TSTP Solution File: SEU530^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU530^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 03:27:59 EDT 2024

% Result   : Theorem 0.19s 0.50s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  135
% Syntax   : Number of formulae    :  167 (  21 unt;  84 typ;   0 def)
%            Number of atoms       :  609 ( 110 equ;   0 cnn)
%            Maximal formula atoms :  165 (   7 avg)
%            Number of connectives : 2032 ( 147   ~; 153   |; 137   &;1251   @)
%                                         (  79 <=>; 265  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  191 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  125 ( 125   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  84 usr;  53 con; 0-3 aty)
%            Number of variables   :  483 (  40   ^ 384   !;  59   ?; 483   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_79,type,
    epred1_0: $o ).

thf(decl_80,type,
    esk1_2: $i > $i > $i ).

thf(decl_81,type,
    esk2_2: $i > $i > $i ).

thf(decl_82,type,
    esk3_2: $i > $i > $i ).

thf(decl_83,type,
    esk4_1: $i > $i ).

thf(decl_84,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_85,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_86,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_87,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_88,type,
    esk9_1: $i > $i ).

thf(decl_89,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_90,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_91,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_92,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_93,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_94,type,
    esk15_2: $i > $i > $i ).

thf(decl_95,type,
    esk16_2: $i > $i > $i ).

thf(decl_96,type,
    esk17_1: $i > $i ).

thf(decl_97,type,
    esk18_1: $i > $i ).

thf(decl_98,type,
    esk19_1: $i > $i ).

thf(decl_99,type,
    esk20_2: $i > $i > $i ).

thf(decl_100,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_101,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_102,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_103,type,
    esk24_1: $i > $i ).

thf(decl_104,type,
    esk25_0: $i ).

thf(decl_105,type,
    esk26_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(descrp,axiom,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ( X1
          @ ( descr
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(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_50,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_51,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_52,plain,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ( X1
          @ ( descr
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descrp]) ).

thf(c_0_53,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_54,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_55,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_56,plain,
    ( prop2set
    = ( ^ [Z0: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Z1: $i] : Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[prop2set]) ).

thf(c_0_57,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_58,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_59,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X149: $i] :
              ( ( X1 @ X149 )
              & ! [X150: $i] :
                  ( ( X1 @ X150 )
                 => ( X149 = X150 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_50,c_0_51]) ).

thf(c_0_60,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X145: $i] :
              ( ( X1 @ X145 )
              & ! [X146: $i] :
                  ( ( X1 @ X146 )
                 => ( X145 = X146 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_52,c_0_51]) ).

thf(c_0_61,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X151: $i] :
              ( ( X1 @ X151 )
              & ! [X152: $i] :
                  ( ( X1 @ X152 )
                 => ( X151 = X152 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_53,c_0_51]) ).

thf(c_0_62,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_63,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_54]) ).

thf(c_0_64,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_65,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_66,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X147: $i] :
              ( ( X1 @ X147 )
              & ! [X148: $i] :
                  ( ( X1 @ X148 )
                 => ( X147 = X148 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_55,c_0_51]) ).

thf(c_0_67,axiom,
    ( prop2setE
    = ( ! [X11: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X11 ) )
         => X11 ) ) ),
    inference(apply_def,[status(thm)],[prop2setE,c_0_56]) ).

thf(c_0_68,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_69,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_54]) ).

thf(c_0_70,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_57,c_0_54]) ).

thf(c_0_71,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_54]) ).

thf(c_0_72,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_73,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X143: $i] :
                  ( ( X6 @ X2 @ X143 )
                  & ! [X144: $i] :
                      ( ( X6 @ X2 @ X144 )
                     => ( X143 = X144 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_58,c_0_51]) ).

