in @ X850 @ X848 )
        | ( in @ X851 @ X849 )
        | ( X850 != X851 )
        | ( X848 != X849 ) )
      & ( ~ ( in @ X851 @ X849 )
        | ( in @ X850 @ X848 )
        | ( X850 != X851 )
        | ( X848 != X849 ) )
      & ( ( X852 @ ( esk38_2 @ X852 @ X853 ) )
        | ~ ( X852 @ X853 )
        | ~ ( X852 @ X855 )
        | ~ ( X852 @ X856 )
        | ( X855 = X856 ) )
      & ( ( X853
         != ( esk38_2 @ X852 @ X853 ) )
        | ~ ( X852 @ X853 )
        | ~ ( X852 @ X855 )
        | ~ ( X852 @ X856 )
        | ( X855 = X856 ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( ( esk39_2 @ X857 @ X858 )
          = ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X858 @ X864 )
        | ( ( esk42_2 @ X857 @ X858 )
          = X864 )
        | ( X861
         != ( esk41_3 @ X857 @ X858 @ X861 ) )
        | ~ ( X857 @ X861 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( ~ ( X857 @ X868 )
        | ( ( esk44_2 @ X857 @ X858 )
          = X868 )
        | ( X865
         != ( esk43_3 @ X857 @ X858 @ X865 ) )
        | ~ ( X858 @ X865 )
        | ( X857 @ ( esk39_2 @ X857 @ X858 ) )
        | ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
      & ( emptyset = emptyset )
      & ( ( X869 != X870 )
        | ( X871 != X872 )
        | ( ( setadjoin @ X869 @ X871 )
          = ( setadjoin @ X870 @ X872 ) ) )
      & ( ( X873 != X874 )
        | ( ( powerset @ X873 )
          = ( powerset @ X874 ) ) )
      & ( ( X875 != X876 )
        | ( ( setunion @ X875 )
          = ( setunion @ X876 ) ) )
      & ( omega = omega )
      & ( ( X877 @ ( esk45_2 @ X877 @ X878 ) )
        | ~ ( X877 @ X878 )
        | ~ ( X877 @ X880 )
        | ~ ( X877 @ X881 )
        | ( X880 = X881 ) )
      & ( ( X878
         != ( esk45_2 @ X877 @ X878 ) )
        | ~ ( X877 @ X878 )
        | ~ ( X877 @ X880 )
        | ~ ( X877 @ X881 )
        | ( X880 = X881 ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( ( esk46_2 @ X882 @ X883 )
          = ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( ( esk46_2 @ X882 @ X883 )
          = ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( ( esk46_2 @ X882 @ X883 )
          = ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( ( esk46_2 @ X882 @ X883 )
          = ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( X888
         != ( esk49_3 @ X882 @ X883 @ X888 ) )
        | ~ ( X883 @ X888 )
        | ( ( descr @ X882 )
          = ( descr @ X883 ) )
        | ( X886
         != ( esk48_3 @ X882 @ X883 @ X886 ) )
        | ~ ( X882 @ X886 )
        | ( X882 @ ( esk46_2 @ X882 @ X883 ) )
        | ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
      & ( ( in @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) @ X890 )
        | ( ( dsetconstr @ X890 @ X892 )
          = ( dsetconstr @ X891 @ X893 ) )
        | ( X890 != X891 ) )
      & ( ( in @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) @ X891 )
        | ( ( dsetconstr @ X890 @ X892 )
          = ( dsetconstr @ X891 @ X893 ) )
        | ( X890 != X891 ) )
      & ( ( ( esk50_4 @ X890 @ X891 @ X892 @ X893 )
          = ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
        | ( ( dsetconstr @ X890 @ X892 )
          = ( dsetconstr @ X891 @ X893 ) )
        | ( X890 != X891 ) )
      & ( ~ ( X892 @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) )
        | ~ ( X893 @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
        | ( ( dsetconstr @ X890 @ X892 )
          = ( dsetconstr @ X891 @ X893 ) )
        | ( X890 != X891 ) )
      & ( ( X892 @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) )
