TSTP Solution File: SEU521^1 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU521^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 03:27:55 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  108
% Syntax   : Number of formulae    :  135 (  17 unt;  68 typ;   0 def)
%            Number of atoms       :  492 (  77 equ;   0 cnn)
%            Maximal formula atoms :  131 (   7 avg)
%            Number of connectives : 1625 ( 114   ~; 119   |; 111   &;1011   @)
%                                         (  60 <=>; 210  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  144 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   98 (  98   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   71 (  68 usr;  45 con; 0-3 aty)
%            Number of variables   :  376 (  32   ^ 298   !;  46   ?; 376   :)

% 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_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,
    epred1_0: $o ).

thf(decl_71,type,
    esk1_2: $i > $i > $i ).

thf(decl_72,type,
    esk2_2: $i > $i > $i ).

thf(decl_73,type,
    esk3_1: $i > $i ).

thf(decl_74,type,
    esk4_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_75,type,
    esk5_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_76,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_77,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_78,type,
    esk8_1: $i > $i ).

thf(decl_79,type,
    esk9_2: ( $i > $o ) > $i > $i ).

thf(decl_80,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_81,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_82,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_83,type,
    esk13_2: $i > $i > $i ).

thf(decl_84,type,
    esk14_2: $i > $i > $i ).

thf(decl_85,type,
    esk15_1: $i > $i ).

thf(decl_86,type,
    esk16_1: $i > $i ).

thf(decl_87,type,
    esk17_1: $i > $i ).

thf(decl_88,type,
    esk18_2: $i > $i > $i ).

thf(decl_89,type,
    esk19_0: $i ).

thf(decl_90,type,
    esk20_0: $i ).

thf(decl_91,type,
    esk21_0: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_0_39,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_40,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_41,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_42,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_43,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_44,plain,
    ( prop2set
    = ( ^ [Z0: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Z1: $i] : Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[prop2set]) ).

thf(c_0_45,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_46,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X118: $i] :
              ( ( X1 @ X118 )
              & ! [X119: $i] :
                  ( ( X1 @ X119 )
                 => ( X118 = X119 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_47,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_48,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_41]) ).

thf(c_0_49,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_42,c_0_41]) ).

thf(c_0_50,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_41]) ).

thf(c_0_51,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X116: $i] :
                  ( ( X6 @ X2 @ X116 )
                  & ! [X117: $i] :
                      ( ( X6 @ X2 @ X117 )
                     => ( X116 = X117 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_43,c_0_40]) ).

thf(c_0_52,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_53,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_54,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_55,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_56,axiom,
    ( prop2setE
    = ( ! [X11: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X11 ) )
         => X11 ) ) ),
    inference(apply_def,[status(thm)],[prop2setE,c_0_44]) ).

thf(c_0_57,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X120: $i] :
              ( ( X1 @ X120 )
              & ! [X121: $i] :
                  ( ( X1 @ X121 )
                 => ( X120 = X121 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_45,c_0_40]) ).

