TSTP Solution File: SEU505^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU505^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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 0.20s 0.54s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   67
% Syntax   : Number of formulae    :   90 (  12 unt;  44 typ;   0 def)
%            Number of atoms       :  330 (  45 equ;   0 cnn)
%            Maximal formula atoms :   85 (   7 avg)
%            Number of connectives : 1173 (  82   ~;  89   |;  87   &; 742   @)
%                                         (  38 <=>; 135  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   93 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   79 (  79   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   47 (  44 usr;  28 con; 0-3 aty)
%            Number of variables   :  256 (  21   ^ 195   !;  40   ?; 256   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(decl_53,type,
    epred1_0: $o ).

thf(decl_54,type,
    esk1_2: $i > $i > $i ).

thf(decl_55,type,
    esk2_2: $i > $i > $i ).

thf(decl_56,type,
    esk3_1: $i > $i ).

thf(decl_57,type,
    esk4_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_58,type,
    esk5_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_59,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_60,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_61,type,
    esk8_1: $i > $i ).

thf(decl_62,type,
    esk9_2: ( $i > $o ) > $i > $i ).

thf(decl_63,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_64,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_65,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_66,type,
    esk13_0: $i ).

thf(decl_67,type,
    esk14_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(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(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(setext,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ! [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(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(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(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(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(c_0_22,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_23,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_24,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_25,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_26,plain,
    ( prop2set
    = ( ^ [Z0: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [Z1: $i] : Z0 ) ) ),
    inference(fof_simplification,[status(thm)],[prop2set]) ).

thf(c_0_27,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X84: $i] :
              ( ( X1 @ X84 )
              & ! [X85: $i] :
                  ( ( X1 @ X85 )
                 => ( X84 = X85 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_28,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X80: $i] :
                  ( ( X6 @ X2 @ X80 )
                  & ! [X81: $i] :
                      ( ( X6 @ X2 @ X81 )
                     => ( X80 = X81 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_24,c_0_23]) ).

thf(c_0_29,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_30,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_31,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_32,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X82: $i] :
              ( ( X1 @ X82 )
              & ! [X83: $i] :
                  ( ( X1 @ X83 )
                 => ( X82 = X83 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_25,c_0_23]) ).

thf(c_0_33,axiom,
    ( prop2setE
    = ( ! [X11: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X11 ) )
         => X11 ) ) ),
    inference(apply_def,[status(thm)],[prop2setE,c_0_26]) ).

