TSTP Solution File: SEU538^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU538^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:28:02 EDT 2024

% Result   : Theorem 0.36s 0.55s
% Output   : CNFRefutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  154
% Syntax   : Number of formulae    :  185 (  19 unt;  95 typ;   0 def)
%            Number of atoms       :  676 ( 118 equ;   0 cnn)
%            Maximal formula atoms :  184 (   7 avg)
%            Number of connectives : 2290 ( 177   ~; 171   |; 157   &;1394   @)
%                                         (  88 <=>; 303  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  222 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  147 ( 147   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  95 usr;  61 con; 0-3 aty)
%            Number of variables   :  554 (  42   ^ 444   !;  68   ?; 554   :)

% 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,
    epred1_0: $o ).

thf(decl_88,type,
    esk1_2: $i > $i > $i ).

thf(decl_89,type,
    esk2_2: $i > $i > $i ).

thf(decl_90,type,
    esk3_2: $i > $i > $i ).

thf(decl_91,type,
    esk4_1: $i > $i ).

thf(decl_92,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_93,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_94,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_95,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_96,type,
    esk9_1: $i > $i ).

thf(decl_97,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_98,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_99,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_100,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_101,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_102,type,
    esk15_2: $i > $i > $i ).

thf(decl_103,type,
    esk16_2: $i > $i > $i ).

thf(decl_104,type,
    esk17_1: $i > $i ).

thf(decl_105,type,
    esk18_1: $i > $i ).

thf(decl_106,type,
    esk19_1: $i > $i ).

thf(decl_107,type,
    esk20_2: $i > $i > $i ).

thf(decl_108,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_109,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_110,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_111,type,
    esk24_1: $i > $i ).

thf(decl_112,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_113,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_114,type,
    esk27_0: $i ).

thf(decl_115,type,
    epred2_0: $i > $o ).

thf(decl_116,type,
    esk28_0: $i ).

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

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

thf(prop2set,axiom,
    ( prop2set
    = ( ^ [X10: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [X2: $i] : X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).

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

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

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

thf(exuE2,axiom,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).

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

thf(replAx,axiom,
    ( replAx
  <=> ! [X6: $i > $i > $o,X4: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( exu
              @ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
       => ? [X5: $i] :
          ! [X2: $i] :
            ( ( in @ X2 @ X5 )
          <=> ? [X3: $i] :
                ( ( in @ X3 @ X4 )
                & ( X6 @ X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).

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

thf(emptyE1,axiom,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [X2: $i] : ( X1 @ X2 ) )
            = emptyset )
         => ~ $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).

thf(prop2setE,axiom,
    ( prop2setE
  <=> ! [X11: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X11 ) )
       => X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).

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

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

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

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

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

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

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

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

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

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

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

thf(upairsetE,axiom,
    ( upairsetE
  <=> ! [X2: $i,X3: $i,X15: $i] :
        ( ( in @ X15 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
       => ( ( X15 = X2 )
          | ( X15 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).

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

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

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

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

thf(emptysetE,axiom,
    ( emptysetE
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ! [X12: $o] : X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).

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

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

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

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

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

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

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

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

thf(setadjoinE,axiom,
    ( setadjoinE
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ! [X13: $o] :
            ( ( ( X3 = X2 )
             => X13 )
           => ( ( ( in @ X3 @ X4 )
               => X13 )
             => X13 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).

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

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

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

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

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

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

thf(setunionE,axiom,
    ( setunionE
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
       => ! [X14: $o] :
            ( ! [X5: $i] :
                ( ( in @ X2 @ X5 )
               => ( ( in @ X5 @ X4 )
                 => X14 ) )
           => X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).

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

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

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

thf(wellorderingAx,axiom,
    ( wellorderingAx
  <=> ! [X4: $i] :
      ? [X5: $i] :
        ( ! [X7: $i] :
            ( ( in @ X7 @ X5 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X7 )
               => ( in @ X2 @ X4 ) ) )
        & ! [X2: $i,X3: $i] :
            ( ( ( in @ X2 @ X4 )
              & ( in @ X3 @ X4 ) )
           => ( ! [X7: $i] :
                  ( ( in @ X7 @ X5 )
                 => ( ( in @ X2 @ X7 )
                  <=> ( in @ X3 @ X7 ) ) )
             => ( X2 = X3 ) ) )
        & ! [X7: $i,X8: $i] :
            ( ( ( in @ X7 @ X5 )
              & ( in @ X8 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X8 ) )
              | ! [X2: $i] :
                  ( ( in @ X2 @ X8 )
                 => ( in @ X2 @ X7 ) ) ) )
        & ! [X7: $i] :
            ( ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X4 ) )
              & ? [X2: $i] : ( in @ X2 @ X7 ) )
           => ? [X8: $i,X2: $i] :
                ( ( in @ X8 @ X5 )
                & ( in @ X2 @ X7 )
                & ~ ? [X3: $i] :
                      ( ( in @ X3 @ X8 )
                      & ( in @ X3 @ X7 ) )
                & ! [X9: $i] :
                    ( ( in @ X9 @ X5 )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X9 )
                         => ( in @ X3 @ X8 ) )
                      | ( in @ X2 @ X9 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).