thf(c_0_58,plain,
    ( epred1_0
  <=> ! [X148: $i] :
      ? [X149: $i] :
        ( ! [X150: $i] :
            ( ( in @ X150 @ X149 )
           => ! [X151: $i] :
                ( ( in @ X151 @ X150 )
               => ( in @ X151 @ X148 ) ) )
        & ! [X152: $i,X153: $i] :
            ( ( ( in @ X152 @ X148 )
              & ( in @ X153 @ X148 ) )
           => ( ! [X154: $i] :
                  ( ( in @ X154 @ X149 )
                 => ( ( in @ X152 @ X154 )
                  <=> ( in @ X153 @ X154 ) ) )
             => ( X152 = X153 ) ) )
        & ! [X155: $i,X156: $i] :
            ( ( ( in @ X155 @ X149 )
              & ( in @ X156 @ X149 ) )
           => ( ! [X157: $i] :
                  ( ( in @ X157 @ X155 )
                 => ( in @ X157 @ X156 ) )
              | ! [X158: $i] :
                  ( ( in @ X158 @ X156 )
                 => ( in @ X158 @ X155 ) ) ) )
        & ! [X159: $i] :
            ( ( ! [X160: $i] :
                  ( ( in @ X160 @ X159 )
                 => ( in @ X160 @ X148 ) )
              & ? [X161: $i] : ( in @ X161 @ X159 ) )
           => ? [X162: $i,X163: $i] :
                ( ( in @ X162 @ X149 )
                & ( in @ X163 @ X159 )
                & ~ ? [X164: $i] :
                      ( ( in @ X164 @ X162 )
                      & ( in @ X164 @ X159 ) )
                & ! [X165: $i] :
                    ( ( in @ X165 @ X149 )
                   => ( ! [X166: $i] :
                          ( ( in @ X166 @ X165 )
                         => ( in @ X166 @ X162 ) )
                      | ( in @ X163 @ X165 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_59,negated_conjecture,
    ~ ( ! [X122: $i,X123: $i] :
          ( ! [X124: $i] :
              ( ( in @ X124 @ X122 )
            <=> ( in @ X124 @ X123 ) )
         => ( X122 = X123 ) )
     => ( ! [X125: $i] :
            ~ ( in @ X125 @ emptyset )
       => ( ! [X126: $i,X127: $i,X128: $i] :
              ( ( in @ X128 @ ( setadjoin @ X126 @ X127 ) )
            <=> ( ( X128 = X126 )
                | ( in @ X128 @ X127 ) ) )
         => ( ! [X129: $i,X130: $i] :
                ( ( in @ X130 @ ( powerset @ X129 ) )
              <=> ! [X131: $i] :
                    ( ( in @ X131 @ X130 )
                   => ( in @ X131 @ X129 ) ) )
           => ( setunionAx
             => ( ( in @ emptyset @ omega )
               => ( ! [X132: $i] :
                      ( ( in @ X132 @ omega )
                     => ( in @ ( setadjoin @ X132 @ X132 ) @ omega ) )
                 => ( ! [X133: $i] :
                        ( ( ( in @ emptyset @ X133 )
                          & ! [X134: $i] :
                              ( ( ( in @ X134 @ omega )
                                & ( in @ X134 @ X133 ) )
                             => ( in @ ( setadjoin @ X134 @ X134 ) @ X133 ) ) )
                       => ! [X135: $i] :
                            ( ( in @ X135 @ omega )
                           => ( in @ X135 @ X133 ) ) )
                   => ( ! [X136: $i > $i > $o,X137: $i] :
                          ( ! [X138: $i] :
                              ( ( in @ X138 @ X137 )
                             => ? [X139: $i] :
                                  ( ( X136 @ X138 @ X139 )
                                  & ! [X140: $i] :
                                      ( ( X136 @ X138 @ X140 )
                                     => ( X139 = X140 ) ) ) )
                         => ? [X141: $i] :
                            ! [X142: $i] :
                              ( ( in @ X142 @ X141 )
                            <=> ? [X143: $i] :
                                  ( ( in @ X143 @ X137 )
                                  & ( X136 @ X143 @ X142 ) ) ) )
                     => ( ! [X144: $i] :
                            ( ? [X145: $i] : ( in @ X145 @ X144 )
                           => ? [X146: $i] :
                                ( ( in @ X146 @ X144 )
                                & ~ ? [X147: $i] :
                                      ( ( in @ X147 @ X146 )
                                      & ( in @ X147 @ X144 ) ) ) )
                       => ( epred1_0
                         => ( descrp
                           => ( ! [X167: $i,X168: $i > $o,X169: $i] :
                                  ( ( in @ X169 @ X167 )
                                 => ( ( X168 @ X169 )
                                   => ( in @ X169 @ ( dsetconstr @ X167 @ X168 ) ) ) )
                             => ( ! [X170: $i,X171: $i > $o,X172: $i] :
                                    ( ( in @ X172 @ ( dsetconstr @ X170 @ X171 ) )
                                   => ( in @ X172 @ X170 ) )
                               => ( ! [X173: $i,X174: $i > $o,X175: $i] :
                                      ( ( in @ X175 @ ( dsetconstr @ X173 @ X174 ) )
                                     => ( X174 @ X175 ) )
                                 => ( ! [X176: $i > $o] :
                                        ( ? [X177: $i] :
                                            ( ( X176 @ X177 )
                                            & ! [X178: $i] :
                                                ( ( X176 @ X178 )
                                               => ( X177 = X178 ) ) )
                                       => ? [X179: $i] :
                                            ( ( X176 @ X179 )
                                            & ! [X180: $i] :
                                                ( ( X176 @ X180 )
                                               => ( X179 = X180 ) ) ) )
                                   => ( ! [X181: $o,X182: $i] :
                                          ( ( in @ X182
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [Z0: $i] : X181 ) )
                                         => X181 )
                                     => ( ! [X183: $i] :
                                            ( ( in @ X183 @ emptyset )
                                           => ! [X184: $o] : X184 )
                                       => ( ! [X185: $i] :
                                              ( ( in @ X185 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X186: $i] :
                                                ~ ( in @ X186 @ emptyset )
                                           => ( ! [X187: $i > $o] :
                                                  ( ? [X188: $i] :