thf(c_0_34,plain,
    ( epred1_0
  <=> ! [X112: $i] :
      ? [X113: $i] :
        ( ! [X114: $i] :
            ( ( in @ X114 @ X113 )
           => ! [X115: $i] :
                ( ( in @ X115 @ X114 )
               => ( in @ X115 @ X112 ) ) )
        & ! [X116: $i,X117: $i] :
            ( ( ( in @ X116 @ X112 )
              & ( in @ X117 @ X112 ) )
           => ( ! [X118: $i] :
                  ( ( in @ X118 @ X113 )
                 => ( ( in @ X116 @ X118 )
                  <=> ( in @ X117 @ X118 ) ) )
             => ( X116 = X117 ) ) )
        & ! [X119: $i,X120: $i] :
            ( ( ( in @ X119 @ X113 )
              & ( in @ X120 @ X113 ) )
           => ( ! [X121: $i] :
                  ( ( in @ X121 @ X119 )
                 => ( in @ X121 @ X120 ) )
              | ! [X122: $i] :
                  ( ( in @ X122 @ X120 )
                 => ( in @ X122 @ X119 ) ) ) )
        & ! [X123: $i] :
            ( ( ! [X124: $i] :
                  ( ( in @ X124 @ X123 )
                 => ( in @ X124 @ X112 ) )
              & ? [X125: $i] : ( in @ X125 @ X123 ) )
           => ? [X126: $i,X127: $i] :
                ( ( in @ X126 @ X113 )
                & ( in @ X127 @ X123 )
                & ~ ? [X128: $i] :
                      ( ( in @ X128 @ X126 )
                      & ( in @ X128 @ X123 ) )
                & ! [X129: $i] :
                    ( ( in @ X129 @ X113 )
                   => ( ! [X130: $i] :
                          ( ( in @ X130 @ X129 )
                         => ( in @ X130 @ X126 ) )
                      | ( in @ X127 @ X129 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_35,negated_conjecture,
    ~ ( ! [X86: $i,X87: $i] :
          ( ! [X88: $i] :
              ( ( in @ X88 @ X86 )
            <=> ( in @ X88 @ X87 ) )
         => ( X86 = X87 ) )
     => ( ! [X89: $i] :
            ~ ( in @ X89 @ emptyset )
       => ( ! [X90: $i,X91: $i,X92: $i] :
              ( ( in @ X92 @ ( setadjoin @ X90 @ X91 ) )
            <=> ( ( X92 = X90 )
                | ( in @ X92 @ X91 ) ) )
         => ( ! [X93: $i,X94: $i] :
                ( ( in @ X94 @ ( powerset @ X93 ) )
              <=> ! [X95: $i] :
                    ( ( in @ X95 @ X94 )
                   => ( in @ X95 @ X93 ) ) )
           => ( setunionAx
             => ( ( in @ emptyset @ omega )
               => ( ! [X96: $i] :
                      ( ( in @ X96 @ omega )
                     => ( in @ ( setadjoin @ X96 @ X96 ) @ omega ) )
                 => ( ! [X97: $i] :
                        ( ( ( in @ emptyset @ X97 )
                          & ! [X98: $i] :
                              ( ( ( in @ X98 @ omega )
                                & ( in @ X98 @ X97 ) )
                             => ( in @ ( setadjoin @ X98 @ X98 ) @ X97 ) ) )
                       => ! [X99: $i] :
                            ( ( in @ X99 @ omega )
                           => ( in @ X99 @ X97 ) ) )
                   => ( ! [X100: $i > $i > $o,X101: $i] :
                          ( ! [X102: $i] :
                              ( ( in @ X102 @ X101 )
                             => ? [X103: $i] :
                                  ( ( X100 @ X102 @ X103 )
                                  & ! [X104: $i] :
                                      ( ( X100 @ X102 @ X104 )
                                     => ( X103 = X104 ) ) ) )
                         => ? [X105: $i] :
                            ! [X106: $i] :
                              ( ( in @ X106 @ X105 )
                            <=> ? [X107: $i] :
                                  ( ( in @ X107 @ X101 )
                                  & ( X100 @ X107 @ X106 ) ) ) )
                     => ( ! [X108: $i] :
                            ( ? [X109: $i] : ( in @ X109 @ X108 )
                           => ? [X110: $i] :
                                ( ( in @ X110 @ X108 )
                                & ~ ? [X111: $i] :
                                      ( ( in @ X111 @ X110 )
                                      & ( in @ X111 @ X108 ) ) ) )
                       => ( epred1_0
                         => ( descrp
                           => ( ! [X131: $i,X132: $i > $o,X133: $i] :
                                  ( ( in @ X133 @ X131 )
                                 => ( ( X132 @ X133 )
                                   => ( in @ X133 @ ( dsetconstr @ X131 @ X132 ) ) ) )
                             => ( ! [X134: $i,X135: $i > $o,X136: $i] :
                                    ( ( in @ X136 @ ( dsetconstr @ X134 @ X135 ) )
                                   => ( in @ X136 @ X134 ) )
                               => ( ! [X137: $i,X138: $i > $o,X139: $i] :
                                      ( ( in @ X139 @ ( dsetconstr @ X137 @ X138 ) )
                                     => ( X138 @ X139 ) )
                                 => ( ! [X140: $i > $o] :
                                        ( ? [X141: $i] :
                                            ( ( X140 @ X141 )
                                            & ! [X142: $i] :
                                                ( ( X140 @ X142 )
                                               => ( X141 = X142 ) ) )
                                       => ? [X143: $i] :
                                            ( ( X140 @ X143 )
                                            & ! [X144: $i] :
                                                ( ( X140 @ X144 )
                                               => ( X143 = X144 ) ) ) )
                                   => ( ! [X145: $o,X146: $i] :
                                          ( ( in @ X146
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [Z0: $i] : X145 ) )
                                         => X145 )
                                     => ( ! [X147: $i] :
                                            ( ( in @ X147 @ emptyset )
                                           => ! [X148: $o] : X148 )
                                       => ( ! [X149: $i] :
                                              ( ( in @ X149 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X150: $i] :
                                                ~ ( in @ X150 @ emptyset )
                                           => ( ! [X151: $i > $o] :
                                                  ( ? [X152: $i] :
                                                      ( ( X151 @ X152 )
                                                      & ! [X153: $i] :
                                                          ( ( X151 @ X153 )
                                                         => ( X152 = X153 ) ) )
                                                 => ? [X154: $i] : ( X151 @ X154 ) )
                                             => ! [X4: $i,X5: $i] :
                                                  ( ! [X2: $i] :
                                                      ( ( in @ X2 @ X4 )
                                                     => ( in @ X2 @ X5 ) )
                                                 => ( ! [X2: $i] :
                                                        ( ( in @ X2 @ X5 )
                                                       => ( in @ X2 @ X4 ) )
                                                   => ( X4 = X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(assume_negation,[status(cth)],[setext]),omegaSAx]),c_0_27]),omegaIndAx]),c_0_28]),foundationAx]),wellorderingAx]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),emptysetE]),emptysetimpfalse]),setextAx]),notinemptyset]),emptysetAx]),setadjoinAx]),powersetAx]),omega0Ax])])]),c_0_34]) ).