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

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

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

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

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

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

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

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

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

thf(c_0_58,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_59,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_60,plain,
    ( prop2set
    = ( ^ [Z0: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Z1: $i] : Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[prop2set]) ).

thf(c_0_61,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_62,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_63,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_64,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_65,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_66,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_67,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_68,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X172: $i] :
              ( ( X1 @ X172 )
              & ! [X173: $i] :
                  ( ( X1 @ X173 )
                 => ( X172 = X173 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_69,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_70,axiom,
    ( prop2setE
    = ( ! [X11: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X11 ) )
         => X11 ) ) ),
    inference(apply_def,[status(thm)],[prop2setE,c_0_60]) ).

thf(c_0_71,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X174: $i] :
              ( ( X1 @ X174 )
              & ! [X175: $i] :
                  ( ( X1 @ X175 )
                 => ( X174 = X175 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_61,c_0_59]) ).

thf(c_0_72,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_73,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_62]) ).

thf(c_0_74,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_63,c_0_62]) ).

thf(c_0_75,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_62]) ).

thf(c_0_76,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_77,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X176: $i] :
              ( ( X1 @ X176 )
              & ! [X177: $i] :
                  ( ( X1 @ X177 )
                 => ( X176 = X177 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_64,c_0_59]) ).

thf(c_0_78,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_62]) ).

thf(c_0_79,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_80,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_81,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X170: $i] :
              ( ( X1 @ X170 )
              & ! [X171: $i] :
                  ( ( X1 @ X171 )
                 => ( X170 = X171 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_65,c_0_59]) ).

thf(c_0_82,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X168: $i] :
                  ( ( X6 @ X2 @ X168 )
                  & ! [X169: $i] :
                      ( ( X6 @ X2 @ X169 )
                     => ( X168 = X169 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_66,c_0_59]) ).