thf(c_0_74,plain,
    ( epred1_0
  <=> ! [X182: $i] :
      ? [X183: $i] :
        ( ! [X184: $i] :
            ( ( in @ X184 @ X183 )
           => ! [X185: $i] :
                ( ( in @ X185 @ X184 )
               => ( in @ X185 @ X182 ) ) )
        & ! [X186: $i,X187: $i] :
            ( ( ( in @ X186 @ X182 )
              & ( in @ X187 @ X182 ) )
           => ( ! [X188: $i] :
                  ( ( in @ X188 @ X183 )
                 => ( ( in @ X186 @ X188 )
                  <=> ( in @ X187 @ X188 ) ) )
             => ( X186 = X187 ) ) )
        & ! [X189: $i,X190: $i] :
            ( ( ( in @ X189 @ X183 )
              & ( in @ X190 @ X183 ) )
           => ( ! [X191: $i] :
                  ( ( in @ X191 @ X189 )
                 => ( in @ X191 @ X190 ) )
              | ! [X192: $i] :
                  ( ( in @ X192 @ X190 )
                 => ( in @ X192 @ X189 ) ) ) )
        & ! [X193: $i] :
            ( ( ! [X194: $i] :
                  ( ( in @ X194 @ X193 )
                 => ( in @ X194 @ X182 ) )
              & ? [X195: $i] : ( in @ X195 @ X193 ) )
           => ? [X196: $i,X197: $i] :
                ( ( in @ X196 @ X183 )
                & ( in @ X197 @ X193 )
                & ~ ? [X198: $i] :
                      ( ( in @ X198 @ X196 )
                      & ( in @ X198 @ X193 ) )
                & ! [X199: $i] :
                    ( ( in @ X199 @ X183 )
                   => ( ! [X200: $i] :
                          ( ( in @ X200 @ X199 )
                         => ( in @ X200 @ X196 ) )
                      | ( in @ X197 @ X199 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_75,negated_conjecture,
    ~ ( ! [X153: $i,X154: $i] :
          ( ! [X155: $i] :
              ( ( in @ X155 @ X153 )
            <=> ( in @ X155 @ X154 ) )
         => ( X153 = X154 ) )
     => ( ! [X156: $i] :
            ~ ( in @ X156 @ emptyset )
       => ( ! [X157: $i,X158: $i,X159: $i] :
              ( ( in @ X159 @ ( setadjoin @ X157 @ X158 ) )
            <=> ( ( X159 = X157 )
                | ( in @ X159 @ X158 ) ) )
         => ( ! [X160: $i,X161: $i] :
                ( ( in @ X161 @ ( powerset @ X160 ) )
              <=> ! [X162: $i] :
                    ( ( in @ X162 @ X161 )
                   => ( in @ X162 @ X160 ) ) )
           => ( ! [X163: $i,X164: $i] :
                  ( ( in @ X164 @ ( setunion @ X163 ) )
                <=> ? [X165: $i] :
                      ( ( in @ X164 @ X165 )
                      & ( in @ X165 @ X163 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X166: $i] :
                      ( ( in @ X166 @ omega )
                     => ( in @ ( setadjoin @ X166 @ X166 ) @ omega ) )
                 => ( ! [X167: $i] :
                        ( ( ( in @ emptyset @ X167 )
                          & ! [X168: $i] :
                              ( ( ( in @ X168 @ omega )
                                & ( in @ X168 @ X167 ) )
                             => ( in @ ( setadjoin @ X168 @ X168 ) @ X167 ) ) )
                       => ! [X169: $i] :
                            ( ( in @ X169 @ omega )
                           => ( in @ X169 @ X167 ) ) )
                   => ( ! [X170: $i > $i > $o,X171: $i] :
                          ( ! [X172: $i] :
                              ( ( in @ X172 @ X171 )
                             => ? [X173: $i] :
                                  ( ( X170 @ X172 @ X173 )
                                  & ! [X174: $i] :
                                      ( ( X170 @ X172 @ X174 )
                                     => ( X173 = X174 ) ) ) )
                         => ? [X175: $i] :
                            ! [X176: $i] :
                              ( ( in @ X176 @ X175 )
                            <=> ? [X177: $i] :
                                  ( ( in @ X177 @ X171 )
                                  & ( X170 @ X177 @ X176 ) ) ) )
                     => ( ! [X178: $i] :
                            ( ? [X179: $i] : ( in @ X179 @ X178 )
                           => ? [X180: $i] :
                                ( ( in @ X180 @ X178 )
                                & ~ ? [X181: $i] :
                                      ( ( in @ X181 @ X180 )
                                      & ( in @ X181 @ X178 ) ) ) )
                       => ( epred1_0
                         => ( ! [X201: $i > $o] :
                                ( ? [X202: $i] :
                                    ( ( X201 @ X202 )
                                    & ! [X203: $i] :
                                        ( ( X201 @ X203 )
                                       => ( X202 = X203 ) ) )
                               => ( X201
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X201 @ Z0 ) ) ) )
                           => ( ! [X204: $i,X205: $i > $o,X206: $i] :
                                  ( ( in @ X206 @ X204 )
                                 => ( ( X205 @ X206 )
                                   => ( in @ X206 @ ( dsetconstr @ X204 @ X205 ) ) ) )
                             => ( ! [X207: $i,X208: $i > $o,X209: $i] :
                                    ( ( in @ X209 @ ( dsetconstr @ X207 @ X208 ) )
                                   => ( in @ X209 @ X207 ) )
                               => ( ! [X210: $i,X211: $i > $o,X212: $i] :
                                      ( ( in @ X212 @ ( dsetconstr @ X210 @ X211 ) )
                                     => ( X211 @ X212 ) )
                                 => ( ! [X213: $i > $o] :
                                        ( ? [X214: $i] :
                                            ( ( X213 @ X214 )
                                            & ! [X215: $i] :
                                                ( ( X213 @ X215 )
                                               => ( X214 = X215 ) ) )
                                       => ? [X216: $i] :
                                            ( ( X213 @ X216 )
                                            & ! [X217: $i] :
                                                ( ( X213 @ X217 )
