TSTP Solution File: SEU554^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU554^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 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 03:28:09 EDT 2024

% Result   : Theorem 0.20s 0.53s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  198
% Syntax   : Number of formulae    :  234 (  20 unt; 126 typ;   0 def)
%            Number of atoms       :  872 ( 237 equ;   0 cnn)
%            Maximal formula atoms :  260 (   8 avg)
%            Number of connectives : 3393 ( 305   ~; 334   |; 229   &;1987   @)
%                                         ( 120 <=>; 418  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  319 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  233 ( 233   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  129 ( 126 usr;  77 con; 0-3 aty)
%            Number of variables   :  748 (  54   ^ 598   !;  96   ?; 748   :)

% 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_41,type,
    descrp: $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_104,type,
    epred1_0: $o ).

thf(decl_105,type,
    esk1_2: $i > $i > $i ).

thf(decl_106,type,
    esk2_2: $i > $i > $i ).

thf(decl_107,type,
    esk3_2: $i > $i > $i ).

thf(decl_108,type,
    esk4_1: $i > $i ).

thf(decl_109,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_110,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_111,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_112,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_113,type,
    esk9_1: $i > $i ).

thf(decl_114,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_115,type,
    esk11_1: ( $i > $o ) > $i ).

thf(decl_116,type,
    esk12_2: ( $i > $o ) > $i > $i ).

thf(decl_117,type,
    esk13_1: ( $i > $o ) > $i ).

thf(decl_118,type,
    esk14_2: $i > $i > $i ).

thf(decl_119,type,
    esk15_2: $i > $i > $i ).

thf(decl_120,type,
    esk16_1: $i > $i ).

thf(decl_121,type,
    esk17_1: $i > $i ).

thf(decl_122,type,
    esk18_1: $i > $i ).

thf(decl_123,type,
    esk19_2: $i > $i > $i ).

thf(decl_124,type,
    esk20_3: $i > $i > $o > $i ).

thf(decl_125,type,
    esk21_2: ( $i > $o ) > $i > $i ).

thf(decl_126,type,
    esk22_1: ( $i > $o ) > $i ).

thf(decl_127,type,
    esk23_1: $i > $i ).

thf(decl_128,type,
    esk24_2: $i > ( $i > $o ) > $i ).

thf(decl_129,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_130,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_131,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_132,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_133,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_134,type,
    esk30_2: ( $i > $o ) > $i > $i ).

thf(decl_135,type,
    esk31_1: ( $i > $o ) > $i ).

thf(decl_136,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_137,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_138,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_139,type,
    esk35_2: ( $i > $o ) > $i > $i ).

thf(decl_140,type,
    esk36_1: ( $i > $o ) > $i ).

thf(decl_141,type,
    esk37_2: ( $i > $o ) > $i > $i ).

thf(decl_142,type,
    esk38_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_143,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_144,type,
    esk40_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_145,type,
    esk41_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_146,type,
    esk42_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_147,type,
    esk43_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_148,type,
    esk44_0: $i ).

thf(decl_149,type,
    esk45_0: $i ).

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(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(exuI1,axiom,
    ( exuI1
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(setadjoinE,axiom,
    ( setadjoinE
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ! [X12: $o] :
            ( ( ( X3 = X2 )
             => X12 )
           => ( ( ( in @ X3 @ X4 )
               => X12 )
             => X12 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(wellorderingAx,axiom,
    ( wellorderingAx
  <=> ! [X4: $i] :
      ? [X5: $i] :
        ( ! [X7: $i] :
            ( ( in @ X7 @ X5 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X7 )
               => ( in @ X2 @ X4 ) ) )
        & ! [X2: $i,X3: $i] :
            ( ( ( in @ X2 @ X4 )
              & ( in @ X3 @ X4 ) )
           => ( ! [X7: $i] :
                  ( ( in @ X7 @ X5 )
                 => ( ( in @ X2 @ X7 )
                  <=> ( in @ X3 @ X7 ) ) )
             => ( X2 = X3 ) ) )
        & ! [X7: $i,X8: $i] :
            ( ( ( in @ X7 @ X5 )
              & ( in @ X8 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X8 ) )
              | ! [X2: $i] :
                  ( ( in @ X2 @ X8 )
                 => ( in @ X2 @ X7 ) ) ) )
        & ! [X7: $i] :
            ( ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X4 ) )
              & ? [X2: $i] : ( in @ X2 @ X7 ) )
           => ? [X8: $i,X2: $i] :
                ( ( in @ X8 @ X5 )
                & ( in @ X2 @ X7 )
                & ~ ? [X3: $i] :
                      ( ( in @ X3 @ X8 )
                      & ( in @ X3 @ X7 ) )
                & ! [X9: $i] :
                    ( ( in @ X9 @ X5 )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X9 )
                         => ( in @ X3 @ X8 ) )
                      | ( in @ X2 @ X9 ) ) ) ) ) ) ),
    file('/export/starexec/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_71,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_72,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_73,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_74,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_75,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_76,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_77,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_78,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_79,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_80,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_81,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_82,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_83,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X220: $i] :
              ( ( X1 @ X220 )
              & ! [X221: $i] :
                  ( ( X1 @ X221 )
                 => ( X220 = X221 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_71,c_0_72]) ).

thf(c_0_84,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X224: $i] :
              ( ( X1 @ X224 )
              & ! [X225: $i] :
                  ( ( X1 @ X225 )
                 => ( X224 = X225 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_73,c_0_72]) ).

thf(c_0_85,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X226: $i] :
                ( ( X1 @ X226 )
                & ! [X227: $i] :
                    ( ( X1 @ X227 )
                   => ( X226 = X227 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_74,c_0_72]) ).

thf(c_0_86,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X228: $i] :
              ( ( X1 @ X228 )
              & ! [X229: $i] :
                  ( ( X1 @ X229 )
                 => ( X228 = X229 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_75,c_0_72]) ).

thf(c_0_87,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X230: $i] :
              ( ( X1 @ X230 )
              & ! [X231: $i] :
                  ( ( X1 @ X231 )
                 => ( X230 = X231 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_76,c_0_72]) ).

thf(c_0_88,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_89,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X232: $i] :
                ( ( X1 @ X232 )
                & ! [X233: $i] :
                    ( ( X1 @ X233 )
                   => ( X232 = X233 ) ) )
          <=> ? [X234: $i] :
                ( ( X17 @ X234 )
                & ! [X235: $i] :
                    ( ( X17 @ X235 )
                   => ( X234 = X235 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_77,c_0_72]) ).

thf(c_0_90,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_78]) ).

thf(c_0_91,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_79,c_0_78]) ).

thf(c_0_92,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_78]) ).

thf(c_0_93,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_94,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X222: $i] :
              ( ( X1 @ X222 )
              & ! [X223: $i] :
                  ( ( X1 @ X223 )
                 => ( X222 = X223 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_80,c_0_72]) ).

thf(c_0_95,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_78]) ).

thf(c_0_96,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_97,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X218: $i] :
              ( ( X1 @ X218 )
              & ! [X219: $i] :
                  ( ( X1 @ X219 )
                 => ( X218 = X219 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_81,c_0_72]) ).

thf(c_0_98,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_99,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_100,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_101,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X216: $i] :
                  ( ( X6 @ X2 @ X216 )
                  & ! [X217: $i] :
                      ( ( X6 @ X2 @ X217 )
                     => ( X216 = X217 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_82,c_0_72]) ).

