TSTP Solution File: SEU504^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU504^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 03:27:48 EDT 2024

% Result   : Theorem 0.17s 0.46s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   78 (  10 unt;  41 typ;   0 def)
%            Number of atoms       :  295 (  36 equ;   0 cnn)
%            Maximal formula atoms :   82 (   7 avg)
%            Number of connectives : 1060 (  72   ~;  75   |;  84   &; 672   @)
%                                         (  36 <=>; 121  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   88 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  72   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  41 usr;  26 con; 0-3 aty)
%            Number of variables   :  239 (  26   ^ 176   !;  37   ?; 239   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_52,type,
    epred1_0: $o ).

thf(decl_53,type,
    esk1_2: $i > $i > $i ).

thf(decl_54,type,
    esk2_2: $i > $i > $i ).

thf(decl_55,type,
    esk3_1: $i > $i ).

thf(decl_56,type,
    esk4_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_57,type,
    esk5_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_58,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_59,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_60,type,
    esk8_1: $i > $i ).

thf(decl_61,type,
    esk9_2: ( $i > $o ) > $i > $i ).

thf(decl_62,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_63,type,
    epred2_0: $i > $o ).

thf(decl_64,type,
    esk11_0: $i ).

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

thf(exuE3e,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ! [X1: $i > $o] :
                                              ( ( exu
                                                @ ^ [X2: $i] : ( X1 @ X2 ) )
                                             => ? [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).

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

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(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(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(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(c_0_21,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_22,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_23,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_24,plain,
    ( prop2set
    = ( ^ [Z0: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Z1: $i] : Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[prop2set]) ).

thf(c_0_25,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X76: $i] :
                  ( ( X6 @ X2 @ X76 )
                  & ! [X77: $i] :
                      ( ( X6 @ X2 @ X77 )
                     => ( X76 = X77 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_26,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_27,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_28,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_29,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X78: $i] :
              ( ( X1 @ X78 )
              & ! [X79: $i] :
                  ( ( X1 @ X79 )
                 => ( X78 = X79 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_23,c_0_22]) ).

thf(c_0_30,axiom,
    ( prop2setE
    = ( ! [X11: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X11 ) )
         => X11 ) ) ),
    inference(apply_def,[status(thm)],[prop2setE,c_0_24]) ).