                                                      ( ( X187 @ X188 )
                                                      & ! [X189: $i] :
                                                          ( ( X187 @ X189 )
                                                         => ( X188 = X189 ) ) )
                                                 => ? [X190: $i] : ( X187 @ X190 ) )
                                             => ( ! [X191: $i,X192: $i] :
                                                    ( ! [X193: $i] :
                                                        ( ( in @ X193 @ X191 )
                                                       => ( in @ X193 @ X192 ) )
                                                   => ( ! [X194: $i] :
                                                          ( ( in @ X194 @ X192 )
                                                         => ( in @ X194 @ X191 ) )
                                                     => ( X191 = X192 ) ) )
                                               => ( ! [X195: $i] :
                                                      ( ! [X196: $i] :
                                                          ~ ( in @ X196 @ X195 )
                                                     => ( X195 = emptyset ) )
                                                 => ( ! [X197: $i] :
                                                        ( ! [X198: $i] :
                                                            ~ ( in @ X198 @ X197 )
                                                       => ( X197 = emptyset ) )
                                                   => ( ! [X199: $i,X200: $i > $o,X201: $i] :
                                                          ( ( in @ X201 @ X199 )
                                                         => ( ( in @ X201 @ ( dsetconstr @ X199 @ X200 ) )
                                                          <=> ( X200 @ X201 ) ) )
                                                     => ( ! [X202: $i] :
                                                            ( ( X202 != emptyset )
                                                           => ? [X203: $i] : ( in @ X203 @ X202 ) )
                                                       => ( ! [X204: $i,X205: $i > $o,X206: $i] :
                                                              ( ( in @ X206 @ X204 )
                                                             => ( ( X205 @ X206 )
                                                               => ( ( dsetconstr @ X204 @ X205 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X207: $i] :
                                                                ( ? [X208: $i] : ( in @ X208 @ X207 )
                                                               => ( X207 != emptyset ) )
                                                           => ( ! [X209: $i,X210: $i] : ( in @ X209 @ ( setadjoin @ X209 @ X210 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X211: $i,X212: $i,X213: $i] :
                                                                      ( ( in @ X213 @ X212 )
                                                                     => ( in @ X213 @ ( setadjoin @ X211 @ X212 ) ) )
                                                                 => ( ! [X214: $i,X215: $i,X216: $i] :
                                                                        ( ( in @ X216 @ ( setadjoin @ X214 @ X215 ) )
                                                                       => ! [X217: $o] :
                                                                            ( ( ( X216 = X214 )
                                                                             => X217 )
                                                                           => ( ( ( in @ X216 @ X215 )
                                                                               => X217 )
                                                                             => X217 ) ) )
                                                                   => ( ! [X218: $i,X219: $i,X220: $i] :
                                                                          ( ( in @ X220 @ ( setadjoin @ X218 @ X219 ) )
                                                                         => ( ( X220 = X218 )
                                                                            | ( in @ X220 @ X219 ) ) )
                                                                     => ( ! [X221: $i] :
                                                                            ( ( dsetconstr @ X221
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X221 )
                                                                       => ( ! [X222: $i,X223: $i] :
                                                                              ( ! [X224: $i] :
                                                                                  ( ( in @ X224 @ X223 )
                                                                                 => ( in @ X224 @ X222 ) )
                                                                             => ( in @ X223 @ ( powerset @ X222 ) ) )
                                                                         => ( ! [X225: $i] : ( in @ emptyset @ ( powerset @ X225 ) )
                                                                           => ( ! [X226: $i] : ( in @ emptyset @ ( powerset @ X226 ) )
                                                                             => ! [X4: $i,X5: $i,X2: $i] :
                                                                                  ( ( in @ X5 @ ( powerset @ X4 ) )
                                                                                 => ( ( in @ X2 @ X5 )
                                                                                   => ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[powersetE]),c_0_46]),emptyInPowerset]),c_0_47]),c_0_48]),c_0_49]),omega0Ax]),c_0_50]),setadjoinIL]),omegaSAx]),emptyinunitempty]),setadjoinIR]),omegaIndAx]),setadjoinE]),setadjoinOr]),c_0_51]),c_0_52]),powersetI]),foundationAx]),emptyinPowerset]),wellorderingAx]),c_0_53]),c_0_54]),c_0_55]),c_0_56]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_57]),setext]),emptyI]),noeltsimpempty]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_58]) ).