thf(c_0_102,plain,
    ( epred1_0
  <=> ! [X265: $i] :
      ? [X266: $i] :
        ( ! [X267: $i] :
            ( ( in @ X267 @ X266 )
           => ! [X268: $i] :
                ( ( in @ X268 @ X267 )
               => ( in @ X268 @ X265 ) ) )
        & ! [X269: $i,X270: $i] :
            ( ( ( in @ X269 @ X265 )
              & ( in @ X270 @ X265 ) )
           => ( ! [X271: $i] :
                  ( ( in @ X271 @ X266 )
                 => ( ( in @ X269 @ X271 )
                  <=> ( in @ X270 @ X271 ) ) )
             => ( X269 = X270 ) ) )
        & ! [X272: $i,X273: $i] :
            ( ( ( in @ X272 @ X266 )
              & ( in @ X273 @ X266 ) )
           => ( ! [X274: $i] :
                  ( ( in @ X274 @ X272 )
                 => ( in @ X274 @ X273 ) )
              | ! [X275: $i] :
                  ( ( in @ X275 @ X273 )
                 => ( in @ X275 @ X272 ) ) ) )
        & ! [X276: $i] :
            ( ( ! [X277: $i] :
                  ( ( in @ X277 @ X276 )
                 => ( in @ X277 @ X265 ) )
              & ? [X278: $i] : ( in @ X278 @ X276 ) )
           => ? [X279: $i,X280: $i] :
                ( ( in @ X279 @ X266 )
                & ( in @ X280 @ X276 )
                & ~ ? [X281: $i] :
                      ( ( in @ X281 @ X279 )
                      & ( in @ X281 @ X276 ) )
                & ! [X282: $i] :
                    ( ( in @ X282 @ X266 )
                   => ( ! [X283: $i] :
                          ( ( in @ X283 @ X282 )
                         => ( in @ X283 @ X279 ) )
                      | ( in @ X280 @ X282 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_103,negated_conjecture,
    ~ ( ! [X236: $i,X237: $i] :
          ( ! [X238: $i] :
              ( ( in @ X238 @ X236 )
            <=> ( in @ X238 @ X237 ) )
         => ( X236 = X237 ) )
     => ( ! [X239: $i] :
            ~ ( in @ X239 @ emptyset )
       => ( ! [X240: $i,X241: $i,X242: $i] :
              ( ( in @ X242 @ ( setadjoin @ X240 @ X241 ) )
            <=> ( ( X242 = X240 )
                | ( in @ X242 @ X241 ) ) )
         => ( ! [X243: $i,X244: $i] :
                ( ( in @ X244 @ ( powerset @ X243 ) )
              <=> ! [X245: $i] :
                    ( ( in @ X245 @ X244 )
                   => ( in @ X245 @ X243 ) ) )
           => ( ! [X246: $i,X247: $i] :
                  ( ( in @ X247 @ ( setunion @ X246 ) )
                <=> ? [X248: $i] :
                      ( ( in @ X247 @ X248 )
                      & ( in @ X248 @ X246 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X249: $i] :
                      ( ( in @ X249 @ omega )
                     => ( in @ ( setadjoin @ X249 @ X249 ) @ omega ) )
                 => ( ! [X250: $i] :
                        ( ( ( in @ emptyset @ X250 )
                          & ! [X251: $i] :
                              ( ( ( in @ X251 @ omega )
                                & ( in @ X251 @ X250 ) )
                             => ( in @ ( setadjoin @ X251 @ X251 ) @ X250 ) ) )
                       => ! [X252: $i] :
                            ( ( in @ X252 @ omega )
                           => ( in @ X252 @ X250 ) ) )
                   => ( ! [X253: $i > $i > $o,X254: $i] :
                          ( ! [X255: $i] :
                              ( ( in @ X255 @ X254 )
                             => ? [X256: $i] :
                                  ( ( X253 @ X255 @ X256 )
                                  & ! [X257: $i] :
                                      ( ( X253 @ X255 @ X257 )
                                     => ( X256 = X257 ) ) ) )
                         => ? [X258: $i] :
                            ! [X259: $i] :
                              ( ( in @ X259 @ X258 )
                            <=> ? [X260: $i] :
                                  ( ( in @ X260 @ X254 )
                                  & ( X253 @ X260 @ X259 ) ) ) )
                     => ( ! [X261: $i] :
                            ( ? [X262: $i] : ( in @ X262 @ X261 )
                           => ? [X263: $i] :
                                ( ( in @ X263 @ X261 )
                                & ~ ? [X264: $i] :
                                      ( ( in @ X264 @ X263 )
                                      & ( in @ X264 @ X261 ) ) ) )
                       => ( epred1_0
                         => ( descrp
                           => ( ! [X284: $i,X285: $i > $o,X286: $i] :
                                  ( ( in @ X286 @ X284 )
                                 => ( ( X285 @ X286 )
                                   => ( in @ X286
                                      @ ( dsetconstr @ X284
                                        @ ^ [Z0: $i] : ( X285 @ Z0 ) ) ) ) )
                             => ( ! [X287: $i,X288: $i > $o,X289: $i] :
                                    ( ( in @ X289
                                      @ ( dsetconstr @ X287
                                        @ ^ [Z0: $i] : ( X288 @ Z0 ) ) )
                                   => ( in @ X289 @ X287 ) )
                               => ( ! [X290: $i,X291: $i > $o,X292: $i] :
                                      ( ( in @ X292
                                        @ ( dsetconstr @ X290
                                          @ ^ [Z0: $i] : ( X291 @ Z0 ) ) )
                                     => ( X291 @ X292 ) )
                                 => ( ! [X293: $i > $o] :
                                        ( ? [X294: $i] :
                                            ( ( X293 @ X294 )
                                            & ! [X295: $i] :
                                                ( ( X293 @ X295 )
                                               => ( X294 = X295 ) ) )
                                       => ? [X296: $i] :
                                            ( ( X293 @ X296 )
                                            & ! [X297: $i] :
                                                ( ( X293 @ X297 )
                                               => ( X296 = X297 ) ) ) )
                                   => ( ! [X298: $o,X299: $i] :
                                          ( ( in @ X299 @ ( prop2set @ X298 ) )
                                         => X298 )
                                     => ( ! [X300: $i] :
                                            ( ( in @ X300 @ emptyset )
                                           => ! [X301: $o] : X301 )
                                       => ( ! [X302: $i] :
                                              ~ ( in @ X302 @ emptyset )
                                         => ( ! [X303: $i] :
                                                ~ ( in @ X303 @ emptyset )
                                           => ( ! [X304: $i > $o] :
                                                  ( ? [X305: $i] :
                                                      ( ( X304 @ X305 )
                                                      & ! [X306: $i] :
                                                          ( ( X304 @ X306 )
                                                         => ( X305 = X306 ) ) )
                                                 => ? [X307: $i] : ( X304 @ X307 ) )
                                             => ( ! [X308: $i,X309: $i] :
                                                    ( ! [X310: $i] :
                                                        ( ( in @ X310 @ X308 )
                                                       => ( in @ X310 @ X309 ) )
                                                   => ( ! [X311: $i] :
                                                          ( ( in @ X311 @ X309 )
                                                         => ( in @ X311 @ X308 ) )
                                                     => ( X308 = X309 ) ) )
                                               => ( ! [X312: $i] :
                                                      ( ! [X313: $i] :
                                                          ~ ( in @ X313 @ X312 )
                                                     => ( X312 = emptyset ) )
                                                 => ( ! [X314: $i] :
                                                        ( ! [X315: $i] :
                                                            ~ ( in @ X315 @ X314 )
                                                       => ( X314 = emptyset ) )
                                                   => ( ! [X316: $i,X317: $i > $o,X318: $i] :
                                                          ( ( in @ X318 @ X316 )
                                                         => ( ( in @ X318
                                                              @ ( dsetconstr @ X316
                                                                @ ^ [Z0: $i] : ( X317 @ Z0 ) ) )
                                                          <=> ( X317 @ X318 ) ) )
                                                     => ( ! [X319: $i] :
                                                            ( ( X319 != emptyset )
                                                           => ? [X320: $i] : ( in @ X320 @ X319 ) )
                                                       => ( ! [X321: $i,X322: $i > $o,X323: $i] :
                                                              ( ( in @ X323 @ X321 )
                                                             => ( ( X322 @ X323 )
                                                               => ( ( dsetconstr @ X321
                                                                    @ ^ [Z0: $i] : ( X322 @ Z0 ) )
                                                                 != emptyset ) ) )
                                                         => ( ! [X324: $i] :
                                                                ( ? [X325: $i] : ( in @ X325 @ X324 )
                                                               => ( X324 != emptyset ) )
                                                           => ( ! [X326: $i,X327: $i] : ( in @ X326 @ ( setadjoin @ X326 @ X327 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X328: $i,X329: $i,X330: $i] :
                                                                      ( ( in @ X330 @ X329 )
                                                                     => ( in @ X330 @ ( setadjoin @ X328 @ X329 ) ) )
                                                                 => ( ! [X331: $i,X332: $i,X333: $i] :
                                                                        ( ( in @ X333 @ ( setadjoin @ X331 @ X332 ) )
                                                                       => ! [X334: $o] :
                                                                            ( ( ( X333 = X331 )
                                                                             => X334 )
                                                                           => ( ( ( in @ X333 @ X332 )
                                                                               => X334 )
                                                                             => X334 ) ) )
                                                                   => ( ! [X335: $i,X336: $i,X337: $i] :
                                                                          ( ( in @ X337 @ ( setadjoin @ X335 @ X336 ) )
                                                                         => ( ( X337 = X335 )
                                                                            | ( in @ X337 @ X336 ) ) )
                                                                     => ( ! [X338: $i] :
                                                                            ( ( dsetconstr @ X338
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X338 )
                                                                       => ( ! [X339: $i,X340: $i] :
                                                                              ( ! [X341: $i] :
                                                                                  ( ( in @ X341 @ X340 )
                                                                                 => ( in @ X341 @ X339 ) )
                                                                             => ( in @ X340 @ ( powerset @ X339 ) ) )
                                                                         => ( ! [X342: $i] : ( in @ emptyset @ ( powerset @ X342 ) )
                                                                           => ( ! [X343: $i] : ( in @ emptyset @ ( powerset @ X343 ) )
                                                                             => ( ! [X344: $i,X345: $i,X346: $i] :
                                                                                    ( ( in @ X345 @ ( powerset @ X344 ) )
                                                                                   => ( ( in @ X346 @ X345 )
                                                                                     => ( in @ X346 @ X344 ) ) )
                                                                               => ( ! [X347: $i,X348: $i,X349: $i] :
                                                                                      ( ( in @ X348 @ X349 )
                                                                                     => ( ( in @ X349 @ X347 )
                                                                                       => ( in @ X348 @ ( setunion @ X347 ) ) ) )