thf(c_0_31,plain,
    ( epred1_0
  <=> ! [X106: $i] :
      ? [X107: $i] :
        ( ! [X108: $i] :
            ( ( in @ X108 @ X107 )
           => ! [X109: $i] :
                ( ( in @ X109 @ X108 )
               => ( in @ X109 @ X106 ) ) )
        & ! [X110: $i,X111: $i] :
            ( ( ( in @ X110 @ X106 )
              & ( in @ X111 @ X106 ) )
           => ( ! [X112: $i] :
                  ( ( in @ X112 @ X107 )
                 => ( ( in @ X110 @ X112 )
                  <=> ( in @ X111 @ X112 ) ) )
             => ( X110 = X111 ) ) )
        & ! [X113: $i,X114: $i] :
            ( ( ( in @ X113 @ X107 )
              & ( in @ X114 @ X107 ) )
           => ( ! [X115: $i] :
                  ( ( in @ X115 @ X113 )
                 => ( in @ X115 @ X114 ) )
              | ! [X116: $i] :
                  ( ( in @ X116 @ X114 )
                 => ( in @ X116 @ X113 ) ) ) )
        & ! [X117: $i] :
            ( ( ! [X118: $i] :
                  ( ( in @ X118 @ X117 )
                 => ( in @ X118 @ X106 ) )
              & ? [X119: $i] : ( in @ X119 @ X117 ) )
           => ? [X120: $i,X121: $i] :
                ( ( in @ X120 @ X107 )
                & ( in @ X121 @ X117 )
                & ~ ? [X122: $i] :
                      ( ( in @ X122 @ X120 )
                      & ( in @ X122 @ X117 ) )
                & ! [X123: $i] :
                    ( ( in @ X123 @ X107 )
                   => ( ! [X124: $i] :
                          ( ( in @ X124 @ X123 )
                         => ( in @ X124 @ X120 ) )
                      | ( in @ X121 @ X123 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_32,negated_conjecture,
    ~ ( ! [X80: $i,X81: $i] :
          ( ! [X82: $i] :
              ( ( in @ X82 @ X80 )
            <=> ( in @ X82 @ X81 ) )
         => ( X80 = X81 ) )
     => ( ! [X83: $i] :
            ~ ( in @ X83 @ emptyset )
       => ( ! [X84: $i,X85: $i,X86: $i] :
              ( ( in @ X86 @ ( setadjoin @ X84 @ X85 ) )
            <=> ( ( X86 = X84 )
                | ( in @ X86 @ X85 ) ) )
         => ( ! [X87: $i,X88: $i] :
                ( ( in @ X88 @ ( powerset @ X87 ) )
              <=> ! [X89: $i] :
                    ( ( in @ X89 @ X88 )
                   => ( in @ X89 @ X87 ) ) )
           => ( setunionAx
             => ( ( in @ emptyset @ omega )
               => ( ! [X90: $i] :
                      ( ( in @ X90 @ omega )
                     => ( in @ ( setadjoin @ X90 @ X90 ) @ omega ) )
                 => ( ! [X91: $i] :
                        ( ( ( in @ emptyset @ X91 )
                          & ! [X92: $i] :
                              ( ( ( in @ X92 @ omega )
                                & ( in @ X92 @ X91 ) )
                             => ( in @ ( setadjoin @ X92 @ X92 ) @ X91 ) ) )
                       => ! [X93: $i] :
                            ( ( in @ X93 @ omega )
                           => ( in @ X93 @ X91 ) ) )
                   => ( ! [X94: $i > $i > $o,X95: $i] :
                          ( ! [X96: $i] :
                              ( ( in @ X96 @ X95 )
                             => ? [X97: $i] :
                                  ( ( X94 @ X96 @ X97 )
                                  & ! [X98: $i] :
                                      ( ( X94 @ X96 @ X98 )
                                     => ( X97 = X98 ) ) ) )
                         => ? [X99: $i] :
                            ! [X100: $i] :
                              ( ( in @ X100 @ X99 )
                            <=> ? [X101: $i] :
                                  ( ( in @ X101 @ X95 )
                                  & ( X94 @ X101 @ X100 ) ) ) )