                                               => ( X216 = X217 ) ) ) )
                                   => ( ! [X218: $o,X219: $i] :
                                          ( ( in @ X219
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [Z0: $i] : X218 ) )
                                         => X218 )
                                     => ( ! [X220: $i] :
                                            ( ( in @ X220 @ emptyset )
                                           => ! [X221: $o] : X221 )
                                       => ( ! [X222: $i] :
                                              ( ( in @ X222 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X223: $i] :
                                                ~ ( in @ X223 @ emptyset )
                                           => ( ! [X224: $i > $o] :
                                                  ( ? [X225: $i] :
                                                      ( ( X224 @ X225 )
                                                      & ! [X226: $i] :
                                                          ( ( X224 @ X226 )
                                                         => ( X225 = X226 ) ) )
                                                 => ? [X227: $i] : ( X224 @ X227 ) )
                                             => ( ! [X228: $i,X229: $i] :
                                                    ( ! [X230: $i] :
                                                        ( ( in @ X230 @ X228 )
                                                       => ( in @ X230 @ X229 ) )
                                                   => ( ! [X231: $i] :
                                                          ( ( in @ X231 @ X229 )
                                                         => ( in @ X231 @ X228 ) )
                                                     => ( X228 = X229 ) ) )
                                               => ( ! [X232: $i] :
                                                      ( ! [X233: $i] :
                                                          ~ ( in @ X233 @ X232 )
                                                     => ( X232 = emptyset ) )
                                                 => ( ! [X234: $i] :
                                                        ( ! [X235: $i] :
                                                            ~ ( in @ X235 @ X234 )
                                                       => ( X234 = emptyset ) )
                                                   => ( ! [X236: $i,X237: $i > $o,X238: $i] :
                                                          ( ( in @ X238 @ X236 )
                                                         => ( ( in @ X238 @ ( dsetconstr @ X236 @ X237 ) )
                                                          <=> ( X237 @ X238 ) ) )
                                                     => ( ! [X239: $i] :
                                                            ( ( X239 != emptyset )
                                                           => ? [X240: $i] : ( in @ X240 @ X239 ) )
                                                       => ( ! [X241: $i,X242: $i > $o,X243: $i] :
                                                              ( ( in @ X243 @ X241 )
                                                             => ( ( X242 @ X243 )
                                                               => ( ( dsetconstr @ X241 @ X242 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X244: $i] :
                                                                ( ? [X245: $i] : ( in @ X245 @ X244 )
                                                               => ( X244 != emptyset ) )
                                                           => ( ! [X246: $i,X247: $i] : ( in @ X246 @ ( setadjoin @ X246 @ X247 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X248: $i,X249: $i,X250: $i] :
                                                                      ( ( in @ X250 @ X249 )
                                                                     => ( in @ X250 @ ( setadjoin @ X248 @ X249 ) ) )
                                                                 => ( ! [X251: $i,X252: $i,X253: $i] :
                                                                        ( ( in @ X253 @ ( setadjoin @ X251 @ X252 ) )
                                                                       => ! [X254: $o] :
                                                                            ( ( ( X253 = X251 )
                                                                             => X254 )
                                                                           => ( ( ( in @ X253 @ X252 )
                                                                               => X254 )
                                                                             => X254 ) ) )
                                                                   => ( ! [X255: $i,X256: $i,X257: $i] :
                                                                          ( ( in @ X257 @ ( setadjoin @ X255 @ X256 ) )
                                                                         => ( ( X257 = X255 )
                                                                            | ( in @ X257 @ X256 ) ) )
                                                                     => ( ! [X258: $i] :
                                                                            ( ( dsetconstr @ X258
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X258 )
                                                                       => ( ! [X259: $i,X260: $i] :
                                                                              ( ! [X261: $i] :
                                                                                  ( ( in @ X261 @ X260 )
                                                                                 => ( in @ X261 @ X259 ) )