                                                                                 => ( ! [X350: $i,X351: $i] :
                                                                                        ( ( in @ X351 @ ( setunion @ X350 ) )
                                                                                       => ! [X352: $o] :
                                                                                            ( ! [X353: $i] :
                                                                                                ( ( in @ X351 @ X353 )
                                                                                               => ( ( in @ X353 @ X350 )
                                                                                                 => X352 ) )
                                                                                           => X352 ) )
                                                                                   => ( ! [X354: $i,X355: $i] :
                                                                                          ( ( in @ X355 @ X354 )
                                                                                         => ( in @ X355 @ ( powerset @ ( setunion @ X354 ) ) ) )
                                                                                     => ( ! [X356: $i > $o] :
                                                                                            ( ? [X357: $i] :
                                                                                                ( ( X356 @ X357 )
                                                                                                & ! [X358: $i] :
                                                                                                    ( ( X356 @ X358 )
                                                                                                   => ( X357 = X358 ) ) )
                                                                                           => ? [X359: $i] :
                                                                                              ! [X360: $i] :
                                                                                                ( ( X356 @ X360 )
                                                                                              <=> ( X360 = X359 ) ) )
                                                                                       => ( ! [X361: $i] :
                                                                                              ( ( X361 != emptyset )
                                                                                             => ? [X362: $i] : ( in @ X362 @ X361 ) )
                                                                                         => ( ! [X363: $i,X364: $i] :
                                                                                                ( ( in @ X363 @ ( setadjoin @ X364 @ emptyset ) )
                                                                                               => ( X363 = X364 ) )
                                                                                           => ( ! [X365: $i,X366: $i] :
                                                                                                  ( ( X365 != X366 )
                                                                                                 => ~ ( in @ X366 @ ( setadjoin @ X365 @ emptyset ) ) )
                                                                                             => ( ! [X367: $i,X368: $i] :
                                                                                                    ( ( X367 = X368 )
                                                                                                   => ( in @ X367 @ ( setadjoin @ X368 @ emptyset ) ) )
                                                                                               => ( ! [X369: $i,X370: $i] :
                                                                                                      ( ( in @ X369 @ ( setadjoin @ X370 @ emptyset ) )
                                                                                                     => ( in @ X370 @ ( setadjoin @ X369 @ emptyset ) ) )
                                                                                                 => ( ! [X371: $i,X372: $i,X373: $i] :
                                                                                                        ( ( in @ X373 @ ( setadjoin @ X371 @ ( setadjoin @ X372 @ emptyset ) ) )
                                                                                                       => ( ( X373 = X371 )
                                                                                                          | ( X373 = X372 ) ) )
                                                                                                   => ( ! [X374: $i,X375: $i] : ( in @ X374 @ ( setadjoin @ X374 @ ( setadjoin @ X375 @ emptyset ) ) )
                                                                                                     => ( ! [X376: $i,X377: $i] : ( in @ X377 @ ( setadjoin @ X376 @ ( setadjoin @ X377 @ emptyset ) ) )
                                                                                                       => ( ! [X378: $i,X379: $i > $o] :
                                                                                                              ( ? [X380: $i] :
                                                                                                                  ( ( in @ X380 @ X378 )
                                                                                                                  & ( X379 @ X380 ) )
                                                                                                             => ( ( dsetconstr @ X378
                                                                                                                  @ ^ [Z0: $i] : ( X379 @ Z0 ) )
                                                                                                               != emptyset ) )
                                                                                                         => ( ! [X381: $i > $o,X382: $i] :
                                                                                                                ( ( in @ X382 @ emptyset )
                                                                                                               => ( X381 @ X382 ) )
                                                                                                           => ( ! [X383: $i,X384: $i > $o] :
                                                                                                                  ( ~ ! [X385: $i] :
                                                                                                                        ( ( in @ X385 @ X383 )
                                                                                                                       => ( X384 @ X385 ) )
                                                                                                                 => ? [X386: $i] :
                                                                                                                      ( ( in @ X386 @ X383 )
                                                                                                                      & ~ ( X384 @ X386 ) ) )
                                                                                                             => ( ! [X387: $i,X388: $i > $o] :
                                                                                                                    ( ! [X389: $i] :
                                                                                                                        ( ( in @ X389 @ X387 )
                                                                                                                       => ~ ( X388 @ X389 ) )
                                                                                                                   => ~ ? [X390: $i] :
                                                                                                                          ( ( in @ X390 @ X387 )
                                                                                                                          & ( X388 @ X390 ) ) )
                                                                                                               => ( ! [X391: $i,X392: $i > $o] :
                                                                                                                      ( ~ ? [X393: $i] :
                                                                                                                            ( ( in @ X393 @ X391 )
                                                                                                                            & ( X392 @ X393 ) )
                                                                                                                     => ! [X394: $i] :
                                                                                                                          ( ( in @ X394 @ X391 )
                                                                                                                         => ~ ( X392 @ X394 ) ) )
                                                                                                                 => ( ! [X395: $i,X396: $i > $o] :
                                                                                                                        ( ? [X397: $i] :
                                                                                                                            ( ( in @ X397 @ X395 )
                                                                                                                            & ~ ( X396 @ X397 ) )
                                                                                                                       => ~ ! [X398: $i] :
                                                                                                                              ( ( in @ X398 @ X395 )
                                                                                                                             => ( X396 @ X398 ) ) )
                                                                                                                   => ( ! [X399: $o] :
                                                                                                                          ( X399
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X399 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X400: $i,X401: $i > $o] :
                                                                                                                              ( ~ ? [X402: $i] :
                                                                                                                                    ( ( in @ X402 @ X400 )
                                                                                                                                    & ( X401 @ X402 ) )
                                                                                                                             => ! [X403: $i] :
                                                                                                                                  ( ( in @ X403 @ X400 )
                                                                                                                                 => ~ ( X401 @ X403 ) ) )
                                                                                                                         => ( ! [X404: $i,X405: $i > $o] :
                                                                                                                                ( ~ ! [X406: $i] :
                                                                                                                                      ( ( in @ X406 @ X404 )
                                                                                                                                     => ( X405 @ X406 ) )
                                                                                                                               => ? [X407: $i] :
                                                                                                                                    ( ( in @ X407 @ X404 )
                                                                                                                                    & ~ ( X405 @ X407 ) ) )
                                                                                                                           => ( ! [X408: $i > $o] :
                                                                                                                                  ( ? [X409: $i] :
                                                                                                                                      ( ( X408 @ X409 )
                                                                                                                                      & ! [X410: $i] :