                     => ( ! [X102: $i] :
                            ( ? [X103: $i] : ( in @ X103 @ X102 )
                           => ? [X104: $i] :
                                ( ( in @ X104 @ X102 )
                                & ~ ? [X105: $i] :
                                      ( ( in @ X105 @ X104 )
                                      & ( in @ X105 @ X102 ) ) ) )
                       => ( epred1_0
                         => ( descrp
                           => ( ! [X125: $i,X126: $i > $o,X127: $i] :
                                  ( ( in @ X127 @ X125 )
                                 => ( ( X126 @ X127 )
                                   => ( in @ X127
                                      @ ( dsetconstr @ X125
                                        @ ^ [Z0: $i] : ( X126 @ Z0 ) ) ) ) )
                             => ( ! [X128: $i,X129: $i > $o,X130: $i] :
                                    ( ( in @ X130
                                      @ ( dsetconstr @ X128
                                        @ ^ [Z0: $i] : ( X129 @ Z0 ) ) )
                                   => ( in @ X130 @ X128 ) )
                               => ( ! [X131: $i,X132: $i > $o,X133: $i] :
                                      ( ( in @ X133
                                        @ ( dsetconstr @ X131
                                          @ ^ [Z0: $i] : ( X132 @ Z0 ) ) )
                                     => ( X132 @ X133 ) )
                                 => ( ! [X134: $i > $o] :
                                        ( ? [X135: $i] :
                                            ( ( X134 @ X135 )
                                            & ! [X136: $i] :
                                                ( ( X134 @ X136 )
                                               => ( X135 = X136 ) ) )
                                       => ? [X137: $i] :
                                            ( ( X134 @ X137 )
                                            & ! [X138: $i] :
                                                ( ( X134 @ X138 )
                                               => ( X137 = X138 ) ) ) )
                                   => ( ! [X139: $o,X140: $i] :
                                          ( ( in @ X140
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [Z0: $i] : X139 ) )
                                         => X139 )
                                     => ( ! [X141: $i] :
                                            ( ( in @ X141 @ emptyset )
                                           => ! [X142: $o] : X142 )
                                       => ( ! [X143: $i] :
                                              ~ ( in @ X143 @ emptyset )
                                         => ( ! [X144: $i] :
                                                ~ ( in @ X144 @ emptyset )
                                           => ! [X1: $i > $o] :
                                                ( ? [X145: $i] :
                                                    ( ( X1 @ X145 )
                                                    & ! [X146: $i] :
                                                        ( ( X1 @ X146 )
                                                       => ( X145 = X146 ) ) )
                                               => ? [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[exuE3e])]),c_0_22]),omegaIndAx]),c_0_25]),foundationAx]),wellorderingAx]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),emptysetE]),setextAx]),emptysetimpfalse]),notinemptyset]),emptysetAx]),setadjoinAx]),powersetAx]),omega0Ax]),omegaSAx])]),c_0_31]) ).

