TSTP Solution File: SEU500^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU500^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 03:27:46 EDT 2024

% Result   : Theorem 0.20s 0.54s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   64
% Syntax   : Number of formulae    :   86 (  13 unt;  42 typ;   0 def)
%            Number of atoms       :  308 (  39 equ;   0 cnn)
%            Maximal formula atoms :   87 (   7 avg)
%            Number of connectives : 1134 (  79   ~;  87   |;  87   &; 731   @)
%                                         (  38 <=>; 112  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   86 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  85   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   45 (  42 usr;  23 con; 0-3 aty)
%            Number of variables   :  244 (  22   ^ 184   !;  38   ?; 244   :)

% 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,
    epred1_0: $o ).

thf(decl_49,type,
    esk1_2: $i > $i > $i ).

thf(decl_50,type,
    esk2_2: $i > $i > $i ).

thf(decl_51,type,
    esk3_2: $i > $i > $i ).

thf(decl_52,type,
    esk4_1: $i > $i ).

thf(decl_53,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_54,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_55,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_56,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_57,type,
    esk9_1: $i > $i ).

thf(decl_58,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_59,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_60,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_61,type,
    epred2_0: $o ).

thf(decl_62,type,
    esk13_0: $i ).

thf(decl_68,type,
    epred3_1: $o > $i > $o ).

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(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(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(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(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,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ! [X11: $o,X2: $i] :
                                      ( ( in @ X2 @ ( prop2set @ X11 ) )
                                     => X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).

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

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

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

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

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

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

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

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

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

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

thf(c_0_19,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_20,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_21,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_22,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_23,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X73: $i] :
                  ( ( X6 @ X2 @ X73 )
                  & ! [X74: $i] :
                      ( ( X6 @ X2 @ X74 )
                     => ( X73 = X74 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_24,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X75: $i] :
              ( ( X1 @ X75 )
              & ! [X76: $i] :
                  ( ( X1 @ X76 )
                 => ( X75 = X76 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_21,c_0_20]) ).

thf(c_0_25,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_26,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_27,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_28,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X77: $i] :
              ( ( X1 @ X77 )
              & ! [X78: $i] :
                  ( ( X1 @ X78 )
                 => ( X77 = X78 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_22,c_0_20]) ).