                                                                                                                                          ( ( X408 @ X410 )
                                                                                                                                         => ( X409 = X410 ) ) )
                                                                                                                                 => ? [X411: $i] :
                                                                                                                                      ( ( X408 @ X411 )
                                                                                                                                      & ! [X412: $i] :
                                                                                                                                          ( ( X408 @ X412 )
                                                                                                                                         => ( X411 = X412 ) ) ) )
                                                                                                                             => ( ! [X413: $i > $o] :
                                                                                                                                    ( ? [X414: $i] : ( X413 @ X414 )
                                                                                                                                   => ( ! [X415: $i,X416: $i] :
                                                                                                                                          ( ( X413 @ X415 )
                                                                                                                                         => ( ( X413 @ X416 )
                                                                                                                                           => ( X415 = X416 ) ) )
                                                                                                                                     => ? [X417: $i] :
                                                                                                                                          ( ( X413 @ X417 )
                                                                                                                                          & ! [X418: $i] :
                                                                                                                                              ( ( X413 @ X418 )
                                                                                                                                             => ( X417 = X418 ) ) ) ) )
                                                                                                                               => ( ! [X419: $i > $o] :
                                                                                                                                      ( ? [X420: $i] :
                                                                                                                                        ! [X421: $i] :
                                                                                                                                          ( ( X419 @ X421 )
                                                                                                                                        <=> ( X421 = X420 ) )
                                                                                                                                     => ? [X422: $i] :
                                                                                                                                          ( ( X419 @ X422 )
                                                                                                                                          & ! [X423: $i] :
                                                                                                                                              ( ( X419 @ X423 )
                                                                                                                                             => ( X422 = X423 ) ) ) )
                                                                                                                                 => ( ! [X424: $i,X425: $i] :
                                                                                                                                        ( ( X424 = X425 )
                                                                                                                                       => ! [X426: $i,X427: $i] :
                                                                                                                                            ( ( X426 = X427 )
                                                                                                                                           => ( ( in @ X426 @ X424 )
                                                                                                                                             => ( in @ X427 @ X425 ) ) ) )
                                                                                                                                   => ( ! [X428: $i,X429: $i] :
                                                                                                                                          ( ( X428 = X429 )
                                                                                                                                         => ! [X430: $i,X431: $i] :
                                                                                                                                              ( ( X430 = X431 )
                                                                                                                                             => ( ( in @ X430 @ X428 )
                                                                                                                                              <=> ( in @ X431 @ X429 ) ) ) )
                                                                                                                                     => ( ! [X432: $i > $o] :
                                                                                                                                            ( ? [X433: $i] :
                                                                                                                                                ( ( X432 @ X433 )
                                                                                                                                                & ! [X434: $i] :
                                                                                                                                                    ( ( X432 @ X434 )
                                                                                                                                                   => ( X433 = X434 ) ) )
                                                                                                                                           => ! [X435: $i,X436: $i] :
                                                                                                                                                ( ( X432 @ X435 )
                                                                                                                                               => ( ( X432 @ X436 )
                                                                                                                                                 => ( X435 = X436 ) ) ) )
                                                                                                                                       => ( ! [X437: $i > $o,X438: $i > $o] :
                                                                                                                                              ( ! [X439: $i,X440: $i] :
                                                                                                                                                  ( ( X439 = X440 )
                                                                                                                                                 => ( ( X437 @ X439 )
                                                                                                                                                  <=> ( X438 @ X440 ) ) )
                                                                                                                                             => ( ? [X441: $i] :
                                                                                                                                                    ( ( X437 @ X441 )
                                                                                                                                                    & ! [X442: $i] :
                                                                                                                                                        ( ( X437 @ X442 )
                                                                                                                                                       => ( X441 = X442 ) ) )
                                                                                                                                              <=> ? [X443: $i] :
                                                                                                                                                    ( ( X438 @ X443 )
                                                                                                                                                    & ! [X444: $i] :
                                                                                                                                                        ( ( X438 @ X444 )
                                                                                                                                                       => ( X443 = X444 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X445: $i,X446: $i] :
                                                                                                                                                  ( ( X445 = X446 )
                                                                                                                                                 => ! [X447: $i,X448: $i] :
                                                                                                                                                      ( ( X447 = X448 )
                                                                                                                                                     => ( ( setadjoin @ X445 @ X447 )
                                                                                                                                                        = ( setadjoin @ X446 @ X448 ) ) ) )
                                                                                                                                             => ( ! [X449: $i,X450: $i] :
                                                                                                                                                    ( ( X449 = X450 )
                                                                                                                                                   => ( ( powerset @ X449 )
                                                                                                                                                      = ( powerset @ X450 ) ) )
                                                                                                                                               => ! [X4: $i,X5: $i] :
                                                                                                                                                    ( ( X4 = X5 )
                                                                                                                                                   => ( ( setunion @ X4 )
                                                                                                                                                      = ( setunion @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setunion__Cong]),emptyinunitempty]),powerset__Cong]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),c_0_83]),notdexE]),notdallE]),setext]),c_0_84]),c_0_85]),emptyI]),c_0_86]),inCongP]),noeltsimpempty]),in__Cong]),c_0_87]),c_0_88]),c_0_89]),emptyset__Cong]),c_0_90]),setadjoin__Cong]),c_0_91]),c_0_92]),setadjoinIL]),upairsetE]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_93]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_94]),c_0_95]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetIL]),upairsetIR]),c_0_96]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_97]),c_0_98]),c_0_99]),c_0_100]),wellorderingAx]),foundationAx]),c_0_101]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_102]) ).