        | ( X893 @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
        | ( ( dsetconstr @ X890 @ X892 )
          = ( dsetconstr @ X891 @ X893 ) )
        | ( X890 != X891 ) )
      & ( ( in @ ( esk52_2 @ X896 @ X897 ) @ X896 )
        | ( subset @ X896 @ X897 ) )
      & ( ~ ( in @ ( esk52_2 @ X896 @ X897 ) @ X897 )
        | ( subset @ X896 @ X897 ) )
      & ( ( X899 != X900 )
        | ( subset @ X900 @ X899 ) )
      & ( ( X901 != X902 )
        | ( subset @ X901 @ X902 ) )
      & ( ( in @ ( esk53_2 @ X903 @ X904 ) @ X903 )
        | ( subset @ X903 @ X904 ) )
      & ( ~ ( in @ ( esk53_2 @ X903 @ X904 ) @ X904 )
        | ( subset @ X903 @ X904 ) )
      & ( subset @ emptyset @ X906 )
      & ( ~ ( subset @ X907 @ X908 )
        | ~ ( in @ X909 @ X907 )
        | ( in @ X909 @ X908 ) )
      & ( ~ ( subset @ X910 @ X911 )
        | ( in @ X912 @ X911 )
        | ~ ( in @ X912 @ X910 ) )
      & ( ~ ( in @ X915 @ X913 )
        | ( in @ X915 @ X914 )
        | ~ ( subset @ X913 @ X914 ) )
      & ( ( subset @ X916 @ X917 )
        | ( X916 != X917 ) )
      & ( ~ ( in @ X920 @ X918 )
        | ( in @ X920 @ X919 )
        | ( X918 != X919 ) )
      & ( subset @ X921 @ X921 )
      & ( ~ ( subset @ X922 @ X923 )
        | ~ ( subset @ X923 @ X924 )
        | ( subset @ X922 @ X924 ) )
      & ( subset @ X926 @ ( setadjoin @ X925 @ X926 ) )
      & ( ~ ( subset @ X927 @ X929 )
        | ( subset @ X927 @ ( setadjoin @ X928 @ X929 ) ) )
      & ( ~ ( subset @ X930 @ X931 )
        | ( in @ X930 @ ( powerset @ X931 ) ) )
      & ( ~ ( subset @ X932 @ X933 )
        | ~ ( subset @ X933 @ X932 )
        | ( X932 = X933 ) )
      & ( ~ ( subset @ X934 @ emptyset )
        | ( X934 = emptyset ) )
      & ( ~ ( subset @ X936 @ X935 )
        | ( in @ X936 @ ( powerset @ X935 ) ) )
      & ( ~ ( in @ X938 @ ( powerset @ X937 ) )
        | ( subset @ X938 @ X937 ) )
      & ( in @ X939 @ ( powerset @ X939 ) )
      & ( ~ ( subset @ X940 @ X941 )
        | ( subset @ ( powerset @ X940 ) @ ( powerset @ X941 ) ) )
      & ( in @ ( dsetconstr @ X942 @ X943 ) @ ( powerset @ X942 ) )
      & ( subset @ ( dsetconstr @ X944 @ X945 ) @ X944 )
      & ( ~ ( in @ X948 @ X946 )
        | ( in @ X948 @ ( binunion @ X946 @ X947 ) ) )
      & ( in @ X950 @ ( setadjoin @ X949 @ ( setadjoin @ X950 @ emptyset ) ) )
      & ( ~ ( in @ X953 @ X952 )
        | ( in @ X953 @ ( binunion @ X951 @ X952 ) ) )
      & ( ( in @ X956 @ X955 )
        | X957
        | ( in @ X956 @ X954 )
        | ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
      & ( ~ X957
        | X957
        | ( in @ X956 @ X954 )
        | ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
      & ( ( in @ X956 @ X955 )
        | X957
        | ~ X957
        | ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
      & ( ~ X957
        | X957
        | ~ X957
        | ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
      & ( ~ ( in @ X960 @ ( binunion @ X958 @ X959 ) )
        | ( in @ X960 @ X958 )
        | ( in @ X960 @ X959 ) )
      & ( subset @ X961 @ ( binunion @ X961 @ X962 ) )
      & ( subset @ X964 @ ( binunion @ X963 @ X964 ) )
      & ( ~ ( in @ X967 @ X965 )
        | ~ ( in @ X967 @ X966 )
        | ( in @ X967 @ ( binintersect @ X965 @ X966 ) ) )
      & ( ~ ( subset @ X970 @ X968 )
        | ~ ( subset @ X970 @ X969 )
        | ( subset @ X970 @ ( binintersect @ X968 @ X969 ) ) )
      & ( ~ ( in @ X973 @ ( binintersect @ X971 @ X972 ) )
        | ( in @ X973 @ X971 ) )
      & ~ ( subset @ ( binintersect @ esk54_0 @ esk55_0 ) @ esk54_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])])])])])]) ).