thf(c_0_60,negated_conjecture,
    ! [X227: $i,X228: $i,X230: $i,X231: $i,X232: $i,X233: $i,X234: $i,X235: $i,X236: $i,X237: $i,X238: $i,X240: $i,X241: $i,X243: $i,X244: $i > $i > $o,X245: $i,X247: $i,X250: $i,X252: $i,X253: $i,X254: $i,X255: $i,X257: $i,X258: $i,X259: $i > $o,X260: $i,X261: $i,X262: $i > $o,X263: $i,X264: $i,X265: $i > $o,X266: $i,X267: $i > $o,X268: $i,X271: $i,X272: $o,X273: $i,X274: $i,X275: $o,X276: $i,X277: $i,X278: $i > $o,X279: $i,X282: $i,X283: $i,X286: $i,X288: $i,X290: $i,X291: $i > $o,X292: $i,X293: $i,X295: $i,X296: $i > $o,X297: $i,X298: $i,X299: $i,X300: $i,X301: $i,X302: $i,X303: $i,X304: $i,X305: $i,X306: $i,X307: $i,X308: $o,X309: $i,X310: $i,X311: $i,X312: $i,X313: $i,X314: $i,X316: $i,X317: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X227 @ X228 ) @ X227 )
        | ~ ( in @ ( esk1_2 @ X227 @ X228 ) @ X228 )
        | ( X227 = X228 ) )
      & ( ( in @ ( esk1_2 @ X227 @ X228 ) @ X227 )
        | ( in @ ( esk1_2 @ X227 @ X228 ) @ X228 )
        | ( X227 = X228 ) )
      & ~ ( in @ X230 @ emptyset )
      & ( ~ ( in @ X233 @ ( setadjoin @ X231 @ X232 ) )
        | ( X233 = X231 )
        | ( in @ X233 @ X232 ) )
      & ( ( X233 != X231 )
        | ( in @ X233 @ ( setadjoin @ X231 @ X232 ) ) )
      & ( ~ ( in @ X233 @ X232 )
        | ( in @ X233 @ ( setadjoin @ X231 @ X232 ) ) )
      & ( ~ ( in @ X235 @ ( powerset @ X234 ) )
        | ~ ( in @ X236 @ X235 )
        | ( in @ X236 @ X234 ) )
      & ( ( in @ ( esk2_2 @ X237 @ X238 ) @ X238 )
        | ( in @ X238 @ ( powerset @ X237 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X237 @ X238 ) @ X237 )
        | ( in @ X238 @ ( powerset @ X237 ) ) )
      & setunionAx
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X240 @ omega )
        | ( in @ ( setadjoin @ X240 @ X240 ) @ omega ) )
      & ( ( in @ ( esk3_1 @ X241 ) @ omega )
        | ~ ( in @ emptyset @ X241 )
        | ~ ( in @ X243 @ omega )
        | ( in @ X243 @ X241 ) )
      & ( ( in @ ( esk3_1 @ X241 ) @ X241 )
        | ~ ( in @ emptyset @ X241 )
        | ~ ( in @ X243 @ omega )
        | ( in @ X243 @ X241 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X241 ) @ ( esk3_1 @ X241 ) ) @ X241 )
        | ~ ( in @ emptyset @ X241 )
        | ~ ( in @ X243 @ omega )
        | ( in @ X243 @ X241 ) )
      & ( ( in @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X245 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( in @ ( esk4_2 @ X244 @ X245 ) @ X245 ) )
      & ( ( X244 @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X250 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( in @ ( esk4_2 @ X244 @ X245 ) @ X245 ) )
      & ( ~ ( in @ X253 @ X245 )
        | ~ ( X244 @ X253 @ X252 )