thf(c_0_33,negated_conjecture,
    ! [X147: $i,X148: $i,X150: $i,X151: $i,X152: $i,X153: $i,X154: $i,X155: $i,X156: $i,X157: $i,X158: $i,X160: $i,X161: $i,X163: $i,X164: $i > $i > $o,X165: $i,X167: $i,X170: $i,X172: $i,X173: $i,X174: $i,X175: $i,X177: $i,X178: $i,X179: $i > $o,X180: $i,X181: $i,X182: $i > $o,X183: $i,X184: $i,X185: $i > $o,X186: $i,X187: $i > $o,X188: $i,X191: $i,X192: $o,X193: $i,X194: $i,X195: $o,X196: $i,X197: $i,X200: $i,X201: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X147 @ X148 ) @ X147 )
        | ~ ( in @ ( esk1_2 @ X147 @ X148 ) @ X148 )
        | ( X147 = X148 ) )
      & ( ( in @ ( esk1_2 @ X147 @ X148 ) @ X147 )
        | ( in @ ( esk1_2 @ X147 @ X148 ) @ X148 )
        | ( X147 = X148 ) )
      & ~ ( in @ X150 @ emptyset )
      & ( ~ ( in @ X153 @ ( setadjoin @ X151 @ X152 ) )
        | ( X153 = X151 )
        | ( in @ X153 @ X152 ) )
      & ( ( X153 != X151 )
        | ( in @ X153 @ ( setadjoin @ X151 @ X152 ) ) )
      & ( ~ ( in @ X153 @ X152 )
        | ( in @ X153 @ ( setadjoin @ X151 @ X152 ) ) )
      & ( ~ ( in @ X155 @ ( powerset @ X154 ) )
        | ~ ( in @ X156 @ X155 )
        | ( in @ X156 @ X154 ) )
      & ( ( in @ ( esk2_2 @ X157 @ X158 ) @ X158 )
        | ( in @ X158 @ ( powerset @ X157 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X157 @ X158 ) @ X157 )
        | ( in @ X158 @ ( powerset @ X157 ) ) )
      & setunionAx
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X160 @ omega )
        | ( in @ ( setadjoin @ X160 @ X160 ) @ omega ) )
      & ( ( in @ ( esk3_1 @ X161 ) @ omega )
        | ~ ( in @ emptyset @ X161 )
        | ~ ( in @ X163 @ omega )
        | ( in @ X163 @ X161 ) )
      & ( ( in @ ( esk3_1 @ X161 ) @ X161 )
        | ~ ( in @ emptyset @ X161 )
        | ~ ( in @ X163 @ omega )
        | ( in @ X163 @ X161 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X161 ) @ ( esk3_1 @ X161 ) ) @ X161 )
        | ~ ( in @ emptyset @ X161 )
        | ~ ( in @ X163 @ omega )
        | ( in @ X163 @ X161 ) )
      & ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
      & ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
      & ( ~ ( in @ X173 @ X165 )
        | ~ ( X164 @ X173 @ X172 )
        | ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
        | ( in @ ( esk4_2 @ X164 @ X165 ) @ X165 ) )
      & ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ~ ( in @ X173 @ X165 )
        | ~ ( X164 @ X173 @ X172 )
        | ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X164 @ ( esk4_2 @ X164 @ X165 ) @ ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ( in @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X165 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X167
         != ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ( X164 @ ( esk7_3 @ X164 @ X165 @ X170 ) @ X170 )
        | ~ ( in @ X170 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X167
         != ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ~ ( in @ X173 @ X165 )
        | ~ ( X164 @ X173 @ X172 )
        | ( in @ X172 @ ( esk6_2 @ X164 @ X165 ) )
        | ( X167
         != ( esk5_3 @ X164 @ X165 @ X167 ) )
        | ~ ( X164 @ ( esk4_2 @ X164 @ X165 ) @ X167 ) )
      & ( ( in @ ( esk8_1 @ X174 ) @ X174 )
        | ~ ( in @ X175 @ X174 ) )
      & ( ~ ( in @ X177 @ ( esk8_1 @ X174 ) )
        | ~ ( in @ X177 @ X174 )
        | ~ ( in @ X175 @ X174 ) )
      & epred1_0
      & descrp
      & ( ~ ( in @ X180 @ X178 )
        | ~ ( X179 @ X180 )
        | ( in @ X180
          @ ( dsetconstr @ X178
            @ ^ [Z0: $i] : ( X179 @ Z0 ) ) ) )
      & ( ~ ( in @ X183
            @ ( dsetconstr @ X181
              @ ^ [Z0: $i] : ( X182 @ Z0 ) ) )
        | ( in @ X183 @ X181 ) )
      & ( ~ ( in @ X186
            @ ( dsetconstr @ X184
              @ ^ [Z0: $i] : ( X185 @ Z0 ) ) )
        | ( X185 @ X186 ) )
      & ( ( X187 @ ( esk10_1 @ X187 ) )
        | ( X187 @ ( esk9_2 @ X187 @ X188 ) )
        | ~ ( X187 @ X188 ) )
      & ( ~ ( X187 @ X191 )
        | ( ( esk10_1 @ X187 )
          = X191 )
        | ( X187 @ ( esk9_2 @ X187 @ X188 ) )
        | ~ ( X187 @ X188 ) )
      & ( ( X187 @ ( esk10_1 @ X187 ) )
        | ( X188
         != ( esk9_2 @ X187 @ X188 ) )
        | ~ ( X187 @ X188 ) )
      & ( ~ ( X187 @ X191 )
        | ( ( esk10_1 @ X187 )
          = X191 )
        | ( X188
         != ( esk9_2 @ X187 @ X188 ) )
        | ~ ( X187 @ X188 ) )
      & ( ~ ( in @ X193
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X192 ) )
        | X192 )
      & ( ~ ( in @ X194 @ emptyset )
        | X195 )
      & ~ ( in @ X196 @ emptyset )
      & ~ ( in @ X197 @ emptyset )
      & ( epred2_0 @ esk11_0 )
      & ( ~ ( epred2_0 @ X200 )
        | ( esk11_0 = X200 ) )
      & ~ ( epred2_0 @ X201 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])]) ).