                                                                             => ( in @ X260 @ ( powerset @ X259 ) ) )
                                                                         => ( ! [X262: $i] : ( in @ emptyset @ ( powerset @ X262 ) )
                                                                           => ( ! [X263: $i] : ( in @ emptyset @ ( powerset @ X263 ) )
                                                                             => ( ! [X264: $i,X265: $i,X266: $i] :
                                                                                    ( ( in @ X265 @ ( powerset @ X264 ) )
                                                                                   => ( ( in @ X266 @ X265 )
                                                                                     => ( in @ X266 @ X264 ) ) )
                                                                               => ( ! [X267: $i,X268: $i,X269: $i] :
                                                                                      ( ( in @ X268 @ X269 )
                                                                                     => ( ( in @ X269 @ X267 )
                                                                                       => ( in @ X268 @ ( setunion @ X267 ) ) ) )
                                                                                 => ( ! [X270: $i,X271: $i] :
                                                                                        ( ( in @ X271 @ ( setunion @ X270 ) )
                                                                                       => ! [X272: $o] :
                                                                                            ( ! [X273: $i] :
                                                                                                ( ( in @ X271 @ X273 )
                                                                                               => ( ( in @ X273 @ X270 )
                                                                                                 => X272 ) )
                                                                                           => X272 ) )
                                                                                   => ( ! [X274: $i,X275: $i] :
                                                                                          ( ( in @ X275 @ X274 )
                                                                                         => ( in @ X275 @ ( powerset @ ( setunion @ X274 ) ) ) )
                                                                                     => ( ! [X276: $i > $o] :
                                                                                            ( ? [X277: $i] :
                                                                                                ( ( X276 @ X277 )
                                                                                                & ! [X278: $i] :
                                                                                                    ( ( X276 @ X278 )
                                                                                                   => ( X277 = X278 ) ) )
                                                                                           => ? [X279: $i] :
                                                                                              ! [X280: $i] :
                                                                                                ( ( X276 @ X280 )
                                                                                              <=> ( X280 = X279 ) ) )
                                                                                       => ( ! [X281: $i] :
                                                                                              ( ( X281 != emptyset )
                                                                                             => ? [X282: $i] :
                                                                                                  ( ( in @ X282 @ X281 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X283: $i,X284: $i] :
                                                                                                ( ( in @ X283 @ ( setadjoin @ X284 @ emptyset ) )
                                                                                               => ( X283 = X284 ) )
                                                                                           => ( ! [X285: $i,X286: $i] :
                                                                                                  ( ( X285 != X286 )
                                                                                                 => ~ ( in @ X286 @ ( setadjoin @ X285 @ emptyset ) ) )
                                                                                             => ( ! [X287: $i,X288: $i] :
                                                                                                    ( ( X287 = X288 )
                                                                                                   => ( in @ X287 @ ( setadjoin @ X288 @ emptyset ) ) )
                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                    ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
                                                                                                   => ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[singletonsswitch]),c_0_59]),setunionI]),c_0_60]),setunionE]),subPowSU]),c_0_61]),c_0_62]),c_0_63]),uniqinunit]),c_0_64]),notinsingleton]),eqinunit]),c_0_65]),c_0_66]),c_0_67]),emptysetE]),emptysetimpfalse]),notinemptyset]),setext]),emptyI]),noeltsimpempty]),c_0_68]),c_0_69]),c_0_70]),c_0_71]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_72]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),wellorderingAx]),foundationAx]),c_0_73]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_74]) ).