        | ( in @ X252 @ ( esk6_2 @ X244 @ X245 ) )
        | ( in @ ( esk4_2 @ X244 @ X245 ) @ X245 ) )
      & ( ( in @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X245 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X244 @ ( esk4_2 @ X244 @ X245 ) @ ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ( X244 @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X250 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X244 @ ( esk4_2 @ X244 @ X245 ) @ ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ~ ( in @ X253 @ X245 )
        | ~ ( X244 @ X253 @ X252 )
        | ( in @ X252 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X244 @ ( esk4_2 @ X244 @ X245 ) @ ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ( in @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X245 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X247
         != ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ( X244 @ ( esk7_3 @ X244 @ X245 @ X250 ) @ X250 )
        | ~ ( in @ X250 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X247
         != ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ~ ( in @ X253 @ X245 )
        | ~ ( X244 @ X253 @ X252 )
        | ( in @ X252 @ ( esk6_2 @ X244 @ X245 ) )
        | ( X247
         != ( esk5_3 @ X244 @ X245 @ X247 ) )
        | ~ ( X244 @ ( esk4_2 @ X244 @ X245 ) @ X247 ) )
      & ( ( in @ ( esk8_1 @ X254 ) @ X254 )
        | ~ ( in @ X255 @ X254 ) )
      & ( ~ ( in @ X257 @ ( esk8_1 @ X254 ) )
        | ~ ( in @ X257 @ X254 )
        | ~ ( in @ X255 @ X254 ) )
      & epred1_0
      & descrp
      & ( ~ ( in @ X260 @ X258 )
        | ~ ( X259 @ X260 )
        | ( in @ X260 @ ( dsetconstr @ X258 @ X259 ) ) )
      & ( ~ ( in @ X263 @ ( dsetconstr @ X261 @ X262 ) )
        | ( in @ X263 @ X261 ) )
      & ( ~ ( in @ X266 @ ( dsetconstr @ X264 @ X265 ) )
        | ( X265 @ X266 ) )
      & ( ( X267 @ ( esk10_1 @ X267 ) )
        | ( X267 @ ( esk9_2 @ X267 @ X268 ) )
        | ~ ( X267 @ X268 ) )
      & ( ~ ( X267 @ X271 )
        | ( ( esk10_1 @ X267 )
          = X271 )
        | ( X267 @ ( esk9_2 @ X267 @ X268 ) )
        | ~ ( X267 @ X268 ) )
      & ( ( X267 @ ( esk10_1 @ X267 ) )
        | ( X268
         != ( esk9_2 @ X267 @ X268 ) )
        | ~ ( X267 @ X268 ) )
      & ( ~ ( X267 @ X271 )
        | ( ( esk10_1 @ X267 )
          = X271 )
        | ( X268
         != ( esk9_2 @ X267 @ X268 ) )
        | ~ ( X267 @ X268 ) )
      & ( ~ ( in @ X273
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X272 ) )
        | X272 )
      & ( ~ ( in @ X274 @ emptyset )
        | X275 )
      & ( ~ ( in @ X276 @ emptyset )
        | ~ $true )
      & ~ ( in @ X277 @ emptyset )
      & ( ( X278 @ ( esk11_2 @ X278 @ X279 ) )