thf(c_0_34,negated_conjecture,
    epred2_0 @ esk11_0,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_35,negated_conjecture,
    ! [X2: $i] :
      ~ ( epred2_0 @ X2 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_34,c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU504^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.11  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sun May 19 16:19:23 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.44  Running higher-order theorem proving
% 0.17/0.44  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
% 0.17/0.46  # Version: 3.1.0-ho
% 0.17/0.46  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46  # Starting sh5l with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46  # new_bool_2 with pid 20438 completed with status 0
% 0.17/0.46  # Result found by new_bool_2
% 0.17/0.46  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46  # Starting sh5l with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46  # Search class: HGHSF-FFMS31-SHSSMSBN
% 0.17/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46  # Starting sh2 with 163s (1) cores
% 0.17/0.46  # sh2 with pid 20439 completed with status 0
% 0.17/0.46  # Result found by sh2
% 0.17/0.46  # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.17/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.46  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.46  # Starting sh5l with 300s (1) cores
% 0.17/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.46  # Starting new_bool_2 with 300s (1) cores
% 0.17/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.46  # Search class: HGHSF-FFMS31-SHSSMSBN
% 0.17/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.46  # Starting sh2 with 163s (1) cores
% 0.17/0.46  # Preprocessing time       : 0.002 s
% 0.17/0.46  # Presaturation interreduction done
% 0.17/0.46  
% 0.17/0.46  # Proof found!
% 0.17/0.46  # SZS status Theorem
% 0.17/0.46  # SZS output start CNFRefutation
% See solution above
% 0.17/0.46  # Parsed axioms                        : 53
% 0.17/0.46  # Removed by relevancy pruning/SinE    : 32
% 0.17/0.46  # Initial clauses                      : 55
% 0.17/0.46  # Removed in clause preprocessing      : 0
% 0.17/0.46  # Initial clauses in saturation        : 55
% 0.17/0.46  # Processed clauses                    : 6
% 0.17/0.46  # ...of these trivial                  : 0
% 0.17/0.46  # ...subsumed                          : 0
% 0.17/0.46  # ...remaining for further processing  : 6
% 0.17/0.46  # Other redundant clauses eliminated   : 0
% 0.17/0.46  # Clauses deleted for lack of memory   : 0
% 0.17/0.46  # Backward-subsumed                    : 0
% 0.17/0.46  # Backward-rewritten                   : 0
% 0.17/0.46  # Generated clauses                    : 1
% 0.17/0.46  # ...of the previous two non-redundant : 0
% 0.17/0.46  # ...aggressively subsumed             : 0
% 0.17/0.46  # Contextual simplify-reflections      : 0
% 0.17/0.46  # Paramodulations                      : 0
% 0.17/0.46  # Factorizations                       : 0
% 0.17/0.46  # NegExts                              : 0
% 0.17/0.46  # Equation resolutions                 : 0
% 0.17/0.46  # Disequality decompositions           : 0
% 0.17/0.46  # Total rewrite steps                  : 0
% 0.17/0.46  # ...of those cached                   : 0
% 0.17/0.46  # Propositional unsat checks           : 0
% 0.17/0.46  #    Propositional check models        : 0
% 0.17/0.46  #    Propositional check unsatisfiable : 0
% 0.17/0.46  #    Propositional clauses             : 0
% 0.17/0.46  #    Propositional clauses after purity: 0
% 0.17/0.46  #    Propositional unsat core size     : 0
% 0.17/0.46  #    Propositional preprocessing time  : 0.000
% 0.17/0.46  #    Propositional encoding time       : 0.000
% 0.17/0.46  #    Propositional solver time         : 0.000
% 0.17/0.46  #    Success case prop preproc time    : 0.000
% 0.17/0.46  #    Success case prop encoding time   : 0.000
% 0.17/0.46  #    Success case prop solver time     : 0.000
% 0.17/0.46  # Current number of processed clauses  : 5
% 0.17/0.46  #    Positive orientable unit clauses  : 4
% 0.17/0.46  #    Positive unorientable unit clauses: 0
% 0.17/0.46  #    Negative unit clauses             : 1
% 0.17/0.46  #    Non-unit-clauses                  : 0
% 0.17/0.46  # Current number of unprocessed clauses: 49
% 0.17/0.46  # ...number of literals in the above   : 171
% 0.17/0.46  # Current number of archived formulas  : 0
% 0.17/0.46  # Current number of archived clauses   : 1
% 0.17/0.46  # Clause-clause subsumption calls (NU) : 0
% 0.17/0.46  # Rec. Clause-clause subsumption calls : 0
% 0.17/0.46  # Non-unit clause-clause subsumptions  : 0
% 0.17/0.46  # Unit Clause-clause subsumption calls : 0
% 0.17/0.46  # Rewrite failures with RHS unbound    : 0
% 0.17/0.46  # BW rewrite match attempts            : 0
% 0.17/0.46  # BW rewrite match successes           : 0
% 0.17/0.46  # Condensation attempts                : 0
% 0.17/0.46  # Condensation successes               : 0
% 0.17/0.46  # Termbank termtop insertions          : 5611
% 0.17/0.46  # Search garbage collected termcells   : 2091
% 0.17/0.46  
% 0.17/0.46  # -------------------------------------------------
% 0.17/0.46  # User time                : 0.007 s
% 0.17/0.46  # System time              : 0.003 s
% 0.17/0.46  # Total time               : 0.010 s
% 0.17/0.46  # Maximum resident set size: 2392 pages
% 0.17/0.46  
% 0.17/0.46  # -------------------------------------------------
% 0.17/0.46  # User time                : 0.008 s
% 0.17/0.46  # System time              : 0.006 s
% 0.17/0.46  # Total time               : 0.014 s
% 0.17/0.46  # Maximum resident set size: 1788 pages
% 0.17/0.46  % E---3.1 exiting
% 0.17/0.46  % E exiting
%------------------------------------------------------------------------------