thf(c_0_29,plain,
    ( epred1_0
  <=> ! [X108: $i] :
      ? [X109: $i] :
        ( ! [X110: $i] :
            ( ( in @ X110 @ X109 )
           => ! [X111: $i] :
                ( ( in @ X111 @ X110 )
               => ( in @ X111 @ X108 ) ) )
        & ! [X112: $i,X113: $i] :
            ( ( ( in @ X112 @ X108 )
              & ( in @ X113 @ X108 ) )
           => ( ! [X114: $i] :
                  ( ( in @ X114 @ X109 )
                 => ( ( in @ X112 @ X114 )
                  <=> ( in @ X113 @ X114 ) ) )
             => ( X112 = X113 ) ) )
        & ! [X115: $i,X116: $i] :
            ( ( ( in @ X115 @ X109 )
              & ( in @ X116 @ X109 ) )
           => ( ! [X117: $i] :
                  ( ( in @ X117 @ X115 )
                 => ( in @ X117 @ X116 ) )
              | ! [X118: $i] :
                  ( ( in @ X118 @ X116 )
                 => ( in @ X118 @ X115 ) ) ) )
        & ! [X119: $i] :
            ( ( ! [X120: $i] :
                  ( ( in @ X120 @ X119 )
                 => ( in @ X120 @ X108 ) )
              & ? [X121: $i] : ( in @ X121 @ X119 ) )
           => ? [X122: $i,X123: $i] :
                ( ( in @ X122 @ X109 )
                & ( in @ X123 @ X119 )
                & ~ ? [X124: $i] :
                      ( ( in @ X124 @ X122 )
                      & ( in @ X124 @ X119 ) )
                & ! [X125: $i] :
                    ( ( in @ X125 @ X109 )
                   => ( ! [X126: $i] :
                          ( ( in @ X126 @ X125 )
                         => ( in @ X126 @ X122 ) )
                      | ( in @ X123 @ X125 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_30,negated_conjecture,
    ~ ( ! [X79: $i,X80: $i] :
          ( ! [X81: $i] :
              ( ( in @ X81 @ X79 )
            <=> ( in @ X81 @ X80 ) )
         => ( X79 = X80 ) )
     => ( ! [X82: $i] :
            ~ ( in @ X82 @ emptyset )
       => ( ! [X83: $i,X84: $i,X85: $i] :
              ( ( in @ X85 @ ( setadjoin @ X83 @ X84 ) )
            <=> ( ( X85 = X83 )
                | ( in @ X85 @ X84 ) ) )
         => ( ! [X86: $i,X87: $i] :
                ( ( in @ X87 @ ( powerset @ X86 ) )
              <=> ! [X88: $i] :
                    ( ( in @ X88 @ X87 )
                   => ( in @ X88 @ X86 ) ) )
           => ( ! [X89: $i,X90: $i] :
                  ( ( in @ X90 @ ( setunion @ X89 ) )
                <=> ? [X91: $i] :
                      ( ( in @ X90 @ X91 )
                      & ( in @ X91 @ X89 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X92: $i] :
                      ( ( in @ X92 @ omega )
                     => ( in @ ( setadjoin @ X92 @ X92 ) @ omega ) )
                 => ( ! [X93: $i] :
                        ( ( ( in @ emptyset @ X93 )
                          & ! [X94: $i] :
                              ( ( ( in @ X94 @ omega )
                                & ( in @ X94 @ X93 ) )
                             => ( in @ ( setadjoin @ X94 @ X94 ) @ X93 ) ) )
                       => ! [X95: $i] :
                            ( ( in @ X95 @ omega )
                           => ( in @ X95 @ X93 ) ) )
                   => ( ! [X96: $i > $i > $o,X97: $i] :
                          ( ! [X98: $i] :
                              ( ( in @ X98 @ X97 )
                             => ? [X99: $i] :
                                  ( ( X96 @ X98 @ X99 )
                                  & ! [X100: $i] :
                                      ( ( X96 @ X98 @ X100 )
                                     => ( X99 = X100 ) ) ) )
                         => ? [X101: $i] :
                            ! [X102: $i] :
                              ( ( in @ X102 @ X101 )
                            <=> ? [X103: $i] :
                                  ( ( in @ X103 @ X97 )
                                  & ( X96 @ X103 @ X102 ) ) ) )
                     => ( ! [X104: $i] :
                            ( ? [X105: $i] : ( in @ X105 @ X104 )
                           => ? [X106: $i] :
                                ( ( in @ X106 @ X104 )
                                & ~ ? [X107: $i] :
                                      ( ( in @ X107 @ X106 )
                                      & ( in @ X107 @ X104 ) ) ) )
                       => ( epred1_0
                         => ( ! [X127: $i > $o] :
                                ( ? [X128: $i] :
                                    ( ( X127 @ X128 )
                                    & ! [X129: $i] :
                                        ( ( X127 @ X129 )
                                       => ( X128 = X129 ) ) )
                               => ( X127
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X127 @ Z0 ) ) ) )
                           => ( ! [X130: $i,X131: $i > $o,X132: $i] :
                                  ( ( in @ X132 @ X130 )
                                 => ( ( X131 @ X132 )
                                   => ( in @ X132 @ ( dsetconstr @ X130 @ X131 ) ) ) )
                             => ( ! [X133: $i,X134: $i > $o,X135: $i] :
                                    ( ( in @ X135 @ ( dsetconstr @ X133 @ X134 ) )
                                   => ( in @ X135 @ X133 ) )
                               => ( ! [X136: $i,X137: $i > $o,X138: $i] :
                                      ( ( in @ X138 @ ( dsetconstr @ X136 @ X137 ) )
                                     => ( X137 @ X138 ) )
                                 => ( ! [X139: $i > $o] :
                                        ( ? [X140: $i] :
                                            ( ( X139 @ X140 )
                                            & ! [X141: $i] :
                                                ( ( X139 @ X141 )
                                               => ( X140 = X141 ) ) )
                                       => ? [X142: $i] :
                                            ( ( X139 @ X142 )
                                            & ! [X143: $i] :
                                                ( ( X139 @ X143 )
                                               => ( X142 = X143 ) ) ) )
                                   => ! [X11: $o,X2: $i] :
                                        ( ( in @ X2 @ ( prop2set @ X11 ) )
                                       => X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(assume_negation,[status(cth)],[prop2setE]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_23]),foundationAx]),wellorderingAx]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])])]),c_0_29]) ).

thf(c_0_31,plain,
    ! [X144: $o] :
      ( ( prop2set @ X144 )
      = ( dsetconstr @ ( powerset @ emptyset )
        @ ^ [Z0: $i] : X144 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[prop2set])]) ).