        | ~ ( X278 @ X279 )
        | ( X278 @ ( esk12_1 @ X278 ) ) )
      & ( ( X279
         != ( esk11_2 @ X278 @ X279 ) )
        | ~ ( X278 @ X279 )
        | ( X278 @ ( esk12_1 @ X278 ) ) )
      & ( ( in @ ( esk14_2 @ X282 @ X283 ) @ X283 )
        | ( X282 = X283 )
        | ( in @ ( esk13_2 @ X282 @ X283 ) @ X282 ) )
      & ( ~ ( in @ ( esk14_2 @ X282 @ X283 ) @ X282 )
        | ( X282 = X283 )
        | ( in @ ( esk13_2 @ X282 @ X283 ) @ X282 ) )
      & ( ( in @ ( esk14_2 @ X282 @ X283 ) @ X283 )
        | ( X282 = X283 )
        | ~ ( in @ ( esk13_2 @ X282 @ X283 ) @ X283 ) )
      & ( ~ ( in @ ( esk14_2 @ X282 @ X283 ) @ X282 )
        | ( X282 = X283 )
        | ~ ( in @ ( esk13_2 @ X282 @ X283 ) @ X283 ) )
      & ( ( in @ ( esk15_1 @ X286 ) @ X286 )
        | ( X286 = emptyset ) )
      & ( ( in @ ( esk16_1 @ X288 ) @ X288 )
        | ( X288 = emptyset ) )
      & ( ~ ( in @ X292 @ ( dsetconstr @ X290 @ X291 ) )
        | ( X291 @ X292 )
        | ~ ( in @ X292 @ X290 ) )
      & ( ~ ( X291 @ X292 )
        | ( in @ X292 @ ( dsetconstr @ X290 @ X291 ) )
        | ~ ( in @ X292 @ X290 ) )
      & ( ( X293 = emptyset )
        | ( in @ ( esk17_1 @ X293 ) @ X293 ) )
      & ( ~ ( in @ X297 @ X295 )
        | ~ ( X296 @ X297 )
        | ( ( dsetconstr @ X295 @ X296 )
         != emptyset ) )
      & ( ~ ( in @ X299 @ X298 )
        | ( X298 != emptyset ) )
      & ( in @ X300 @ ( setadjoin @ X300 @ X301 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X304 @ X303 )
        | ( in @ X304 @ ( setadjoin @ X302 @ X303 ) ) )
      & ( ( in @ X307 @ X306 )
        | X308
        | ( X307 = X305 )
        | ~ ( in @ X307 @ ( setadjoin @ X305 @ X306 ) ) )
      & ( ~ X308
        | X308
        | ( X307 = X305 )
        | ~ ( in @ X307 @ ( setadjoin @ X305 @ X306 ) ) )
      & ( ( in @ X307 @ X306 )
        | X308
        | ~ X308
        | ~ ( in @ X307 @ ( setadjoin @ X305 @ X306 ) ) )
      & ( ~ X308
        | X308
        | ~ X308
        | ~ ( in @ X307 @ ( setadjoin @ X305 @ X306 ) ) )
      & ( ~ ( in @ X311 @ ( setadjoin @ X309 @ X310 ) )
        | ( X311 = X309 )
        | ( in @ X311 @ X310 ) )
      & ( ( dsetconstr @ X312
          @ ^ [Z0: $i] : $true )
        = X312 )
      & ( ( in @ ( esk18_2 @ X313 @ X314 ) @ X314 )
        | ( in @ X314 @ ( powerset @ X313 ) ) )
      & ( ~ ( in @ ( esk18_2 @ X313 @ X314 ) @ X313 )
        | ( in @ X314 @ ( powerset @ X313 ) ) )
      & ( in @ emptyset @ ( powerset @ X316 ) )
      & ( in @ emptyset @ ( powerset @ X317 ) )
      & ( in @ esk20_0 @ ( powerset @ esk19_0 ) )
      & ( in @ esk21_0 @ esk20_0 )
      & ~ ( in @ esk21_0 @ esk19_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])])]) ).