thf(c_0_83,plain,
    ( epred1_0
  <=> ! [X207: $i] :
      ? [X208: $i] :
        ( ! [X209: $i] :
            ( ( in @ X209 @ X208 )
           => ! [X210: $i] :
                ( ( in @ X210 @ X209 )
               => ( in @ X210 @ X207 ) ) )
        & ! [X211: $i,X212: $i] :
            ( ( ( in @ X211 @ X207 )
              & ( in @ X212 @ X207 ) )
           => ( ! [X213: $i] :
                  ( ( in @ X213 @ X208 )
                 => ( ( in @ X211 @ X213 )
                  <=> ( in @ X212 @ X213 ) ) )
             => ( X211 = X212 ) ) )
        & ! [X214: $i,X215: $i] :
            ( ( ( in @ X214 @ X208 )
              & ( in @ X215 @ X208 ) )
           => ( ! [X216: $i] :
                  ( ( in @ X216 @ X214 )
                 => ( in @ X216 @ X215 ) )
              | ! [X217: $i] :
                  ( ( in @ X217 @ X215 )
                 => ( in @ X217 @ X214 ) ) ) )
        & ! [X218: $i] :
            ( ( ! [X219: $i] :
                  ( ( in @ X219 @ X218 )
                 => ( in @ X219 @ X207 ) )
              & ? [X220: $i] : ( in @ X220 @ X218 ) )
           => ? [X221: $i,X222: $i] :
                ( ( in @ X221 @ X208 )
                & ( in @ X222 @ X218 )
                & ~ ? [X223: $i] :
                      ( ( in @ X223 @ X221 )
                      & ( in @ X223 @ X218 ) )
                & ! [X224: $i] :
                    ( ( in @ X224 @ X208 )
                   => ( ! [X225: $i] :
                          ( ( in @ X225 @ X224 )
                         => ( in @ X225 @ X221 ) )
                      | ( in @ X222 @ X224 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_84,negated_conjecture,
    ~ ( ! [X178: $i,X179: $i] :
          ( ! [X180: $i] :
              ( ( in @ X180 @ X178 )
            <=> ( in @ X180 @ X179 ) )
         => ( X178 = X179 ) )
     => ( ! [X181: $i] :
            ~ ( in @ X181 @ emptyset )
       => ( ! [X182: $i,X183: $i,X184: $i] :
              ( ( in @ X184 @ ( setadjoin @ X182 @ X183 ) )
            <=> ( ( X184 = X182 )
                | ( in @ X184 @ X183 ) ) )
         => ( ! [X185: $i,X186: $i] :
                ( ( in @ X186 @ ( powerset @ X185 ) )
              <=> ! [X187: $i] :
                    ( ( in @ X187 @ X186 )
                   => ( in @ X187 @ X185 ) ) )
           => ( ! [X188: $i,X189: $i] :
                  ( ( in @ X189 @ ( setunion @ X188 ) )
                <=> ? [X190: $i] :
                      ( ( in @ X189 @ X190 )
                      & ( in @ X190 @ X188 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X191: $i] :
                      ( ( in @ X191 @ omega )
                     => ( in @ ( setadjoin @ X191 @ X191 ) @ omega ) )
                 => ( ! [X192: $i] :
                        ( ( ( in @ emptyset @ X192 )
                          & ! [X193: $i] :
                              ( ( ( in @ X193 @ omega )
                                & ( in @ X193 @ X192 ) )
                             => ( in @ ( setadjoin @ X193 @ X193 ) @ X192 ) ) )
                       => ! [X194: $i] :
                            ( ( in @ X194 @ omega )
                           => ( in @ X194 @ X192 ) ) )
                   => ( ! [X195: $i > $i > $o,X196: $i] :
                          ( ! [X197: $i] :
                              ( ( in @ X197 @ X196 )
                             => ? [X198: $i] :
                                  ( ( X195 @ X197 @ X198 )
                                  & ! [X199: $i] :
                                      ( ( X195 @ X197 @ X199 )
                                     => ( X198 = X199 ) ) ) )
                         => ? [X200: $i] :
                            ! [X201: $i] :
                              ( ( in @ X201 @ X200 )
                            <=> ? [X202: $i] :
                                  ( ( in @ X202 @ X196 )
                                  & ( X195 @ X202 @ X201 ) ) ) )
                     => ( ! [X203: $i] :
                            ( ? [X204: $i] : ( in @ X204 @ X203 )
                           => ? [X205: $i] :
                                ( ( in @ X205 @ X203 )
                                & ~ ? [X206: $i] :
                                      ( ( in @ X206 @ X205 )
                                      & ( in @ X206 @ X203 ) ) ) )
                       => ( epred1_0
                         => ( ! [X226: $i > $o] :
                                ( ? [X227: $i] :
                                    ( ( X226 @ X227 )
                                    & ! [X228: $i] :
                                        ( ( X226 @ X228 )
                                       => ( X227 = X228 ) ) )
                               => ( X226
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X226 @ Z0 ) ) ) )
                           => ( ! [X229: $i,X230: $i > $o,X231: $i] :
                                  ( ( in @ X231 @ X229 )
                                 => ( ( X230 @ X231 )
                                   => ( in @ X231 @ ( dsetconstr @ X229 @ X230 ) ) ) )
                             => ( ! [X232: $i,X233: $i > $o,X234: $i] :
                                    ( ( in @ X234 @ ( dsetconstr @ X232 @ X233 ) )
                                   => ( in @ X234 @ X232 ) )
                               => ( ! [X235: $i,X236: $i > $o,X237: $i] :
                                      ( ( in @ X237 @ ( dsetconstr @ X235 @ X236 ) )
                                     => ( X236 @ X237 ) )
                                 => ( ! [X238: $i > $o] :
                                        ( ? [X239: $i] :
                                            ( ( X238 @ X239 )
                                            & ! [X240: $i] :
                                                ( ( X238 @ X240 )
                                               => ( X239 = X240 ) ) )
                                       => ? [X241: $i] :
                                            ( ( X238 @ X241 )
                                            & ! [X242: $i] :
                                                ( ( X238 @ X242 )
                                               => ( X241 = X242 ) ) ) )
                                   => ( ! [X243: $o,X244: $i] :
                                          ( ( in @ X244
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [Z0: $i] : X243 ) )
                                         => X243 )
                                     => ( ! [X245: $i] :
                                            ( ( in @ X245 @ emptyset )
                                           => ! [X246: $o] : X246 )
                                       => ( ! [X247: $i] :
                                              ( ( in @ X247 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X248: $i] :
                                                ~ ( in @ X248 @ emptyset )
                                           => ( ! [X249: $i > $o] :
                                                  ( ? [X250: $i] :
                                                      ( ( X249 @ X250 )
                                                      & ! [X251: $i] :
                                                          ( ( X249 @ X251 )
                                                         => ( X250 = X251 ) ) )
                                                 => ? [X252: $i] : ( X249 @ X252 ) )
                                             => ( ! [X253: $i,X254: $i] :
                                                    ( ! [X255: $i] :
                                                        ( ( in @ X255 @ X253 )
                                                       => ( in @ X255 @ X254 ) )
                                                   => ( ! [X256: $i] :
                                                          ( ( in @ X256 @ X254 )
                                                         => ( in @ X256 @ X253 ) )
                                                     => ( X253 = X254 ) ) )
                                               => ( ! [X257: $i] :
                                                      ( ! [X258: $i] :
                                                          ~ ( in @ X258 @ X257 )
                                                     => ( X257 = emptyset ) )
                                                 => ( ! [X259: $i] :
                                                        ( ! [X260: $i] :
                                                            ~ ( in @ X260 @ X259 )
                                                       => ( X259 = emptyset ) )
                                                   => ( ! [X261: $i,X262: $i > $o,X263: $i] :
                                                          ( ( in @ X263 @ X261 )
                                                         => ( ( in @ X263 @ ( dsetconstr @ X261 @ X262 ) )
                                                          <=> ( X262 @ X263 ) ) )
                                                     => ( ! [X264: $i] :
                                                            ( ( X264 != emptyset )
                                                           => ? [X265: $i] : ( in @ X265 @ X264 ) )
                                                       => ( ! [X266: $i,X267: $i > $o,X268: $i] :
                                                              ( ( in @ X268 @ X266 )
                                                             => ( ( X267 @ X268 )
                                                               => ( ( dsetconstr @ X266 @ X267 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X269: $i] :
                                                                ( ? [X270: $i] : ( in @ X270 @ X269 )
                                                               => ( X269 != emptyset ) )
                                                           => ( ! [X271: $i,X272: $i] : ( in @ X271 @ ( setadjoin @ X271 @ X272 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X273: $i,X274: $i,X275: $i] :
                                                                      ( ( in @ X275 @ X274 )
                                                                     => ( in @ X275 @ ( setadjoin @ X273 @ X274 ) ) )
                                                                 => ( ! [X276: $i,X277: $i,X278: $i] :
                                                                        ( ( in @ X278 @ ( setadjoin @ X276 @ X277 ) )
                                                                       => ! [X279: $o] :
                                                                            ( ( ( X278 = X276 )
                                                                             => X279 )
                                                                           => ( ( ( in @ X278 @ X277 )
                                                                               => X279 )
                                                                             => X279 ) ) )
                                                                   => ( ! [X280: $i,X281: $i,X282: $i] :
                                                                          ( ( in @ X282 @ ( setadjoin @ X280 @ X281 ) )
                                                                         => ( ( X282 = X280 )
                                                                            | ( in @ X282 @ X281 ) ) )
                                                                     => ( ! [X283: $i] :
                                                                            ( ( dsetconstr @ X283
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X283 )