thf(c_0_104,negated_conjecture,
    ! [X451: $i,X452: $i,X454: $i,X455: $i,X456: $i,X457: $i,X458: $i,X459: $i,X460: $i,X461: $i,X462: $i,X464: $i,X465: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X473: $i,X474: $i > $i > $o,X475: $i,X477: $i,X480: $i,X482: $i,X483: $i,X484: $i,X485: $i,X487: $i,X488: $i,X489: $i > $o,X490: $i,X491: $i,X492: $i > $o,X493: $i,X494: $i,X495: $i > $o,X496: $i,X497: $i > $o,X498: $i,X501: $i,X502: $o,X503: $i,X504: $i,X505: $o,X506: $i,X507: $i,X508: $i > $o,X509: $i,X512: $i,X513: $i,X516: $i,X518: $i,X520: $i,X521: $i > $o,X522: $i,X523: $i,X525: $i,X526: $i > $o,X527: $i,X528: $i,X529: $i,X530: $i,X531: $i,X532: $i,X533: $i,X534: $i,X535: $i,X536: $i,X537: $i,X538: $o,X539: $i,X540: $i,X541: $i,X542: $i,X543: $i,X544: $i,X546: $i,X547: $i,X548: $i,X549: $i,X550: $i,X551: $i,X552: $i,X553: $i,X554: $i,X555: $i,X556: $o,X558: $i,X559: $i,X560: $i > $o,X561: $i,X564: $i,X565: $i,X566: $i,X568: $i,X569: $i,X570: $i,X571: $i,X572: $i,X573: $i,X574: $i,X575: $i,X576: $i,X577: $i,X578: $i,X579: $i,X580: $i,X581: $i,X582: $i,X583: $i,X584: $i > $o,X585: $i,X586: $i > $o,X587: $i,X588: $i,X589: $i > $o,X590: $i,X592: $i,X593: $i > $o,X595: $i,X596: $i,X597: $i > $o,X599: $i,X600: $i,X601: $i > $o,X602: $i,X604: $o,X605: $i,X606: $i > $o,X608: $i,X609: $i,X610: $i > $o,X611: $i,X613: $i > $o,X614: $i,X617: $i,X618: $i > $o,X619: $i,X623: $i,X624: $i > $o,X625: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i > $o,X638: $i,X640: $i,X641: $i,X642: $i > $o,X643: $i > $o,X646: $i,X649: $i,X650: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X451 @ X452 ) @ X451 )
        | ~ ( in @ ( esk1_2 @ X451 @ X452 ) @ X452 )
        | ( X451 = X452 ) )
      & ( ( in @ ( esk1_2 @ X451 @ X452 ) @ X451 )
        | ( in @ ( esk1_2 @ X451 @ X452 ) @ X452 )
        | ( X451 = X452 ) )
      & ~ ( in @ X454 @ emptyset )
      & ( ~ ( in @ X457 @ ( setadjoin @ X455 @ X456 ) )
        | ( X457 = X455 )
        | ( in @ X457 @ X456 ) )
      & ( ( X457 != X455 )
        | ( in @ X457 @ ( setadjoin @ X455 @ X456 ) ) )
      & ( ~ ( in @ X457 @ X456 )
        | ( in @ X457 @ ( setadjoin @ X455 @ X456 ) ) )
      & ( ~ ( in @ X459 @ ( powerset @ X458 ) )
        | ~ ( in @ X460 @ X459 )
        | ( in @ X460 @ X458 ) )
      & ( ( in @ ( esk2_2 @ X461 @ X462 ) @ X462 )
        | ( in @ X462 @ ( powerset @ X461 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X461 @ X462 ) @ X461 )
        | ( in @ X462 @ ( powerset @ X461 ) ) )
      & ( ( in @ X465 @ ( esk3_2 @ X464 @ X465 ) )
        | ~ ( in @ X465 @ ( setunion @ X464 ) ) )
      & ( ( in @ ( esk3_2 @ X464 @ X465 ) @ X464 )
        | ~ ( in @ X465 @ ( setunion @ X464 ) ) )
      & ( ~ ( in @ X468 @ X469 )
        | ~ ( in @ X469 @ X467 )
        | ( in @ X468 @ ( setunion @ X467 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X470 @ omega )
        | ( in @ ( setadjoin @ X470 @ X470 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X471 ) @ omega )
        | ~ ( in @ emptyset @ X471 )
        | ~ ( in @ X473 @ omega )
        | ( in @ X473 @ X471 ) )
      & ( ( in @ ( esk4_1 @ X471 ) @ X471 )
        | ~ ( in @ emptyset @ X471 )
        | ~ ( in @ X473 @ omega )
        | ( in @ X473 @ X471 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X471 ) @ ( esk4_1 @ X471 ) ) @ X471 )
        | ~ ( in @ emptyset @ X471 )
        | ~ ( in @ X473 @ omega )
        | ( in @ X473 @ X471 ) )
      & ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
      & ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
      & ( ~ ( in @ X483 @ X475 )
        | ~ ( X474 @ X483 @ X482 )
        | ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
        | ( in @ ( esk5_2 @ X474 @ X475 ) @ X475 ) )
      & ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ~ ( in @ X483 @ X475 )
        | ~ ( X474 @ X483 @ X482 )
        | ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X474 @ ( esk5_2 @ X474 @ X475 ) @ ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ( in @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X475 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X477
         != ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ( X474 @ ( esk8_3 @ X474 @ X475 @ X480 ) @ X480 )
        | ~ ( in @ X480 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X477
         != ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ~ ( in @ X483 @ X475 )
        | ~ ( X474 @ X483 @ X482 )
        | ( in @ X482 @ ( esk7_2 @ X474 @ X475 ) )
        | ( X477
         != ( esk6_3 @ X474 @ X475 @ X477 ) )
        | ~ ( X474 @ ( esk5_2 @ X474 @ X475 ) @ X477 ) )
      & ( ( in @ ( esk9_1 @ X484 ) @ X484 )
        | ~ ( in @ X485 @ X484 ) )
      & ( ~ ( in @ X487 @ ( esk9_1 @ X484 ) )
        | ~ ( in @ X487 @ X484 )
        | ~ ( in @ X485 @ X484 ) )
      & epred1_0
      & descrp
      & ( ~ ( in @ X490 @ X488 )
        | ~ ( X489 @ X490 )
        | ( in @ X490
          @ ( dsetconstr @ X488
            @ ^ [Z0: $i] : ( X489 @ Z0 ) ) ) )
      & ( ~ ( in @ X493
            @ ( dsetconstr @ X491
              @ ^ [Z0: $i] : ( X492 @ Z0 ) ) )
        | ( in @ X493 @ X491 ) )
      & ( ~ ( in @ X496
            @ ( dsetconstr @ X494
              @ ^ [Z0: $i] : ( X495 @ Z0 ) ) )
        | ( X495 @ X496 ) )
      & ( ( X497 @ ( esk11_1 @ X497 ) )
        | ( X497 @ ( esk10_2 @ X497 @ X498 ) )
        | ~ ( X497 @ X498 ) )
      & ( ~ ( X497 @ X501 )
        | ( ( esk11_1 @ X497 )
          = X501 )
        | ( X497 @ ( esk10_2 @ X497 @ X498 ) )
        | ~ ( X497 @ X498 ) )