thf(c_0_61,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i] :
      ( ( in @ X4 @ X3 )
      | ~ ( in @ X2 @ ( powerset @ X3 ) )
      | ~ ( in @ X4 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_62,negated_conjecture,
    in @ esk20_0 @ ( powerset @ esk19_0 ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_63,negated_conjecture,
    ~ ( in @ esk21_0 @ esk19_0 ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_64,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk19_0 )
      | ~ ( in @ X2 @ esk20_0 ) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

thf(c_0_65,negated_conjecture,
    in @ esk21_0 @ esk20_0,
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_66,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU521^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 17:57:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.48  Running higher-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51  # Version: 3.1.0-ho
% 0.21/0.51  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # Starting new_bool_2 with 300s (1) cores
% 0.21/0.51  # new_bool_1 with pid 14769 completed with status 0
% 0.21/0.51  # Result found by new_bool_1
% 0.21/0.51  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51  # Search class: HGHSM-FFMM31-SHFSMSBN
% 0.21/0.51  # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 181s (1) cores
% 0.21/0.51  # new_ho_10 with pid 14772 completed with status 0
% 0.21/0.51  # Result found by new_ho_10
% 0.21/0.51  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51  # Search class: HGHSM-FFMM31-SHFSMSBN
% 0.21/0.51  # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 181s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.003 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 89
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 50
% 0.21/0.51  # Initial clauses                      : 81
% 0.21/0.51  # Removed in clause preprocessing      : 3
% 0.21/0.51  # Initial clauses in saturation        : 78
% 0.21/0.51  # Processed clauses                    : 130
% 0.21/0.51  # ...of these trivial                  : 3
% 0.21/0.51  # ...subsumed                          : 12
% 0.21/0.51  # ...remaining for further processing  : 115
% 0.21/0.51  # Other redundant clauses eliminated   : 3
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 0
% 0.21/0.51  # Backward-rewritten                   : 2
% 0.21/0.51  # Generated clauses                    : 111
% 0.21/0.51  # ...of the previous two non-redundant : 91
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 0
% 0.21/0.51  # Paramodulations                      : 108
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 3
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 25
% 0.21/0.51  # ...of those cached                   : 15
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 45
% 0.21/0.51  #    Positive orientable unit clauses  : 14
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 2
% 0.21/0.51  #    Non-unit-clauses                  : 29
% 0.21/0.51  # Current number of unprocessed clauses: 105
% 0.21/0.51  # ...number of literals in the above   : 320
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 68
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 1190
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 489
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 8
% 0.21/0.51  # Unit Clause-clause subsumption calls : 9
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 9
% 0.21/0.51  # BW rewrite match successes           : 2
% 0.21/0.51  # Condensation attempts                : 130
% 0.21/0.51  # Condensation successes               : 3
% 0.21/0.51  # Termbank termtop insertions          : 12359
% 0.21/0.51  # Search garbage collected termcells   : 3753
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.019 s
% 0.21/0.51  # System time              : 0.005 s
% 0.21/0.51  # Total time               : 0.025 s
% 0.21/0.51  # Maximum resident set size: 2800 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.022 s
% 0.21/0.51  # System time              : 0.007 s
% 0.21/0.51  # Total time               : 0.029 s
% 0.21/0.51  # Maximum resident set size: 1816 pages
% 0.21/0.51  % E---3.1 exiting
% 0.21/0.52  % E exiting
%------------------------------------------------------------------------------