thf(c_0_36,negated_conjecture,
    ! [X155: $i,X156: $i,X158: $i,X159: $i,X160: $i,X161: $i,X162: $i,X163: $i,X164: $i,X165: $i,X166: $i,X168: $i,X169: $i,X171: $i,X172: $i > $i > $o,X173: $i,X175: $i,X178: $i,X180: $i,X181: $i,X182: $i,X183: $i,X185: $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,X200: $o,X201: $i,X202: $i,X203: $o,X204: $i,X205: $i,X206: $i > $o,X207: $i,X212: $i,X213: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X155 @ X156 ) @ X155 )
        | ~ ( in @ ( esk1_2 @ X155 @ X156 ) @ X156 )
        | ( X155 = X156 ) )
      & ( ( in @ ( esk1_2 @ X155 @ X156 ) @ X155 )
        | ( in @ ( esk1_2 @ X155 @ X156 ) @ X156 )
        | ( X155 = X156 ) )
      & ~ ( in @ X158 @ emptyset )
      & ( ~ ( in @ X161 @ ( setadjoin @ X159 @ X160 ) )
        | ( X161 = X159 )
        | ( in @ X161 @ X160 ) )
      & ( ( X161 != X159 )
        | ( in @ X161 @ ( setadjoin @ X159 @ X160 ) ) )
      & ( ~ ( in @ X161 @ X160 )
        | ( in @ X161 @ ( setadjoin @ X159 @ X160 ) ) )
      & ( ~ ( in @ X163 @ ( powerset @ X162 ) )
        | ~ ( in @ X164 @ X163 )
        | ( in @ X164 @ X162 ) )
      & ( ( in @ ( esk2_2 @ X165 @ X166 ) @ X166 )
        | ( in @ X166 @ ( powerset @ X165 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X165 @ X166 ) @ X165 )
        | ( in @ X166 @ ( powerset @ X165 ) ) )
      & setunionAx
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X168 @ omega )
        | ( in @ ( setadjoin @ X168 @ X168 ) @ omega ) )
      & ( ( in @ ( esk3_1 @ X169 ) @ omega )
        | ~ ( in @ emptyset @ X169 )
        | ~ ( in @ X171 @ omega )
        | ( in @ X171 @ X169 ) )
      & ( ( in @ ( esk3_1 @ X169 ) @ X169 )
        | ~ ( in @ emptyset @ X169 )
        | ~ ( in @ X171 @ omega )
        | ( in @ X171 @ X169 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk3_1 @ X169 ) @ ( esk3_1 @ X169 ) ) @ X169 )
        | ~ ( in @ emptyset @ X169 )
        | ~ ( in @ X171 @ omega )
        | ( in @ X171 @ X169 ) )
      & ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
      & ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
      & ( ~ ( in @ X181 @ X173 )
        | ~ ( X172 @ X181 @ X180 )
        | ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
        | ( in @ ( esk4_2 @ X172 @ X173 ) @ X173 ) )
      & ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ~ ( in @ X181 @ X173 )
        | ~ ( X172 @ X181 @ X180 )
        | ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X172 @ ( esk4_2 @ X172 @ X173 ) @ ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ( in @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X173 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X175
         != ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ( X172 @ ( esk7_3 @ X172 @ X173 @ X178 ) @ X178 )
        | ~ ( in @ X178 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X175
         != ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ~ ( in @ X181 @ X173 )
        | ~ ( X172 @ X181 @ X180 )
        | ( in @ X180 @ ( esk6_2 @ X172 @ X173 ) )
        | ( X175
         != ( esk5_3 @ X172 @ X173 @ X175 ) )
        | ~ ( X172 @ ( esk4_2 @ X172 @ X173 ) @ X175 ) )
      & ( ( in @ ( esk8_1 @ X182 ) @ X182 )
        | ~ ( in @ X183 @ X182 ) )
      & ( ~ ( in @ X185 @ ( esk8_1 @ X182 ) )
        | ~ ( in @ X185 @ X182 )
        | ~ ( in @ X183 @ X182 ) )
      & epred1_0
      & descrp
      & ( ~ ( 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 @ ( esk10_1 @ X195 ) )
        | ( X195 @ ( esk9_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ ( X195 @ X199 )
        | ( ( esk10_1 @ X195 )
          = X199 )
        | ( X195 @ ( esk9_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ( X195 @ ( esk10_1 @ X195 ) )
        | ( X196
         != ( esk9_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ ( X195 @ X199 )
        | ( ( esk10_1 @ X195 )
          = X199 )
        | ( X196
         != ( esk9_2 @ X195 @ X196 ) )
        | ~ ( X195 @ X196 ) )
      & ( ~ ( in @ X201
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [Z0: $i] : X200 ) )
        | X200 )
      & ( ~ ( in @ X202 @ emptyset )
        | X203 )
      & ( ~ ( in @ X204 @ emptyset )
        | ~ $true )
      & ~ ( in @ X205 @ emptyset )
      & ( ( X206 @ ( esk11_2 @ X206 @ X207 ) )
        | ~ ( X206 @ X207 )
        | ( X206 @ ( esk12_1 @ X206 ) ) )
      & ( ( X207
         != ( esk11_2 @ X206 @ X207 ) )
        | ~ ( X206 @ X207 )
        | ( X206 @ ( esk12_1 @ X206 ) ) )
      & ( ~ ( in @ X212 @ esk13_0 )
        | ( in @ X212 @ esk14_0 ) )
      & ( ~ ( in @ X213 @ esk14_0 )
        | ( in @ X213 @ esk13_0 ) )
      & ( esk13_0 != esk14_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])])])]) ).