      & ( ( X497 @ ( esk11_1 @ X497 ) )
        | ( X498
         != ( esk10_2 @ X497 @ X498 ) )
        | ~ ( X497 @ X498 ) )
      & ( ~ ( X497 @ X501 )
        | ( ( esk11_1 @ X497 )
          = X501 )
        | ( X498
         != ( esk10_2 @ X497 @ X498 ) )
        | ~ ( X497 @ X498 ) )
      & ( ~ ( in @ X503 @ ( prop2set @ X502 ) )
        | X502 )
      & ( ~ ( in @ X504 @ emptyset )
        | X505 )
      & ~ ( in @ X506 @ emptyset )
      & ~ ( in @ X507 @ emptyset )
      & ( ( X508 @ ( esk12_2 @ X508 @ X509 ) )
        | ~ ( X508 @ X509 )
        | ( X508 @ ( esk13_1 @ X508 ) ) )
      & ( ( X509
         != ( esk12_2 @ X508 @ X509 ) )
        | ~ ( X508 @ X509 )
        | ( X508 @ ( esk13_1 @ X508 ) ) )
      & ( ( in @ ( esk15_2 @ X512 @ X513 ) @ X513 )
        | ( X512 = X513 )
        | ( in @ ( esk14_2 @ X512 @ X513 ) @ X512 ) )
      & ( ~ ( in @ ( esk15_2 @ X512 @ X513 ) @ X512 )
        | ( X512 = X513 )
        | ( in @ ( esk14_2 @ X512 @ X513 ) @ X512 ) )
      & ( ( in @ ( esk15_2 @ X512 @ X513 ) @ X513 )
        | ( X512 = X513 )
        | ~ ( in @ ( esk14_2 @ X512 @ X513 ) @ X513 ) )
      & ( ~ ( in @ ( esk15_2 @ X512 @ X513 ) @ X512 )
        | ( X512 = X513 )
        | ~ ( in @ ( esk14_2 @ X512 @ X513 ) @ X513 ) )
      & ( ( in @ ( esk16_1 @ X516 ) @ X516 )
        | ( X516 = emptyset ) )
      & ( ( in @ ( esk17_1 @ X518 ) @ X518 )
        | ( X518 = emptyset ) )
      & ( ~ ( in @ X522
            @ ( dsetconstr @ X520
              @ ^ [Z0: $i] : ( X521 @ Z0 ) ) )
        | ( X521 @ X522 )
        | ~ ( in @ X522 @ X520 ) )
      & ( ~ ( X521 @ X522 )
        | ( in @ X522
          @ ( dsetconstr @ X520
            @ ^ [Z0: $i] : ( X521 @ Z0 ) ) )
        | ~ ( in @ X522 @ X520 ) )
      & ( ( X523 = emptyset )
        | ( in @ ( esk18_1 @ X523 ) @ X523 ) )
      & ( ~ ( in @ X527 @ X525 )
        | ~ ( X526 @ X527 )
        | ( ( dsetconstr @ X525
            @ ^ [Z0: $i] : ( X526 @ Z0 ) )
         != emptyset ) )
      & ( ~ ( in @ X529 @ X528 )
        | ( X528 != emptyset ) )
      & ( in @ X530 @ ( setadjoin @ X530 @ X531 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X534 @ X533 )
        | ( in @ X534 @ ( setadjoin @ X532 @ X533 ) ) )
      & ( ( in @ X537 @ X536 )
        | X538
        | ( X537 = X535 )
        | ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
      & ( ~ X538
        | X538
        | ( X537 = X535 )
        | ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
      & ( ( in @ X537 @ X536 )
        | X538
        | ~ X538
        | ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
      & ( ~ X538
        | X538
        | ~ X538
        | ~ ( in @ X537 @ ( setadjoin @ X535 @ X536 ) ) )
      & ( ~ ( in @ X541 @ ( setadjoin @ X539 @ X540 ) )
        | ( X541 = X539 )
        | ( in @ X541 @ X540 ) )
      & ( ( dsetconstr @ X542
          @ ^ [Z0: $i] : $true )
        = X542 )
      & ( ( in @ ( esk19_2 @ X543 @ X544 ) @ X544 )
        | ( in @ X544 @ ( powerset @ X543 ) ) )
      & ( ~ ( in @ ( esk19_2 @ X543 @ X544 ) @ X543 )
        | ( in @ X544 @ ( powerset @ X543 ) ) )
      & ( in @ emptyset @ ( powerset @ X546 ) )
      & ( in @ emptyset @ ( powerset @ X547 ) )
      & ( ~ ( in @ X549 @ ( powerset @ X548 ) )
        | ~ ( in @ X550 @ X549 )
        | ( in @ X550 @ X548 ) )
      & ( ~ ( in @ X552 @ X553 )
        | ~ ( in @ X553 @ X551 )
        | ( in @ X552 @ ( setunion @ X551 ) ) )
      & ( ( in @ X555 @ ( esk20_3 @ X554 @ X555 @ X556 ) )
        | X556
        | ~ ( in @ X555 @ ( setunion @ X554 ) ) )
      & ( ( in @ ( esk20_3 @ X554 @ X555 @ X556 ) @ X554 )
        | X556
        | ~ ( in @ X555 @ ( setunion @ X554 ) ) )
      & ( ~ X556
        | X556
        | ~ ( in @ X555 @ ( setunion @ X554 ) ) )
      & ( ~ ( in @ X559 @ X558 )
        | ( in @ X559 @ ( powerset @ ( setunion @ X558 ) ) ) )
      & ( ~ ( X560 @ X564 )
        | ( X564
          = ( esk22_1 @ X560 ) )
        | ( X560 @ ( esk21_2 @ X560 @ X561 ) )
        | ~ ( X560 @ X561 ) )
      & ( ( X565
         != ( esk22_1 @ X560 ) )
        | ( X560 @ X565 )
        | ( X560 @ ( esk21_2 @ X560 @ X561 ) )
        | ~ ( X560 @ X561 ) )
      & ( ~ ( X560 @ X564 )
        | ( X564
          = ( esk22_1 @ X560 ) )
        | ( X561
         != ( esk21_2 @ X560 @ X561 ) )
        | ~ ( X560 @ X561 ) )
      & ( ( X565
         != ( esk22_1 @ X560 ) )
        | ( X560 @ X565 )
        | ( X561
         != ( esk21_2 @ X560 @ X561 ) )
        | ~ ( X560 @ X561 ) )
      & ( ( X566 = emptyset )
        | ( in @ ( esk23_1 @ X566 ) @ X566 ) )
      & ( ~ ( in @ X568 @ ( setadjoin @ X569 @ emptyset ) )
        | ( X568 = X569 ) )
      & ( ( X570 = X571 )
        | ~ ( in @ X571 @ ( setadjoin @ X570 @ emptyset ) ) )
      & ( ( X572 != X573 )
        | ( in @ X572 @ ( setadjoin @ X573 @ emptyset ) ) )
      & ( ~ ( in @ X574 @ ( setadjoin @ X575 @ emptyset ) )
        | ( in @ X575 @ ( setadjoin @ X574 @ emptyset ) ) )
      & ( ~ ( in @ X578 @ ( setadjoin @ X576 @ ( setadjoin @ X577 @ emptyset ) ) )
        | ( X578 = X576 )
        | ( X578 = X577 ) )
      & ( in @ X579 @ ( setadjoin @ X579 @ ( setadjoin @ X580 @ emptyset ) ) )
      & ( in @ X582 @ ( setadjoin @ X581 @ ( setadjoin @ X582 @ emptyset ) ) )
      & ( ~ ( in @ X585 @ X583 )
        | ~ ( X584 @ X585 )
        | ( ( dsetconstr @ X583
            @ ^ [Z0: $i] : ( X584 @ Z0 ) )
         != emptyset ) )
      & ( ~ ( in @ X587 @ emptyset )
        | ( X586 @ X587 ) )
      & ( ( in @ ( esk24_2 @ X588 @ X589 ) @ X588 )
        | ~ ( in @ X590 @ X588 )