thf(c_0_76,negated_conjecture,
    ! [X289: $i,X290: $i,X292: $i,X293: $i,X294: $i,X295: $i,X296: $i,X297: $i,X298: $i,X299: $i,X300: $i,X302: $i,X303: $i,X305: $i,X306: $i,X307: $i,X308: $i,X309: $i,X311: $i,X312: $i > $i > $o,X313: $i,X315: $i,X318: $i,X320: $i,X321: $i,X322: $i,X323: $i,X325: $i,X326: $i > $o,X327: $i,X329: $i,X330: $i > $o,X331: $i,X332: $i,X333: $i > $o,X334: $i,X335: $i,X336: $i > $o,X337: $i,X338: $i > $o,X339: $i,X342: $i,X343: $o,X344: $i,X345: $i,X346: $o,X347: $i,X348: $i,X349: $i > $o,X350: $i,X353: $i,X354: $i,X357: $i,X359: $i,X361: $i,X362: $i > $o,X363: $i,X364: $i,X366: $i,X367: $i > $o,X368: $i,X369: $i,X370: $i,X371: $i,X372: $i,X373: $i,X374: $i,X375: $i,X376: $i,X377: $i,X378: $i,X379: $o,X380: $i,X381: $i,X382: $i,X383: $i,X384: $i,X385: $i,X387: $i,X388: $i,X389: $i,X390: $i,X391: $i,X392: $i,X393: $i,X394: $i,X395: $i,X396: $i,X397: $o,X399: $i,X400: $i,X401: $i > $o,X402: $i,X405: $i,X406: $i,X407: $i,X409: $i,X410: $i,X411: $i,X412: $i,X413: $i,X414: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X289 @ X290 ) @ X289 )
        | ~ ( in @ ( esk1_2 @ X289 @ X290 ) @ X290 )
        | ( X289 = X290 ) )
      & ( ( in @ ( esk1_2 @ X289 @ X290 ) @ X289 )
        | ( in @ ( esk1_2 @ X289 @ X290 ) @ X290 )
        | ( X289 = X290 ) )
      & ~ ( in @ X292 @ emptyset )
      & ( ~ ( in @ X295 @ ( setadjoin @ X293 @ X294 ) )
        | ( X295 = X293 )
        | ( in @ X295 @ X294 ) )
      & ( ( X295 != X293 )
        | ( in @ X295 @ ( setadjoin @ X293 @ X294 ) ) )
      & ( ~ ( in @ X295 @ X294 )
        | ( in @ X295 @ ( setadjoin @ X293 @ X294 ) ) )
      & ( ~ ( in @ X297 @ ( powerset @ X296 ) )
        | ~ ( in @ X298 @ X297 )
        | ( in @ X298 @ X296 ) )
      & ( ( in @ ( esk2_2 @ X299 @ X300 ) @ X300 )
        | ( in @ X300 @ ( powerset @ X299 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X299 @ X300 ) @ X299 )
        | ( in @ X300 @ ( powerset @ X299 ) ) )
      & ( ( in @ X303 @ ( esk3_2 @ X302 @ X303 ) )
        | ~ ( in @ X303 @ ( setunion @ X302 ) ) )
      & ( ( in @ ( esk3_2 @ X302 @ X303 ) @ X302 )
        | ~ ( in @ X303 @ ( setunion @ X302 ) ) )
      & ( ~ ( in @ X306 @ X307 )
        | ~ ( in @ X307 @ X305 )
        | ( in @ X306 @ ( setunion @ X305 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X308 @ omega )
        | ( in @ ( setadjoin @ X308 @ X308 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X309 ) @ omega )
        | ~ ( in @ emptyset @ X309 )
        | ~ ( in @ X311 @ omega )
        | ( in @ X311 @ X309 ) )
      & ( ( in @ ( esk4_1 @ X309 ) @ X309 )
        | ~ ( in @ emptyset @ X309 )
        | ~ ( in @ X311 @ omega )
        | ( in @ X311 @ X309 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X309 ) @ ( esk4_1 @ X309 ) ) @ X309 )
        | ~ ( in @ emptyset @ X309 )
        | ~ ( in @ X311 @ omega )
        | ( in @ X311 @ X309 ) )
      & ( ( in @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X313 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( in @ ( esk5_2 @ X312 @ X313 ) @ X313 ) )
      & ( ( X312 @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X318 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( in @ ( esk5_2 @ X312 @ X313 ) @ X313 ) )
      & ( ~ ( in @ X321 @ X313 )
        | ~ ( X312 @ X321 @ X320 )
        | ( in @ X320 @ ( esk7_2 @ X312 @ X313 ) )
        | ( in @ ( esk5_2 @ X312 @ X313 ) @ X313 ) )