thf(c_0_32,negated_conjecture,
    ! [X146: $i,X147: $i,X149: $i,X150: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X159: $i,X160: $i,X162: $i,X163: $i,X164: $i,X165: $i,X166: $i,X168: $i,X169: $i > $i > $o,X170: $i,X172: $i,X175: $i,X177: $i,X178: $i,X179: $i,X180: $i,X182: $i,X183: $i > $o,X184: $i,X186: $i,X187: $i > $o,X188: $i,X189: $i,X190: $i > $o,X191: $i,X192: $i,X193: $i > $o,X194: $i,X195: $i > $o,X196: $i,X199: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X146 @ X147 ) @ X146 )
        | ~ ( in @ ( esk1_2 @ X146 @ X147 ) @ X147 )
        | ( X146 = X147 ) )
      & ( ( in @ ( esk1_2 @ X146 @ X147 ) @ X146 )
        | ( in @ ( esk1_2 @ X146 @ X147 ) @ X147 )
        | ( X146 = X147 ) )
      & ~ ( in @ X149 @ emptyset )
      & ( ~ ( in @ X152 @ ( setadjoin @ X150 @ X151 ) )
        | ( X152 = X150 )
        | ( in @ X152 @ X151 ) )
      & ( ( X152 != X150 )
        | ( in @ X152 @ ( setadjoin @ X150 @ X151 ) ) )
      & ( ~ ( in @ X152 @ X151 )
        | ( in @ X152 @ ( setadjoin @ X150 @ X151 ) ) )
      & ( ~ ( in @ X154 @ ( powerset @ X153 ) )
        | ~ ( in @ X155 @ X154 )
        | ( in @ X155 @ X153 ) )
      & ( ( in @ ( esk2_2 @ X156 @ X157 ) @ X157 )
        | ( in @ X157 @ ( powerset @ X156 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X156 @ X157 ) @ X156 )
        | ( in @ X157 @ ( powerset @ X156 ) ) )
      & ( ( in @ X160 @ ( esk3_2 @ X159 @ X160 ) )
        | ~ ( in @ X160 @ ( setunion @ X159 ) ) )
      & ( ( in @ ( esk3_2 @ X159 @ X160 ) @ X159 )
        | ~ ( in @ X160 @ ( setunion @ X159 ) ) )
      & ( ~ ( in @ X163 @ X164 )
        | ~ ( in @ X164 @ X162 )
        | ( in @ X163 @ ( setunion @ X162 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X165 @ omega )
        | ( in @ ( setadjoin @ X165 @ X165 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X166 ) @ omega )
        | ~ ( in @ emptyset @ X166 )
        | ~ ( in @ X168 @ omega )
        | ( in @ X168 @ X166 ) )
      & ( ( in @ ( esk4_1 @ X166 ) @ X166 )
        | ~ ( in @ emptyset @ X166 )
        | ~ ( in @ X168 @ omega )
        | ( in @ X168 @ X166 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X166 ) @ ( esk4_1 @ X166 ) ) @ X166 )
        | ~ ( in @ emptyset @ X166 )
        | ~ ( in @ X168 @ omega )
        | ( in @ X168 @ X166 ) )
      & ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
      & ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
      & ( ~ ( in @ X178 @ X170 )
        | ~ ( X169 @ X178 @ X177 )
        | ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
        | ( in @ ( esk5_2 @ X169 @ X170 ) @ X170 ) )
      & ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ~ ( in @ X178 @ X170 )
        | ~ ( X169 @ X178 @ X177 )
        | ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X169 @ ( esk5_2 @ X169 @ X170 ) @ ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ( in @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X170 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X172
         != ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ( X169 @ ( esk8_3 @ X169 @ X170 @ X175 ) @ X175 )
        | ~ ( in @ X175 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X172
         != ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ~ ( in @ X178 @ X170 )
        | ~ ( X169 @ X178 @ X177 )
        | ( in @ X177 @ ( esk7_2 @ X169 @ X170 ) )
        | ( X172
         != ( esk6_3 @ X169 @ X170 @ X172 ) )
        | ~ ( X169 @ ( esk5_2 @ X169 @ X170 ) @ X172 ) )
      & ( ( in @ ( esk9_1 @ X179 ) @ X179 )
        | ~ ( in @ X180 @ X179 ) )
      & ( ~ ( in @ X182 @ ( esk9_1 @ X179 ) )
        | ~ ( in @ X182 @ X179 )
        | ~ ( in @ X180 @ X179 ) )
      & epred1_0
      & ( ( X183 @ ( esk10_2 @ X183 @ X184 ) )
        | ~ ( X183 @ X184 )
        | ( X183 @ ( descr @ X183 ) ) )
      & ( ( X184
         != ( esk10_2 @ X183 @ X184 ) )
        | ~ ( X183 @ X184 )
        | ( X183 @ ( descr @ X183 ) ) )
      & ( ~ ( in @ X188 @ X186 )
        | ~ ( X187 @ X188 )
        | ( in @ X188 @ ( dsetconstr @ X186 @ X187 ) ) )
      & ( ~ ( in @ X191 @ ( dsetconstr @ X189 @ X190 ) )
        | ( in @ X191 @ X189 ) )
      & ( ~ ( in @ X194 @ ( dsetconstr @ X192 @ X193 ) )
        | ( X193 @ X194 ) )
      & ( ( X195 @ ( esk12_1 @ X195 ) )
        | ( X195 @ ( esk11_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ ( X195 @ X199 )
        | ( ( esk12_1 @ X195 )
          = X199 )
        | ( X195 @ ( esk11_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ( X195 @ ( esk12_1 @ X195 ) )
        | ( X196
         != ( esk11_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ ( X195 @ X199 )
        | ( ( esk12_1 @ X195 )
          = X199 )
        | ( X196
         != ( esk11_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ epred2_0
        | ( in @ esk13_0 @ ( prop2set @ $true ) ) )
      & ( epred2_0
        | ( in @ esk13_0 @ ( prop2set @ $false ) ) )
      & ~ epred2_0 ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[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_30])])])])])])])]) ).