                                                                       => ( ! [X284: $i,X285: $i] :
                                                                              ( ! [X286: $i] :
                                                                                  ( ( in @ X286 @ X285 )
                                                                                 => ( in @ X286 @ X284 ) )
                                                                             => ( in @ X285 @ ( powerset @ X284 ) ) )
                                                                         => ( ! [X287: $i] : ( in @ emptyset @ ( powerset @ X287 ) )
                                                                           => ( ! [X288: $i] : ( in @ emptyset @ ( powerset @ X288 ) )
                                                                             => ( ! [X289: $i,X290: $i,X291: $i] :
                                                                                    ( ( in @ X290 @ ( powerset @ X289 ) )
                                                                                   => ( ( in @ X291 @ X290 )
                                                                                     => ( in @ X291 @ X289 ) ) )
                                                                               => ( ! [X292: $i,X293: $i,X294: $i] :
                                                                                      ( ( in @ X293 @ X294 )
                                                                                     => ( ( in @ X294 @ X292 )
                                                                                       => ( in @ X293 @ ( setunion @ X292 ) ) ) )
                                                                                 => ( ! [X295: $i,X296: $i] :
                                                                                        ( ( in @ X296 @ ( setunion @ X295 ) )
                                                                                       => ! [X297: $o] :
                                                                                            ( ! [X298: $i] :
                                                                                                ( ( in @ X296 @ X298 )
                                                                                               => ( ( in @ X298 @ X295 )
                                                                                                 => X297 ) )
                                                                                           => X297 ) )
                                                                                   => ( ! [X299: $i,X300: $i] :
                                                                                          ( ( in @ X300 @ X299 )
                                                                                         => ( in @ X300 @ ( powerset @ ( setunion @ X299 ) ) ) )
                                                                                     => ( ! [X301: $i > $o] :
                                                                                            ( ? [X302: $i] :
                                                                                                ( ( X301 @ X302 )
                                                                                                & ! [X303: $i] :
                                                                                                    ( ( X301 @ X303 )
                                                                                                   => ( X302 = X303 ) ) )
                                                                                           => ? [X304: $i] :
                                                                                              ! [X305: $i] :
                                                                                                ( ( X301 @ X305 )
                                                                                              <=> ( X305 = X304 ) ) )
                                                                                       => ( ! [X306: $i] :
                                                                                              ( ( X306 != emptyset )
                                                                                             => ? [X307: $i] :
                                                                                                  ( ( in @ X307 @ X306 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X308: $i,X309: $i] :
                                                                                                ( ( in @ X308 @ ( setadjoin @ X309 @ emptyset ) )
                                                                                               => ( X308 = X309 ) )
                                                                                           => ( ! [X310: $i,X311: $i] :
                                                                                                  ( ( X310 != X311 )
                                                                                                 => ~ ( in @ X311 @ ( setadjoin @ X310 @ emptyset ) ) )
                                                                                             => ( ! [X312: $i,X313: $i] :
                                                                                                    ( ( X312 = X313 )
                                                                                                   => ( in @ X312 @ ( setadjoin @ X313 @ emptyset ) ) )
                                                                                               => ( ! [X314: $i,X315: $i] :
                                                                                                      ( ( in @ X314 @ ( setadjoin @ X315 @ emptyset ) )
                                                                                                     => ( in @ X315 @ ( setadjoin @ X314 @ emptyset ) ) )
                                                                                                 => ( ! [X316: $i,X317: $i,X318: $i] :
                                                                                                        ( ( in @ X318 @ ( setadjoin @ X316 @ ( setadjoin @ X317 @ emptyset ) ) )
                                                                                                       => ( ( X318 = X316 )
                                                                                                          | ( X318 = X317 ) ) )
                                                                                                   => ( ! [X319: $i,X320: $i] : ( in @ X319 @ ( setadjoin @ X319 @ ( setadjoin @ X320 @ emptyset ) ) )
                                                                                                     => ( ! [X321: $i,X322: $i] : ( in @ X322 @ ( setadjoin @ X321 @ ( setadjoin @ X322 @ emptyset ) ) )
                                                                                                       => ( ! [X323: $i,X324: $i > $o] :
                                                                                                              ( ? [X325: $i] :
                                                                                                                  ( ( in @ X325 @ X323 )
                                                                                                                  & ( X324 @ X325 ) )
                                                                                                             => ( ( ( dsetconstr @ X323 @ X324 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X326: $i > $o,X327: $i] :
                                                                                                                ( ( in @ X327 @ emptyset )
                                                                                                               => ( X326 @ X327 ) )
                                                                                                           => ( ! [X328: $i,X329: $i > $o] :
                                                                                                                  ( ~ ! [X330: $i] :
                                                                                                                        ( ( in @ X330 @ X328 )
                                                                                                                       => ( X329 @ X330 ) )
                                                                                                                 => ? [X331: $i] :
                                                                                                                      ( ( in @ X331 @ X328 )
                                                                                                                      & ~ ( X329 @ X331 ) ) )
                                                                                                             => ( ! [X332: $i,X333: $i > $o] :
                                                                                                                    ( ! [X334: $i] :
                                                                                                                        ( ( in @ X334 @ X332 )
                                                                                                                       => ~ ( X333 @ X334 ) )
                                                                                                                   => ~ ? [X335: $i] :
                                                                                                                          ( ( in @ X335 @ X332 )
                                                                                                                          & ( X333 @ X335 ) ) )
                                                                                                               => ! [X4: $i,X1: $i > $o] :
                                                                                                                    ( ~ ? [X2: $i] :
                                                                                                                          ( ( in @ X2 @ X4 )
                                                                                                                          & ( X1 @ X2 ) )
                                                                                                                   => ! [X2: $i] :
                                                                                                                        ( ( in @ X2 @ X4 )
                                                                                                                       => ~ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(assume_negation,[status(cth)],[quantDeMorgan3]),quantDeMorgan2]),eqinunit]),singletonsswitch]),upairsetE]),c_0_67]),upairsetIL]),upairsetIR]),c_0_68]),c_0_69]),vacuousDall]),c_0_70]),quantDeMorgan1]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_71]),setext]),emptyI]),noeltsimpempty]),c_0_72]),c_0_73]),c_0_74]),c_0_75]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_76]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_77]),c_0_78]),uniqinunit]),notinsingleton]),c_0_79]),c_0_80]),c_0_81]),wellorderingAx]),foundationAx]),c_0_82]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_83]) ).