      & ( ( in @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X313 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X312 @ ( esk5_2 @ X312 @ X313 ) @ ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ( X312 @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X318 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X312 @ ( esk5_2 @ X312 @ X313 ) @ ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ~ ( in @ X321 @ X313 )
        | ~ ( X312 @ X321 @ X320 )
        | ( in @ X320 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X312 @ ( esk5_2 @ X312 @ X313 ) @ ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ( in @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X313 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X315
         != ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ( X312 @ ( esk8_3 @ X312 @ X313 @ X318 ) @ X318 )
        | ~ ( in @ X318 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X315
         != ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ~ ( in @ X321 @ X313 )
        | ~ ( X312 @ X321 @ X320 )
        | ( in @ X320 @ ( esk7_2 @ X312 @ X313 ) )
        | ( X315
         != ( esk6_3 @ X312 @ X313 @ X315 ) )
        | ~ ( X312 @ ( esk5_2 @ X312 @ X313 ) @ X315 ) )
      & ( ( in @ ( esk9_1 @ X322 ) @ X322 )
        | ~ ( in @ X323 @ X322 ) )
      & ( ~ ( in @ X325 @ ( esk9_1 @ X322 ) )
        | ~ ( in @ X325 @ X322 )
        | ~ ( in @ X323 @ X322 ) )
      & epred1_0
      & ( ( X326 @ ( esk10_2 @ X326 @ X327 ) )
        | ~ ( X326 @ X327 )
        | ( X326 @ ( descr @ X326 ) ) )
      & ( ( X327
         != ( esk10_2 @ X326 @ X327 ) )
        | ~ ( X326 @ X327 )
        | ( X326 @ ( descr @ X326 ) ) )
      & ( ~ ( in @ X331 @ X329 )
        | ~ ( X330 @ X331 )
        | ( in @ X331 @ ( dsetconstr @ X329 @ X330 ) ) )
      & ( ~ ( in @ X334 @ ( dsetconstr @ X332 @ X333 ) )
        | ( in @ X334 @ X332 ) )
      & ( ~ ( in @ X337 @ ( dsetconstr @ X335 @ X336 ) )
        | ( X336 @ X337 ) )
      & ( ( X338 @ ( esk12_1 @ X338 ) )
        | ( X338 @ ( esk11_2 @ X338 @ X339 ) )
        | ~ ( X338 @ X339 ) )
      & ( ~ ( X338 @ X342 )
        | ( ( esk12_1 @ X338 )
          = X342 )
        | ( X338 @ ( esk11_2 @ X338 @ X339 ) )
        | ~ ( X338 @ X339 ) )
      & ( ( X338 @ ( esk12_1 @ X338 ) )
        | ( X339
         != ( esk11_2 @ X338 @ X339 ) )
        | ~ ( X338 @ X339 ) )
      & ( ~ ( X338 @ X342 )
        | ( ( esk12_1 @ X338 )
          = X342 )
        | ( X339
         != ( esk11_2 @ X338 @ X339 ) )
        | ~ ( X338 @ X339 ) )
      & ( ~ ( in @ X344
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X343 ) )
        | X343 )
      & ( ~ ( in @ X345 @ emptyset )
        | X346 )
      & ( ~ ( in @ X347 @ emptyset )
        | ~ $true )
      & ~ ( in @ X348 @ emptyset )
      & ( ( X349 @ ( esk13_2 @ X349 @ X350 ) )
        | ~ ( X349 @ X350 )
        | ( X349 @ ( esk14_1 @ X349 ) ) )
      & ( ( X350
         != ( esk13_2 @ X349 @ X350 ) )
        | ~ ( X349 @ X350 )
        | ( X349 @ ( esk14_1 @ X349 ) ) )
      & ( ( in @ ( esk16_2 @ X353 @ X354 ) @ X354 )
        | ( X353 = X354 )
        | ( in @ ( esk15_2 @ X353 @ X354 ) @ X353 ) )
      & ( ~ ( in @ ( esk16_2 @ X353 @ X354 ) @ X353 )
        | ( X353 = X354 )
        | ( in @ ( esk15_2 @ X353 @ X354 ) @ X353 ) )
      & ( ( in @ ( esk16_2 @ X353 @ X354 ) @ X354 )
        | ( X353 = X354 )
        | ~ ( in @ ( esk15_2 @ X353 @ X354 ) @ X354 ) )
      & ( ~ ( in @ ( esk16_2 @ X353 @ X354 ) @ X353 )
        | ( X353 = X354 )
        | ~ ( in @ ( esk15_2 @ X353 @ X354 ) @ X354 ) )
      & ( ( in @ ( esk17_1 @ X357 ) @ X357 )
        | ( X357 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X359 ) @ X359 )