thf(c_0_33,plain,
    ! [X145: $o] :
      ( ( prop2set @ X145 )
      = ( dsetconstr @ ( powerset @ emptyset )
        @ ^ [Z0: $i] : X145 ) ),
    inference(variable_rename,[status(thm)],[c_0_31]) ).

thf(c_0_34,plain,
    ! [X221: $i,X10: $o] :
      ( ( epred3_1 @ X10 @ X221 )
    <=> X10 ),
    introduced(definition) ).

thf(c_0_35,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i > $o] :
      ( ( X1 @ X2 )
      | ~ ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_36,plain,
    ! [X10: $o] :
      ( ( prop2set @ X10 )
      = ( dsetconstr @ ( powerset @ emptyset ) @ ( epred3_1 @ X10 ) ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_33]),c_0_34]) ).

thf(c_0_37,negated_conjecture,
    ( epred2_0
    | ( in @ esk13_0 @ ( prop2set @ ~ $true ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_38,negated_conjecture,
    ~ epred2_0,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_39,plain,
    ! [X222: $i,X223: $o] :
      ( ( ~ ( epred3_1 @ X223 @ X222 )
        | X223 )
      & ( ~ X223
        | ( epred3_1 @ X223 @ X222 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_40,negated_conjecture,
    ! [X2: $i,X10: $o] :
      ( ( epred3_1 @ X10 @ X2 )
      | ~ ( in @ X2 @ ( prop2set @ X10 ) ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

thf(c_0_41,negated_conjecture,
    in @ esk13_0 @ ( prop2set @ ~ $true ),
    inference(sr,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_42,plain,
    ! [X2: $i] :
      ~ ( epred3_1 @ ~ $true @ X2 ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_39])])]) ).