        | ( X589 @ X590 ) )
      & ( ~ ( X589 @ ( esk24_2 @ X588 @ X589 ) )
        | ~ ( in @ X590 @ X588 )
        | ( X589 @ X590 ) )
      & ( ( in @ ( esk25_2 @ X592 @ X593 ) @ X592 )
        | ~ ( in @ X595 @ X592 )
        | ~ ( X593 @ X595 ) )
      & ( ( X593 @ ( esk25_2 @ X592 @ X593 ) )
        | ~ ( in @ X595 @ X592 )
        | ~ ( X593 @ X595 ) )
      & ( ( in @ ( esk26_2 @ X596 @ X597 ) @ X596 )
        | ~ ( in @ X599 @ X596 )
        | ~ ( X597 @ X599 ) )
      & ( ( X597 @ ( esk26_2 @ X596 @ X597 ) )
        | ~ ( in @ X599 @ X596 )
        | ~ ( X597 @ X599 ) )
      & ( ( in @ ( esk27_2 @ X600 @ X601 ) @ X600 )
        | ~ ( in @ X602 @ X600 )
        | ( X601 @ X602 ) )
      & ( ~ ( X601 @ ( esk27_2 @ X600 @ X601 ) )
        | ~ ( in @ X602 @ X600 )
        | ( X601 @ X602 ) )
      & ( ~ X604
        | ( in @ emptyset @ ( prop2set @ X604 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk28_2 @ X605 @ X606 ) @ X605 )
        | ~ ( in @ X608 @ X605 )
        | ~ ( X606 @ X608 ) )
      & ( ( X606 @ ( esk28_2 @ X605 @ X606 ) )
        | ~ ( in @ X608 @ X605 )
        | ~ ( X606 @ X608 ) )
      & ( ( in @ ( esk29_2 @ X609 @ X610 ) @ X609 )
        | ~ ( in @ X611 @ X609 )
        | ( X610 @ X611 ) )
      & ( ~ ( X610 @ ( esk29_2 @ X609 @ X610 ) )
        | ~ ( in @ X611 @ X609 )
        | ( X610 @ X611 ) )
      & ( ( X613 @ ( esk31_1 @ X613 ) )
        | ( X613 @ ( esk30_2 @ X613 @ X614 ) )
        | ~ ( X613 @ X614 ) )
      & ( ~ ( X613 @ X617 )
        | ( ( esk31_1 @ X613 )
          = X617 )
        | ( X613 @ ( esk30_2 @ X613 @ X614 ) )
        | ~ ( X613 @ X614 ) )
      & ( ( X613 @ ( esk31_1 @ X613 ) )
        | ( X614
         != ( esk30_2 @ X613 @ X614 ) )
        | ~ ( X613 @ X614 ) )
      & ( ~ ( X613 @ X617 )
        | ( ( esk31_1 @ X613 )
          = X617 )
        | ( X614
         != ( esk30_2 @ X613 @ X614 ) )
        | ~ ( X613 @ X614 ) )
      & ( ( X618 @ ( esk34_1 @ X618 ) )
        | ( X618 @ ( esk32_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ~ ( X618 @ X623 )
        | ( ( esk34_1 @ X618 )
          = X623 )
        | ( X618 @ ( esk32_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ( X618 @ ( esk34_1 @ X618 ) )
        | ( X618 @ ( esk33_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ~ ( X618 @ X623 )
        | ( ( esk34_1 @ X618 )
          = X623 )
        | ( X618 @ ( esk33_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ( X618 @ ( esk34_1 @ X618 ) )
        | ( ( esk32_1 @ X618 )
         != ( esk33_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ~ ( X618 @ X623 )
        | ( ( esk34_1 @ X618 )
          = X623 )
        | ( ( esk32_1 @ X618 )
         != ( esk33_1 @ X618 ) )
        | ~ ( X618 @ X619 ) )
      & ( ( X624 @ ( esk36_1 @ X624 ) )
        | ~ ( X624 @ ( esk35_2 @ X624 @ X625 ) )
        | ( ( esk35_2 @ X624 @ X625 )
         != X625 ) )
      & ( ~ ( X624 @ X628 )
        | ( ( esk36_1 @ X624 )
          = X628 )
        | ~ ( X624 @ ( esk35_2 @ X624 @ X625 ) )
        | ( ( esk35_2 @ X624 @ X625 )
         != X625 ) )
      & ( ( X624 @ ( esk36_1 @ X624 ) )
        | ( X624 @ ( esk35_2 @ X624 @ X625 ) )
        | ( ( esk35_2 @ X624 @ X625 )
          = X625 ) )
      & ( ~ ( X624 @ X628 )
        | ( ( esk36_1 @ X624 )
          = X628 )
        | ( X624 @ ( esk35_2 @ X624 @ X625 ) )
        | ( ( esk35_2 @ X624 @ X625 )
          = X625 ) )
      & ( ( X629 != X630 )
        | ( X631 != X632 )
        | ~ ( in @ X631 @ X629 )
        | ( in @ X632 @ X630 ) )
      & ( ~ ( in @ X635 @ X633 )
        | ( in @ X636 @ X634 )
        | ( X635 != X636 )
        | ( X633 != X634 ) )
      & ( ~ ( in @ X636 @ X634 )
        | ( in @ X635 @ X633 )
        | ( X635 != X636 )
        | ( X633 != X634 ) )
      & ( ( X637 @ ( esk37_2 @ X637 @ X638 ) )
        | ~ ( X637 @ X638 )
        | ~ ( X637 @ X640 )
        | ~ ( X637 @ X641 )
        | ( X640 = X641 ) )
      & ( ( X638
         != ( esk37_2 @ X637 @ X638 ) )
        | ~ ( X637 @ X638 )
        | ~ ( X637 @ X640 )
        | ~ ( X637 @ X641 )
        | ( X640 = X641 ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( ( esk38_2 @ X642 @ X643 )
          = ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ~ ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ~ ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X642 @ ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X643 @ ( esk41_2 @ X642 @ X643 ) )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X643 @ X649 )
        | ( ( esk41_2 @ X642 @ X643 )
          = X649 )
        | ( X646
         != ( esk40_3 @ X642 @ X643 @ X646 ) )
        | ~ ( X642 @ X646 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X643 @ ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ( X642 @ ( esk43_2 @ X642 @ X643 ) )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( ~ ( X642 @ X653 )
        | ( ( esk43_2 @ X642 @ X643 )
          = X653 )
        | ( X650
         != ( esk42_3 @ X642 @ X643 @ X650 ) )
        | ~ ( X643 @ X650 )
        | ( X642 @ ( esk38_2 @ X642 @ X643 ) )
        | ( X643 @ ( esk39_2 @ X642 @ X643 ) ) )
      & ( emptyset = emptyset )
      & ( ( X654 != X655 )
        | ( X656 != X657 )
        | ( ( setadjoin @ X654 @ X656 )
          = ( setadjoin @ X655 @ X657 ) ) )
      & ( ( X658 != X659 )
        | ( ( powerset @ X658 )
          = ( powerset @ X659 ) ) )
      & ( esk44_0 = esk45_0 )
      & ( ( setunion @ esk44_0 )
       != ( setunion @ esk45_0 ) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])])])]) ).