thf(c_0_85,negated_conjecture,
    ! [X336: $i,X337: $i,X339: $i,X340: $i,X341: $i,X342: $i,X343: $i,X344: $i,X345: $i,X346: $i,X347: $i,X349: $i,X350: $i,X352: $i,X353: $i,X354: $i,X355: $i,X356: $i,X358: $i,X359: $i > $i > $o,X360: $i,X362: $i,X365: $i,X367: $i,X368: $i,X369: $i,X370: $i,X372: $i,X373: $i > $o,X374: $i,X376: $i,X377: $i > $o,X378: $i,X379: $i,X380: $i > $o,X381: $i,X382: $i,X383: $i > $o,X384: $i,X385: $i > $o,X386: $i,X389: $i,X390: $o,X391: $i,X392: $i,X393: $o,X394: $i,X395: $i,X396: $i > $o,X397: $i,X400: $i,X401: $i,X404: $i,X406: $i,X408: $i,X409: $i > $o,X410: $i,X411: $i,X413: $i,X414: $i > $o,X415: $i,X416: $i,X417: $i,X418: $i,X419: $i,X420: $i,X421: $i,X422: $i,X423: $i,X424: $i,X425: $i,X426: $o,X427: $i,X428: $i,X429: $i,X430: $i,X431: $i,X432: $i,X434: $i,X435: $i,X436: $i,X437: $i,X438: $i,X439: $i,X440: $i,X441: $i,X442: $i,X443: $i,X444: $o,X446: $i,X447: $i,X448: $i > $o,X449: $i,X452: $i,X453: $i,X454: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X463: $i,X464: $i,X465: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X472: $i > $o,X473: $i,X474: $i > $o,X475: $i,X476: $i,X477: $i > $o,X478: $i,X480: $i,X481: $i > $o,X483: $i,X486: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X336 @ X337 ) @ X336 )
        | ~ ( in @ ( esk1_2 @ X336 @ X337 ) @ X337 )
        | ( X336 = X337 ) )
      & ( ( in @ ( esk1_2 @ X336 @ X337 ) @ X336 )
        | ( in @ ( esk1_2 @ X336 @ X337 ) @ X337 )
        | ( X336 = X337 ) )
      & ~ ( in @ X339 @ emptyset )
      & ( ~ ( in @ X342 @ ( setadjoin @ X340 @ X341 ) )
        | ( X342 = X340 )
        | ( in @ X342 @ X341 ) )
      & ( ( X342 != X340 )
        | ( in @ X342 @ ( setadjoin @ X340 @ X341 ) ) )
      & ( ~ ( in @ X342 @ X341 )
        | ( in @ X342 @ ( setadjoin @ X340 @ X341 ) ) )
      & ( ~ ( in @ X344 @ ( powerset @ X343 ) )
        | ~ ( in @ X345 @ X344 )
        | ( in @ X345 @ X343 ) )
      & ( ( in @ ( esk2_2 @ X346 @ X347 ) @ X347 )
        | ( in @ X347 @ ( powerset @ X346 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X346 @ X347 ) @ X346 )
        | ( in @ X347 @ ( powerset @ X346 ) ) )
      & ( ( in @ X350 @ ( esk3_2 @ X349 @ X350 ) )
        | ~ ( in @ X350 @ ( setunion @ X349 ) ) )
      & ( ( in @ ( esk3_2 @ X349 @ X350 ) @ X349 )
        | ~ ( in @ X350 @ ( setunion @ X349 ) ) )
      & ( ~ ( in @ X353 @ X354 )
        | ~ ( in @ X354 @ X352 )
        | ( in @ X353 @ ( setunion @ X352 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X355 @ omega )
        | ( in @ ( setadjoin @ X355 @ X355 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X356 ) @ omega )
        | ~ ( in @ emptyset @ X356 )
        | ~ ( in @ X358 @ omega )
        | ( in @ X358 @ X356 ) )
      & ( ( in @ ( esk4_1 @ X356 ) @ X356 )
        | ~ ( in @ emptyset @ X356 )
        | ~ ( in @ X358 @ omega )
        | ( in @ X358 @ X356 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X356 ) @ ( esk4_1 @ X356 ) ) @ X356 )
        | ~ ( in @ emptyset @ X356 )
        | ~ ( in @ X358 @ omega )
        | ( in @ X358 @ X356 ) )
      & ( ( in @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X360 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( in @ ( esk5_2 @ X359 @ X360 ) @ X360 ) )
      & ( ( X359 @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X365 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( in @ ( esk5_2 @ X359 @ X360 ) @ X360 ) )
      & ( ~ ( in @ X368 @ X360 )
        | ~ ( X359 @ X368 @ X367 )
        | ( in @ X367 @ ( esk7_2 @ X359 @ X360 ) )
        | ( in @ ( esk5_2 @ X359 @ X360 ) @ X360 ) )
      & ( ( in @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X360 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X359 @ ( esk5_2 @ X359 @ X360 ) @ ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ( X359 @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X365 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X359 @ ( esk5_2 @ X359 @ X360 ) @ ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ~ ( in @ X368 @ X360 )