thf(c_0_156,plain,
    ! [X660: $i,X661: $i] :
      ( ( binintersect @ X660 @ X661 )
      = ( dsetconstr @ X660
        @ ^ [Z0: $i] : ( in @ Z0 @ X661 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

thf(c_0_157,negated_conjecture,
    ! [X1: $i > $o,X2: $i] : ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ),
    inference(split_conjunct,[status(thm)],[c_0_155]) ).

thf(c_0_158,plain,
    ! [X2: $i,X3: $i] :
      ( ( binintersect @ X2 @ X3 )
      = ( dsetconstr @ X2
        @ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_156]) ).

thf(c_0_159,negated_conjecture,
    ~ ( subset @ ( binintersect @ esk54_0 @ esk55_0 ) @ esk54_0 ),
    inference(split_conjunct,[status(thm)],[c_0_155]) ).

thf(c_0_160,negated_conjecture,
    ! [X3: $i,X2: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ),
    inference(spm,[status(thm)],[c_0_157,c_0_158]) ).

thf(c_0_161,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU592^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 17:12:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  Running higher-order theorem proving
% 0.21/0.51  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
% 0.82/300.03  # Version: 3.1.0-ho
% 0.82/300.03  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03  # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03  # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03  # Starting new_bool_5 with 300s (1) cores
% 0.82/300.03  # Starting pre_casc_3 with 300s (1) cores
% 0.82/300.03  # Starting ho_unfolding_8 with 300s (1) cores
% 0.82/300.03  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.82/300.03  # Starting new_bool_3 with 300s (1) cores
% 0.82/300.03  # Starting new_ho_5 with 300s (1) cores
% 0.82/300.03  # almost_fo_3_lam with pid 23097 completed with status 0
% 0.82/300.03  # Result found by almost_fo_3_lam
% 0.82/300.03  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03  # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03  # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03  # No SInE strategy applied
% 0.82/300.03  # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.82/300.03  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.82/300.03  # Starting pre_casc_7 with 163s (1) cores
% 0.82/300.03  # pre_casc_7 with pid 23114 completed with status 0
% 0.82/300.03  # Result found by pre_casc_7
% 0.82/300.03  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03  # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03  # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03  # No SInE strategy applied
% 0.82/300.03  # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.82/300.03  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.82/300.03  # Starting pre_casc_7 with 163s (1) cores
% 0.82/300.03  # Preprocessing time       : 0.004 s
% 0.82/300.03  
% 0.82/300.03  # Proof found!