thf(c_0_105,negated_conjecture,
    ( ( setunion @ esk44_0 )
   != ( setunion @ esk45_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

thf(c_0_106,negated_conjecture,
    esk44_0 = esk45_0,
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

thf(c_0_107,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU554^1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.07/0.14  % 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 18:07:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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
% 0.20/0.53  # Version: 3.1.0-ho
% 0.20/0.53  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53  # Starting sh5l with 300s (1) cores
% 0.20/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53  # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53  # new_bool_2 with pid 4210 completed with status 0
% 0.20/0.53  # Result found by new_bool_2
% 0.20/0.53  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53  # Starting sh5l with 300s (1) cores
% 0.20/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53  # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53  # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53  # ho_unfolding_3 with pid 4211 completed with status 0
% 0.20/0.53  # Result found by ho_unfolding_3
% 0.20/0.53  # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53  # Starting sh5l with 300s (1) cores
% 0.20/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53  # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53  # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53  # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53  # Preprocessing time       : 0.004 s
% 0.20/0.53  # Presaturation interreduction done
% 0.20/0.53  
% 0.20/0.53  # Proof found!
% 0.20/0.53  # SZS status Theorem
% 0.20/0.53  # SZS output start CNFRefutation
% See solution above
% 0.20/0.53  # Parsed axioms                        : 155
% 0.20/0.53  # Removed by relevancy pruning/SinE    : 84
% 0.20/0.53  # Initial clauses                      : 162
% 0.20/0.53  # Removed in clause preprocessing      : 10
% 0.20/0.53  # Initial clauses in saturation        : 152
% 0.20/0.53  # Processed clauses                    : 5
% 0.20/0.53  # ...of these trivial                  : 0
% 0.20/0.53  # ...subsumed                          : 0
% 0.20/0.53  # ...remaining for further processing  : 4
% 0.20/0.53  # Other redundant clauses eliminated   : 0
% 0.20/0.53  # Clauses deleted for lack of memory   : 0
% 0.20/0.53  # Backward-subsumed                    : 0
% 0.20/0.53  # Backward-rewritten                   : 0
% 0.20/0.53  # Generated clauses                    : 0
% 0.20/0.53  # ...of the previous two non-redundant : 0
% 0.20/0.53  # ...aggressively subsumed             : 0
% 0.20/0.53  # Contextual simplify-reflections      : 0
% 0.20/0.53  # Paramodulations                      : 0
% 0.20/0.53  # Factorizations                       : 0
% 0.20/0.53  # NegExts                              : 0
% 0.20/0.53  # Equation resolutions                 : 0
% 0.20/0.53  # Disequality decompositions           : 0
% 0.20/0.53  # Total rewrite steps                  : 1
% 0.20/0.53  # ...of those cached                   : 0
% 0.20/0.53  # Propositional unsat checks           : 0
% 0.20/0.53  #    Propositional check models        : 0
% 0.20/0.53  #    Propositional check unsatisfiable : 0
% 0.20/0.53  #    Propositional clauses             : 0
% 0.20/0.53  #    Propositional clauses after purity: 0
% 0.20/0.53  #    Propositional unsat core size     : 0
% 0.20/0.53  #    Propositional preprocessing time  : 0.000
% 0.20/0.53  #    Propositional encoding time       : 0.000
% 0.20/0.53  #    Propositional solver time         : 0.000
% 0.20/0.53  #    Success case prop preproc time    : 0.000
% 0.20/0.53  #    Success case prop encoding time   : 0.000
% 0.20/0.53  #    Success case prop solver time     : 0.000
% 0.20/0.53  # Current number of processed clauses  : 4
% 0.20/0.53  #    Positive orientable unit clauses  : 4
% 0.20/0.53  #    Positive unorientable unit clauses: 0
% 0.20/0.53  #    Negative unit clauses             : 0
% 0.20/0.53  #    Non-unit-clauses                  : 0
% 0.20/0.53  # Current number of unprocessed clauses: 147
% 0.20/0.53  # ...number of literals in the above   : 497
% 0.20/0.53  # Current number of archived formulas  : 0
% 0.20/0.53  # Current number of archived clauses   : 0
% 0.20/0.53  # Clause-clause subsumption calls (NU) : 0
% 0.20/0.53  # Rec. Clause-clause subsumption calls : 0
% 0.20/0.53  # Non-unit clause-clause subsumptions  : 0
% 0.20/0.53  # Unit Clause-clause subsumption calls : 0
% 0.20/0.53  # Rewrite failures with RHS unbound    : 0
% 0.20/0.53  # BW rewrite match attempts            : 0
% 0.20/0.53  # BW rewrite match successes           : 0
% 0.20/0.53  # Condensation attempts                : 5
% 0.20/0.53  # Condensation successes               : 0
% 0.20/0.53  # Termbank termtop insertions          : 17757
% 0.20/0.53  # Search garbage collected termcells   : 6568
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.018 s
% 0.20/0.53  # System time              : 0.007 s
% 0.20/0.53  # Total time               : 0.025 s
% 0.20/0.53  # Maximum resident set size: 3864 pages
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.023 s
% 0.20/0.53  # System time              : 0.010 s
% 0.20/0.53  # Total time               : 0.032 s
% 0.20/0.53  # Maximum resident set size: 1920 pages
% 0.20/0.53  % E---3.1 exiting
% 0.20/0.53  % E exiting
%------------------------------------------------------------------------------