        | ~ ( X359 @ X368 @ X367 )
        | ( in @ X367 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X359 @ ( esk5_2 @ X359 @ X360 ) @ ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ( in @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X360 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X362
         != ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ( X359 @ ( esk8_3 @ X359 @ X360 @ X365 ) @ X365 )
        | ~ ( in @ X365 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X362
         != ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ~ ( in @ X368 @ X360 )
        | ~ ( X359 @ X368 @ X367 )
        | ( in @ X367 @ ( esk7_2 @ X359 @ X360 ) )
        | ( X362
         != ( esk6_3 @ X359 @ X360 @ X362 ) )
        | ~ ( X359 @ ( esk5_2 @ X359 @ X360 ) @ X362 ) )
      & ( ( in @ ( esk9_1 @ X369 ) @ X369 )
        | ~ ( in @ X370 @ X369 ) )
      & ( ~ ( in @ X372 @ ( esk9_1 @ X369 ) )
        | ~ ( in @ X372 @ X369 )
        | ~ ( in @ X370 @ X369 ) )
      & epred1_0
      & ( ( X373 @ ( esk10_2 @ X373 @ X374 ) )
        | ~ ( X373 @ X374 )
        | ( X373 @ ( descr @ X373 ) ) )
      & ( ( X374
         != ( esk10_2 @ X373 @ X374 ) )
        | ~ ( X373 @ X374 )
        | ( X373 @ ( descr @ X373 ) ) )
      & ( ~ ( in @ X378 @ X376 )
        | ~ ( X377 @ X378 )
        | ( in @ X378 @ ( dsetconstr @ X376 @ X377 ) ) )
      & ( ~ ( in @ X381 @ ( dsetconstr @ X379 @ X380 ) )
        | ( in @ X381 @ X379 ) )
      & ( ~ ( in @ X384 @ ( dsetconstr @ X382 @ X383 ) )
        | ( X383 @ X384 ) )
      & ( ( X385 @ ( esk12_1 @ X385 ) )
        | ( X385 @ ( esk11_2 @ X385 @ X386 ) )
        | ~ ( X385 @ X386 ) )
      & ( ~ ( X385 @ X389 )
        | ( ( esk12_1 @ X385 )
          = X389 )
        | ( X385 @ ( esk11_2 @ X385 @ X386 ) )
        | ~ ( X385 @ X386 ) )
      & ( ( X385 @ ( esk12_1 @ X385 ) )
        | ( X386
         != ( esk11_2 @ X385 @ X386 ) )
        | ~ ( X385 @ X386 ) )
      & ( ~ ( X385 @ X389 )
        | ( ( esk12_1 @ X385 )
          = X389 )
        | ( X386
         != ( esk11_2 @ X385 @ X386 ) )
        | ~ ( X385 @ X386 ) )
      & ( ~ ( in @ X391
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X390 ) )
        | X390 )
      & ( ~ ( in @ X392 @ emptyset )
        | X393 )
      & ( ~ ( in @ X394 @ emptyset )
        | ~ $true )
      & ~ ( in @ X395 @ emptyset )
      & ( ( X396 @ ( esk13_2 @ X396 @ X397 ) )
        | ~ ( X396 @ X397 )
        | ( X396 @ ( esk14_1 @ X396 ) ) )
      & ( ( X397
         != ( esk13_2 @ X396 @ X397 ) )
        | ~ ( X396 @ X397 )
        | ( X396 @ ( esk14_1 @ X396 ) ) )
      & ( ( in @ ( esk16_2 @ X400 @ X401 ) @ X401 )
        | ( X400 = X401 )
        | ( in @ ( esk15_2 @ X400 @ X401 ) @ X400 ) )
      & ( ~ ( in @ ( esk16_2 @ X400 @ X401 ) @ X400 )
        | ( X400 = X401 )
        | ( in @ ( esk15_2 @ X400 @ X401 ) @ X400 ) )
      & ( ( in @ ( esk16_2 @ X400 @ X401 ) @ X401 )
        | ( X400 = X401 )
        | ~ ( in @ ( esk15_2 @ X400 @ X401 ) @ X401 ) )
      & ( ~ ( in @ ( esk16_2 @ X400 @ X401 ) @ X400 )
        | ( X400 = X401 )
        | ~ ( in @ ( esk15_2 @ X400 @ X401 ) @ X401 ) )
      & ( ( in @ ( esk17_1 @ X404 ) @ X404 )
        | ( X404 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X406 ) @ X406 )
        | ( X406 = emptyset ) )
      & ( ~ ( in @ X410 @ ( dsetconstr @ X408 @ X409 ) )
        | ( X409 @ X410 )
        | ~ ( in @ X410 @ X408 ) )
      & ( ~ ( X409 @ X410 )
        | ( in @ X410 @ ( dsetconstr @ X408 @ X409 ) )
        | ~ ( in @ X410 @ X408 ) )
      & ( ( X411 = emptyset )
        | ( in @ ( esk19_1 @ X411 ) @ X411 ) )
      & ( ~ ( in @ X415 @ X413 )
        | ~ ( X414 @ X415 )
        | ( ( dsetconstr @ X413 @ X414 )
         != emptyset ) )
      & ( ~ ( in @ X417 @ X416 )
        | ( X416 != emptyset ) )
      & ( in @ X418 @ ( setadjoin @ X418 @ X419 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X422 @ X421 )