thf(c_0_43,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SEU500^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15  % Command    : run_E %s %d THM
% 0.13/0.36  % Computer : n004.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Sun May 19 15:20:23 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.20/0.51  Running higher-order theorem proving
% 0.20/0.51  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.54  # Version: 3.1.0-ho
% 0.20/0.54  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54  # Starting sh5l with 300s (1) cores
% 0.20/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54  # Starting new_bool_2 with 300s (1) cores
% 0.20/0.54  # new_ho_10 with pid 19488 completed with status 0
% 0.20/0.54  # Result found by new_ho_10
% 0.20/0.54  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54  # No SInE strategy applied
% 0.20/0.54  # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.20/0.54  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54  # Starting new_ho_10 with 901s (1) cores
% 0.20/0.54  # Starting sh5l with 151s (1) cores
% 0.20/0.54  # Starting new_bool_1 with 151s (1) cores
% 0.20/0.54  # Starting new_bool_2 with 151s (1) cores
% 0.20/0.54  # Starting new_bool_9 with 146s (1) cores
% 0.20/0.54  # new_ho_10 with pid 19492 completed with status 0
% 0.20/0.54  # Result found by new_ho_10
% 0.20/0.54  # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.54  # No SInE strategy applied
% 0.20/0.54  # Search class: HGHSS-FFMS31-SHFSMSBN
% 0.20/0.54  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54  # Starting new_ho_10 with 901s (1) cores
% 0.20/0.54  # Preprocessing time       : 0.005 s
% 0.20/0.54  # Presaturation interreduction done
% 0.20/0.54  
% 0.20/0.54  # Proof found!
% 0.20/0.54  # SZS status Theorem
% 0.20/0.54  # SZS output start CNFRefutation
% See solution above
% 0.20/0.54  # Parsed axioms                        : 45
% 0.20/0.54  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.54  # Initial clauses                      : 83
% 0.20/0.54  # Removed in clause preprocessing      : 26
% 0.20/0.54  # Initial clauses in saturation        : 57
% 0.20/0.54  # Processed clauses                    : 72
% 0.20/0.54  # ...of these trivial                  : 0
% 0.20/0.54  # ...subsumed                          : 1
% 0.20/0.54  # ...remaining for further processing  : 71
% 0.20/0.54  # Other redundant clauses eliminated   : 1
% 0.20/0.54  # Clauses deleted for lack of memory   : 0
% 0.20/0.54  # Backward-subsumed                    : 0
% 0.20/0.54  # Backward-rewritten                   : 0
% 0.20/0.54  # Generated clauses                    : 3
% 0.20/0.54  # ...of the previous two non-redundant : 2
% 0.20/0.54  # ...aggressively subsumed             : 0
% 0.20/0.54  # Contextual simplify-reflections      : 0
% 0.20/0.54  # Paramodulations                      : 2
% 0.20/0.54  # Factorizations                       : 0
% 0.20/0.54  # NegExts                              : 0
% 0.20/0.54  # Equation resolutions                 : 1
% 0.20/0.54  # Disequality decompositions           : 0
% 0.20/0.54  # Total rewrite steps                  : 13
% 0.20/0.54  # ...of those cached                   : 12
% 0.20/0.54  # Propositional unsat checks           : 0
% 0.20/0.54  #    Propositional check models        : 0
% 0.20/0.54  #    Propositional check unsatisfiable : 0
% 0.20/0.54  #    Propositional clauses             : 0
% 0.20/0.54  #    Propositional clauses after purity: 0
% 0.20/0.54  #    Propositional unsat core size     : 0
% 0.20/0.54  #    Propositional preprocessing time  : 0.000
% 0.20/0.54  #    Propositional encoding time       : 0.000
% 0.20/0.54  #    Propositional solver time         : 0.000
% 0.20/0.54  #    Success case prop preproc time    : 0.000
% 0.20/0.54  #    Success case prop encoding time   : 0.000
% 0.20/0.54  #    Success case prop solver time     : 0.000
% 0.20/0.54  # Current number of processed clauses  : 14
% 0.20/0.54  #    Positive orientable unit clauses  : 6
% 0.20/0.54  #    Positive unorientable unit clauses: 0
% 0.20/0.54  #    Negative unit clauses             : 3
% 0.20/0.54  #    Non-unit-clauses                  : 5
% 0.20/0.54  # Current number of unprocessed clauses: 43
% 0.20/0.54  # ...number of literals in the above   : 150
% 0.20/0.54  # Current number of archived formulas  : 0
% 0.20/0.54  # Current number of archived clauses   : 56
% 0.20/0.54  # Clause-clause subsumption calls (NU) : 1033
% 0.20/0.54  # Rec. Clause-clause subsumption calls : 435
% 0.20/0.54  # Non-unit clause-clause subsumptions  : 3
% 0.20/0.54  # Unit Clause-clause subsumption calls : 2
% 0.20/0.54  # Rewrite failures with RHS unbound    : 0
% 0.20/0.54  # BW rewrite match attempts            : 0
% 0.20/0.54  # BW rewrite match successes           : 0
% 0.20/0.54  # Condensation attempts                : 72
% 0.20/0.54  # Condensation successes               : 3
% 0.20/0.54  # Termbank termtop insertions          : 8351
% 0.20/0.54  # Search garbage collected termcells   : 2581
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.010 s
% 0.20/0.54  # System time              : 0.008 s
% 0.20/0.54  # Total time               : 0.019 s
% 0.20/0.54  # Maximum resident set size: 2356 pages
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.031 s
% 0.20/0.54  # System time              : 0.046 s
% 0.20/0.54  # Total time               : 0.076 s
% 0.20/0.54  # Maximum resident set size: 1776 pages
% 0.20/0.54  % E---3.1 exiting
% 0.20/0.54  % E exiting
%------------------------------------------------------------------------------