        | ( X359 = emptyset ) )
      & ( ~ ( in @ X363 @ ( dsetconstr @ X361 @ X362 ) )
        | ( X362 @ X363 )
        | ~ ( in @ X363 @ X361 ) )
      & ( ~ ( X362 @ X363 )
        | ( in @ X363 @ ( dsetconstr @ X361 @ X362 ) )
        | ~ ( in @ X363 @ X361 ) )
      & ( ( X364 = emptyset )
        | ( in @ ( esk19_1 @ X364 ) @ X364 ) )
      & ( ~ ( in @ X368 @ X366 )
        | ~ ( X367 @ X368 )
        | ( ( dsetconstr @ X366 @ X367 )
         != emptyset ) )
      & ( ~ ( in @ X370 @ X369 )
        | ( X369 != emptyset ) )
      & ( in @ X371 @ ( setadjoin @ X371 @ X372 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X375 @ X374 )
        | ( in @ X375 @ ( setadjoin @ X373 @ X374 ) ) )
      & ( ( in @ X378 @ X377 )
        | X379
        | ( X378 = X376 )
        | ~ ( in @ X378 @ ( setadjoin @ X376 @ X377 ) ) )
      & ( ~ X379
        | X379
        | ( X378 = X376 )
        | ~ ( in @ X378 @ ( setadjoin @ X376 @ X377 ) ) )
      & ( ( in @ X378 @ X377 )
        | X379
        | ~ X379
        | ~ ( in @ X378 @ ( setadjoin @ X376 @ X377 ) ) )
      & ( ~ X379
        | X379
        | ~ X379
        | ~ ( in @ X378 @ ( setadjoin @ X376 @ X377 ) ) )
      & ( ~ ( in @ X382 @ ( setadjoin @ X380 @ X381 ) )
        | ( X382 = X380 )
        | ( in @ X382 @ X381 ) )
      & ( ( dsetconstr @ X383
          @ ^ [Z0: $i] : $true )
        = X383 )
      & ( ( in @ ( esk20_2 @ X384 @ X385 ) @ X385 )
        | ( in @ X385 @ ( powerset @ X384 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X384 @ X385 ) @ X384 )
        | ( in @ X385 @ ( powerset @ X384 ) ) )
      & ( in @ emptyset @ ( powerset @ X387 ) )
      & ( in @ emptyset @ ( powerset @ X388 ) )
      & ( ~ ( in @ X390 @ ( powerset @ X389 ) )
        | ~ ( in @ X391 @ X390 )
        | ( in @ X391 @ X389 ) )
      & ( ~ ( in @ X393 @ X394 )
        | ~ ( in @ X394 @ X392 )
        | ( in @ X393 @ ( setunion @ X392 ) ) )
      & ( ( in @ X396 @ ( esk21_3 @ X395 @ X396 @ X397 ) )
        | X397
        | ~ ( in @ X396 @ ( setunion @ X395 ) ) )
      & ( ( in @ ( esk21_3 @ X395 @ X396 @ X397 ) @ X395 )
        | X397
        | ~ ( in @ X396 @ ( setunion @ X395 ) ) )
      & ( ~ X397
        | X397
        | ~ ( in @ X396 @ ( setunion @ X395 ) ) )
      & ( ~ ( in @ X400 @ X399 )
        | ( in @ X400 @ ( powerset @ ( setunion @ X399 ) ) ) )
      & ( ~ ( X401 @ X405 )
        | ( X405
          = ( esk23_1 @ X401 ) )
        | ( X401 @ ( esk22_2 @ X401 @ X402 ) )
        | ~ ( X401 @ X402 ) )
      & ( ( X406
         != ( esk23_1 @ X401 ) )
        | ( X401 @ X406 )
        | ( X401 @ ( esk22_2 @ X401 @ X402 ) )
        | ~ ( X401 @ X402 ) )
      & ( ~ ( X401 @ X405 )
        | ( X405
          = ( esk23_1 @ X401 ) )
        | ( X402
         != ( esk22_2 @ X401 @ X402 ) )
        | ~ ( X401 @ X402 ) )
      & ( ( X406
         != ( esk23_1 @ X401 ) )
        | ( X401 @ X406 )
        | ( X402
         != ( esk22_2 @ X401 @ X402 ) )
        | ~ ( X401 @ X402 ) )
      & ( ( in @ ( esk24_1 @ X407 ) @ X407 )
        | ( X407 = emptyset ) )
      & ( $true
        | ( X407 = emptyset ) )
      & ( ~ ( in @ X409 @ ( setadjoin @ X410 @ emptyset ) )
        | ( X409 = X410 ) )
      & ( ( X411 = X412 )
        | ~ ( in @ X412 @ ( setadjoin @ X411 @ emptyset ) ) )
      & ( ( X413 != X414 )
        | ( in @ X413 @ ( setadjoin @ X414 @ emptyset ) ) )
      & ( in @ esk25_0 @ ( setadjoin @ esk26_0 @ emptyset ) )
      & ~ ( in @ esk26_0 @ ( setadjoin @ esk25_0 @ emptyset ) ) ),
    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_75])])])])])])]) ).