        | ( in @ X422 @ ( setadjoin @ X420 @ X421 ) ) )
      & ( ( in @ X425 @ X424 )
        | X426
        | ( X425 = X423 )
        | ~ ( in @ X425 @ ( setadjoin @ X423 @ X424 ) ) )
      & ( ~ X426
        | X426
        | ( X425 = X423 )
        | ~ ( in @ X425 @ ( setadjoin @ X423 @ X424 ) ) )
      & ( ( in @ X425 @ X424 )
        | X426
        | ~ X426
        | ~ ( in @ X425 @ ( setadjoin @ X423 @ X424 ) ) )
      & ( ~ X426
        | X426
        | ~ X426
        | ~ ( in @ X425 @ ( setadjoin @ X423 @ X424 ) ) )
      & ( ~ ( in @ X429 @ ( setadjoin @ X427 @ X428 ) )
        | ( X429 = X427 )
        | ( in @ X429 @ X428 ) )
      & ( ( dsetconstr @ X430
          @ ^ [Z0: $i] : $true )
        = X430 )
      & ( ( in @ ( esk20_2 @ X431 @ X432 ) @ X432 )
        | ( in @ X432 @ ( powerset @ X431 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X431 @ X432 ) @ X431 )
        | ( in @ X432 @ ( powerset @ X431 ) ) )
      & ( in @ emptyset @ ( powerset @ X434 ) )
      & ( in @ emptyset @ ( powerset @ X435 ) )
      & ( ~ ( in @ X437 @ ( powerset @ X436 ) )
        | ~ ( in @ X438 @ X437 )
        | ( in @ X438 @ X436 ) )
      & ( ~ ( in @ X440 @ X441 )
        | ~ ( in @ X441 @ X439 )
        | ( in @ X440 @ ( setunion @ X439 ) ) )
      & ( ( in @ X443 @ ( esk21_3 @ X442 @ X443 @ X444 ) )
        | X444
        | ~ ( in @ X443 @ ( setunion @ X442 ) ) )
      & ( ( in @ ( esk21_3 @ X442 @ X443 @ X444 ) @ X442 )
        | X444
        | ~ ( in @ X443 @ ( setunion @ X442 ) ) )
      & ( ~ X444
        | X444
        | ~ ( in @ X443 @ ( setunion @ X442 ) ) )
      & ( ~ ( in @ X447 @ X446 )
        | ( in @ X447 @ ( powerset @ ( setunion @ X446 ) ) ) )
      & ( ~ ( X448 @ X452 )
        | ( X452
          = ( esk23_1 @ X448 ) )
        | ( X448 @ ( esk22_2 @ X448 @ X449 ) )
        | ~ ( X448 @ X449 ) )
      & ( ( X453
         != ( esk23_1 @ X448 ) )
        | ( X448 @ X453 )
        | ( X448 @ ( esk22_2 @ X448 @ X449 ) )
        | ~ ( X448 @ X449 ) )
      & ( ~ ( X448 @ X452 )
        | ( X452
          = ( esk23_1 @ X448 ) )
        | ( X449
         != ( esk22_2 @ X448 @ X449 ) )
        | ~ ( X448 @ X449 ) )
      & ( ( X453
         != ( esk23_1 @ X448 ) )
        | ( X448 @ X453 )
        | ( X449
         != ( esk22_2 @ X448 @ X449 ) )
        | ~ ( X448 @ X449 ) )
      & ( ( in @ ( esk24_1 @ X454 ) @ X454 )
        | ( X454 = emptyset ) )
      & ( $true
        | ( X454 = emptyset ) )
      & ( ~ ( in @ X456 @ ( setadjoin @ X457 @ emptyset ) )
        | ( X456 = X457 ) )
      & ( ( X458 = X459 )
        | ~ ( in @ X459 @ ( setadjoin @ X458 @ emptyset ) ) )
      & ( ( X460 != X461 )
        | ( in @ X460 @ ( setadjoin @ X461 @ emptyset ) ) )
      & ( ~ ( in @ X462 @ ( setadjoin @ X463 @ emptyset ) )
        | ( in @ X463 @ ( setadjoin @ X462 @ emptyset ) ) )
      & ( ~ ( in @ X466 @ ( setadjoin @ X464 @ ( setadjoin @ X465 @ emptyset ) ) )
        | ( X466 = X464 )
        | ( X466 = X465 ) )
      & ( in @ X467 @ ( setadjoin @ X467 @ ( setadjoin @ X468 @ emptyset ) ) )
      & ( in @ X470 @ ( setadjoin @ X469 @ ( setadjoin @ X470 @ emptyset ) ) )
      & ( ~ ( in @ X473 @ X471 )
        | ~ ( X472 @ X473 )
        | ( ( dsetconstr @ X471 @ X472 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X475 @ emptyset )
        | ( X474 @ X475 ) )
      & ( ( in @ ( esk25_2 @ X476 @ X477 ) @ X476 )
        | ~ ( in @ X478 @ X476 )
        | ( X477 @ X478 ) )
      & ( ~ ( X477 @ ( esk25_2 @ X476 @ X477 ) )
        | ~ ( in @ X478 @ X476 )
        | ( X477 @ X478 ) )
      & ( ( in @ ( esk26_2 @ X480 @ X481 ) @ X480 )
        | ~ ( in @ X483 @ X480 )
        | ~ ( X481 @ X483 ) )
      & ( ( X481 @ ( esk26_2 @ X480 @ X481 ) )
        | ~ ( in @ X483 @ X480 )
        | ~ ( X481 @ X483 ) )
      & ( ~ ( in @ X486 @ esk27_0 )
        | ~ ( epred2_0 @ X486 ) )
      & ( in @ esk28_0 @ esk27_0 )
      & ( epred2_0 @ esk28_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_84])])])])])])]) ).