% 0.82/300.03  # SZS status Theorem
% 0.82/300.03  # SZS output start CNFRefutation
% See solution above
% 0.82/300.03  # Parsed axioms                        : 237
% 0.82/300.03  # Removed by relevancy pruning/SinE    : 0
% 0.82/300.03  # Initial clauses                      : 348
% 0.82/300.03  # Removed in clause preprocessing      : 142
% 0.82/300.03  # Initial clauses in saturation        : 206
% 0.82/300.03  # Processed clauses                    : 53
% 0.82/300.03  # ...of these trivial                  : 3
% 0.82/300.03  # ...subsumed                          : 8
% 0.82/300.03  # ...remaining for further processing  : 42
% 0.82/300.03  # Other redundant clauses eliminated   : 7
% 0.82/300.03  # Clauses deleted for lack of memory   : 0
% 0.82/300.03  # Backward-subsumed                    : 0
% 0.82/300.03  # Backward-rewritten                   : 3
% 0.82/300.03  # Generated clauses                    : 36
% 0.82/300.03  # ...of the previous two non-redundant : 20
% 0.82/300.03  # ...aggressively subsumed             : 0
% 0.82/300.03  # Contextual simplify-reflections      : 0
% 0.82/300.03  # Paramodulations                      : 26
% 0.82/300.03  # Factorizations                       : 0
% 0.82/300.03  # NegExts                              : 0
% 0.82/300.03  # Equation resolutions                 : 7
% 0.82/300.03  # Disequality decompositions           : 0
% 0.82/300.03  # Total rewrite steps                  : 17
% 0.82/300.03  # ...of those cached                   : 6
% 0.82/300.03  # Propositional unsat checks           : 0
% 0.82/300.03  #    Propositional check models        : 0
% 0.82/300.03  #    Propositional check unsatisfiable : 0
% 0.82/300.03  #    Propositional clauses             : 0
% 0.82/300.03  #    Propositional clauses after purity: 0
% 0.82/300.03  #    Propositional unsat core size     : 0
% 0.82/300.03  #    Propositional preprocessing time  : 0.000
% 0.82/300.03  #    Propositional encoding time       : 0.000
% 0.82/300.03  #    Propositional solver time         : 0.000
% 0.82/300.03  #    Success case prop preproc time    : 0.000
% 0.82/300.03  #    Success case prop encoding time   : 0.000
% 0.82/300.03  #    Success case prop solver time     : 0.000
% 0.82/300.03  # Current number of processed clauses  : 35
% 0.82/300.03  #    Positive orientable unit clauses  : 21
% 0.82/300.03  #    Positive unorientable unit clauses: 0
% 0.82/300.03  #    Negative unit clauses             : 1
% 0.82/300.03  #    Non-unit-clauses                  : 13
% 0.82/300.03  # Current number of unprocessed clauses: 173
% 0.82/300.03  # ...number of literals in the above   : 641
% 0.82/300.03  # Current number of archived formulas  : 0
% 0.82/300.03  # Current number of archived clauses   : 3
% 0.82/300.03  # Clause-clause subsumption calls (NU) : 18
% 0.82/300.03  # Rec. Clause-clause subsumption calls : 17
% 0.82/300.03  # Non-unit clause-clause subsumptions  : 1
% 0.82/300.03  # Unit Clause-clause subsumption calls : 3
% 0.82/300.03  # Rewrite failures with RHS unbound    : 0
% 0.82/300.03  # BW rewrite match attempts            : 7
% 0.82/300.03  # BW rewrite match successes           : 3
% 0.82/300.03  # Condensation attempts                : 53
% 0.82/300.03  # Condensation successes               : 1
% 0.82/300.03  # Termbank termtop insertions          : 28316
% 0.82/300.03  # Search garbage collected termcells   : 11270
% 0.82/300.03  
% 0.82/300.03  # -------------------------------------------------
% 0.82/300.03  # User time                : 0.035 s
% 0.82/300.03  # System time              : 0.009 s
% 0.82/300.03  # Total time               : 0.044 s
% 0.82/300.03  # Maximum resident set size: 4664 pages
% 0.82/300.03  
% 0.82/300.03  # -------------------------------------------------
% 0.82/300.03  # User time                : 0.041 s
% 0.82/300.03  # System time              : 0.012 s
% 0.82/300.03  # Total time               : 0.053 s
% 0.82/300.03  # Maximum resident set size: 2044 pages
% 0.82/300.03  % E---3.1 exiting
% 0.82/300.03  % E exiting
%------------------------------------------------------------------------------