thf(c_0_77,negated_conjecture,
    ! [X3: $i,X2: $i] :
      ( ( X2 = X3 )
      | ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

thf(c_0_78,negated_conjecture,
    in @ esk25_0 @ ( setadjoin @ esk26_0 @ emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

thf(c_0_79,negated_conjecture,
    ~ ( in @ esk26_0 @ ( setadjoin @ esk25_0 @ emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

thf(c_0_80,negated_conjecture,
    esk26_0 = esk25_0,
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

thf(c_0_81,negated_conjecture,
    ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

thf(c_0_82,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SEU530^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 16:58:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  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
% 0.19/0.50  # Version: 3.1.0-ho
% 0.19/0.50  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50  # Starting sh5l with 300s (1) cores
% 0.19/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.50  # Starting new_bool_2 with 300s (1) cores
% 0.19/0.50  # sh5l with pid 13388 completed with status 0
% 0.19/0.50  # Result found by sh5l
% 0.19/0.50  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50  # Starting sh5l with 300s (1) cores
% 0.19/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.50  # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.19/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting new_ho_10 with 181s (1) cores
% 0.19/0.50  # new_ho_10 with pid 13393 completed with status 0
% 0.19/0.50  # Result found by new_ho_10
% 0.19/0.50  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50  # Starting sh5l with 300s (1) cores
% 0.19/0.50  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.50  # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.19/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting new_ho_10 with 181s (1) cores
% 0.19/0.50  # Preprocessing time       : 0.003 s
% 0.19/0.50  # Presaturation interreduction done
% 0.19/0.50  
% 0.19/0.50  # Proof found!
% 0.19/0.50  # SZS status Theorem
% 0.19/0.50  # SZS output start CNFRefutation
% See solution above
% 0.19/0.50  # Parsed axioms                        : 107
% 0.19/0.50  # Removed by relevancy pruning/SinE    : 57
% 0.19/0.50  # Initial clauses                      : 98
% 0.19/0.50  # Removed in clause preprocessing      : 5
% 0.19/0.50  # Initial clauses in saturation        : 93
% 0.19/0.50  # Processed clauses                    : 118
% 0.19/0.50  # ...of these trivial                  : 1
% 0.19/0.50  # ...subsumed                          : 14
% 0.19/0.50  # ...remaining for further processing  : 103
% 0.19/0.50  # Other redundant clauses eliminated   : 6
% 0.19/0.50  # Clauses deleted for lack of memory   : 0
% 0.19/0.50  # Backward-subsumed                    : 0
% 0.19/0.50  # Backward-rewritten                   : 3
% 0.19/0.50  # Generated clauses                    : 18
% 0.19/0.50  # ...of the previous two non-redundant : 15
% 0.19/0.50  # ...aggressively subsumed             : 0
% 0.19/0.50  # Contextual simplify-reflections      : 0
% 0.19/0.50  # Paramodulations                      : 12
% 0.19/0.50  # Factorizations                       : 0
% 0.19/0.50  # NegExts                              : 0
% 0.19/0.50  # Equation resolutions                 : 6
% 0.19/0.50  # Disequality decompositions           : 0
% 0.19/0.50  # Total rewrite steps                  : 20
% 0.19/0.50  # ...of those cached                   : 12
% 0.19/0.50  # Propositional unsat checks           : 0
% 0.19/0.50  #    Propositional check models        : 0
% 0.19/0.50  #    Propositional check unsatisfiable : 0
% 0.19/0.50  #    Propositional clauses             : 0
% 0.19/0.50  #    Propositional clauses after purity: 0
% 0.19/0.50  #    Propositional unsat core size     : 0
% 0.19/0.50  #    Propositional preprocessing time  : 0.000
% 0.19/0.50  #    Propositional encoding time       : 0.000
% 0.19/0.50  #    Propositional solver time         : 0.000
% 0.19/0.50  #    Success case prop preproc time    : 0.000
% 0.19/0.50  #    Success case prop encoding time   : 0.000
% 0.19/0.50  #    Success case prop solver time     : 0.000
% 0.19/0.50  # Current number of processed clauses  : 18
% 0.19/0.50  #    Positive orientable unit clauses  : 8
% 0.19/0.50  #    Positive unorientable unit clauses: 0
% 0.19/0.50  #    Negative unit clauses             : 1
% 0.19/0.50  #    Non-unit-clauses                  : 9
% 0.19/0.50  # Current number of unprocessed clauses: 67
% 0.19/0.50  # ...number of literals in the above   : 211
% 0.19/0.50  # Current number of archived formulas  : 0
% 0.19/0.50  # Current number of archived clauses   : 80
% 0.19/0.50  # Clause-clause subsumption calls (NU) : 1939
% 0.19/0.50  # Rec. Clause-clause subsumption calls : 789
% 0.19/0.50  # Non-unit clause-clause subsumptions  : 11
% 0.19/0.50  # Unit Clause-clause subsumption calls : 7
% 0.19/0.50  # Rewrite failures with RHS unbound    : 0
% 0.19/0.50  # BW rewrite match attempts            : 9
% 0.19/0.50  # BW rewrite match successes           : 3
% 0.19/0.50  # Condensation attempts                : 118
% 0.19/0.50  # Condensation successes               : 3
% 0.19/0.50  # Termbank termtop insertions          : 14161
% 0.19/0.50  # Search garbage collected termcells   : 4904
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.016 s
% 0.19/0.50  # System time              : 0.006 s
% 0.19/0.50  # Total time               : 0.022 s
% 0.19/0.50  # Maximum resident set size: 3040 pages
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.020 s
% 0.19/0.50  # System time              : 0.007 s
% 0.19/0.50  # Total time               : 0.027 s
% 0.19/0.50  # Maximum resident set size: 1832 pages
% 0.19/0.50  % E---3.1 exiting
% 0.19/0.50  % E exiting
%------------------------------------------------------------------------------