thf(c_0_86,negated_conjecture,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ esk27_0 )
      | ~ ( epred2_0 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

thf(c_0_87,negated_conjecture,
    in @ esk28_0 @ esk27_0,
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

thf(c_0_88,negated_conjecture,
    epred2_0 @ esk28_0,
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

thf(c_0_89,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU538^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 16:12:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  Running higher-order theorem proving
% 0.21/0.50  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.55  # Version: 3.1.0-ho
% 0.36/0.55  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.36/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.36/0.55  # Starting sh5l with 300s (1) cores
% 0.36/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.36/0.55  # Starting new_bool_2 with 300s (1) cores
% 0.36/0.55  # sh5l with pid 15789 completed with status 0
% 0.36/0.55  # Result found by sh5l
% 0.36/0.55  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.36/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.36/0.55  # Starting sh5l with 300s (1) cores
% 0.36/0.55  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.36/0.55  # Search class: HGHSM-FFMS31-SHSSMSBN
% 0.36/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.55  # Starting new_ho_10 with 181s (1) cores
% 0.36/0.55  # new_ho_10 with pid 15792 completed with status 0
% 0.36/0.55  # Result found by new_ho_10
% 0.36/0.55  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.36/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.36/0.55  # Starting sh5l with 300s (1) cores
% 0.36/0.55  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.36/0.55  # Search class: HGHSM-FFMS31-SHSSMSBN
% 0.36/0.55  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.36/0.55  # Starting new_ho_10 with 181s (1) cores
% 0.36/0.55  # Preprocessing time       : 0.005 s
% 0.36/0.55  # Presaturation interreduction done
% 0.36/0.55  
% 0.36/0.55  # Proof found!
% 0.36/0.55  # SZS status Theorem
% 0.36/0.55  # SZS output start CNFRefutation
% See solution above
% 0.36/0.55  # Parsed axioms                        : 123
% 0.36/0.55  # Removed by relevancy pruning/SinE    : 65
% 0.36/0.55  # Initial clauses                      : 109
% 0.36/0.55  # Removed in clause preprocessing      : 5
% 0.36/0.55  # Initial clauses in saturation        : 104
% 0.36/0.55  # Processed clauses                    : 114
% 0.36/0.55  # ...of these trivial                  : 3
% 0.36/0.55  # ...subsumed                          : 14
% 0.36/0.55  # ...remaining for further processing  : 97
% 0.36/0.55  # Other redundant clauses eliminated   : 5
% 0.36/0.55  # Clauses deleted for lack of memory   : 0
% 0.36/0.55  # Backward-subsumed                    : 0
% 0.36/0.55  # Backward-rewritten                   : 1
% 0.36/0.55  # Generated clauses                    : 6
% 0.36/0.55  # ...of the previous two non-redundant : 4
% 0.36/0.55  # ...aggressively subsumed             : 0
% 0.36/0.55  # Contextual simplify-reflections      : 0
% 0.36/0.55  # Paramodulations                      : 1
% 0.36/0.55  # Factorizations                       : 0
% 0.36/0.55  # NegExts                              : 0
% 0.36/0.55  # Equation resolutions                 : 5
% 0.36/0.55  # Disequality decompositions           : 0
% 0.36/0.55  # Total rewrite steps                  : 19
% 0.36/0.55  # ...of those cached                   : 12
% 0.36/0.55  # Propositional unsat checks           : 0
% 0.36/0.55  #    Propositional check models        : 0
% 0.36/0.55  #    Propositional check unsatisfiable : 0
% 0.36/0.55  #    Propositional clauses             : 0
% 0.36/0.55  #    Propositional clauses after purity: 0
% 0.36/0.55  #    Propositional unsat core size     : 0
% 0.36/0.55  #    Propositional preprocessing time  : 0.000
% 0.36/0.55  #    Propositional encoding time       : 0.000
% 0.36/0.55  #    Propositional solver time         : 0.000
% 0.36/0.55  #    Success case prop preproc time    : 0.000
% 0.36/0.55  #    Success case prop encoding time   : 0.000
% 0.36/0.55  #    Success case prop solver time     : 0.000
% 0.36/0.55  # Current number of processed clauses  : 6
% 0.36/0.55  #    Positive orientable unit clauses  : 4
% 0.36/0.55  #    Positive unorientable unit clauses: 0
% 0.36/0.55  #    Negative unit clauses             : 1
% 0.36/0.55  #    Non-unit-clauses                  : 1
% 0.36/0.55  # Current number of unprocessed clauses: 79
% 0.36/0.55  # ...number of literals in the above   : 236
% 0.36/0.55  # Current number of archived formulas  : 0
% 0.36/0.55  # Current number of archived clauses   : 86
% 0.36/0.55  # Clause-clause subsumption calls (NU) : 2571
% 0.36/0.55  # Rec. Clause-clause subsumption calls : 1075
% 0.36/0.55  # Non-unit clause-clause subsumptions  : 12
% 0.36/0.55  # Unit Clause-clause subsumption calls : 1
% 0.36/0.55  # Rewrite failures with RHS unbound    : 0
% 0.36/0.55  # BW rewrite match attempts            : 3
% 0.36/0.55  # BW rewrite match successes           : 1
% 0.36/0.55  # Condensation attempts                : 114
% 0.36/0.55  # Condensation successes               : 3
% 0.36/0.55  # Termbank termtop insertions          : 15897
% 0.36/0.55  # Search garbage collected termcells   : 5636
% 0.36/0.55  
% 0.36/0.55  # -------------------------------------------------
% 0.36/0.55  # User time                : 0.020 s
% 0.36/0.55  # System time              : 0.010 s
% 0.36/0.55  # Total time               : 0.030 s
% 0.36/0.55  # Maximum resident set size: 3328 pages
% 0.36/0.55  
% 0.36/0.55  # -------------------------------------------------
% 0.36/0.55  # User time                : 0.024 s
% 0.36/0.55  # System time              : 0.012 s
% 0.36/0.55  # Total time               : 0.036 s
% 0.36/0.55  # Maximum resident set size: 1852 pages
% 0.36/0.55  % E---3.1 exiting
% 0.36/0.55  % E exiting
%------------------------------------------------------------------------------