thf(c_0_37,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk13_0 )
      | ~ ( in @ X2 @ esk14_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_38,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ ( esk1_2 @ X2 @ X3 ) @ X2 )
      | ( in @ ( esk1_2 @ X2 @ X3 ) @ X3 )
      | ( X2 = X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_39,negated_conjecture,
    ! [X2: $i] :
      ( ( esk14_0 = X2 )
      | ( in @ ( esk1_2 @ esk14_0 @ X2 ) @ esk13_0 )
      | ( in @ ( esk1_2 @ esk14_0 @ X2 ) @ X2 ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_40,negated_conjecture,
    esk13_0 != esk14_0,
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_41,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( X2 = X3 )
      | ~ ( in @ ( esk1_2 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ ( esk1_2 @ X2 @ X3 ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_42,negated_conjecture,
    in @ ( esk1_2 @ esk14_0 @ esk13_0 ) @ esk13_0,
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_39]),c_0_40]) ).

thf(c_0_43,negated_conjecture,
    ~ ( in @ ( esk1_2 @ esk14_0 @ esk13_0 ) @ esk14_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]) ).

thf(c_0_44,negated_conjecture,
    ! [X2: $i] :
      ( ( in @ X2 @ esk14_0 )
      | ~ ( in @ X2 @ esk13_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU505^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 19 17:22:52 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  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_bool_1 with pid 30206 completed with status 0
% 0.20/0.54  # Result found by new_bool_1
% 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  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.54  # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.54  # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.54  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54  # Starting new_ho_10 with 181s (1) cores
% 0.20/0.54  # new_ho_10 with pid 30209 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  # Starting sh5l with 300s (1) cores
% 0.20/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.54  # Search class: HGHSF-FFMS31-SHFSMSBN
% 0.20/0.54  # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.54  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54  # Starting new_ho_10 with 181s (1) cores
% 0.20/0.54  # Preprocessing time       : 0.003 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                        : 55
% 0.20/0.54  # Removed by relevancy pruning/SinE    : 33
% 0.20/0.54  # Initial clauses                      : 57
% 0.20/0.54  # Removed in clause preprocessing      : 0
% 0.20/0.54  # Initial clauses in saturation        : 57
% 0.20/0.54  # Processed clauses                    : 179
% 0.20/0.54  # ...of these trivial                  : 3
% 0.20/0.54  # ...subsumed                          : 16
% 0.20/0.54  # ...remaining for further processing  : 160
% 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                   : 2
% 0.20/0.54  # Generated clauses                    : 835
% 0.20/0.54  # ...of the previous two non-redundant : 808
% 0.20/0.54  # ...aggressively subsumed             : 0
% 0.20/0.54  # Contextual simplify-reflections      : 0
% 0.20/0.54  # Paramodulations                      : 828
% 0.20/0.54  # Factorizations                       : 6
% 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                  : 57
% 0.20/0.54  # ...of those cached                   : 42
% 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  : 103
% 0.20/0.54  #    Positive orientable unit clauses  : 15
% 0.20/0.54  #    Positive unorientable unit clauses: 0
% 0.20/0.54  #    Negative unit clauses             : 12
% 0.20/0.54  #    Non-unit-clauses                  : 76
% 0.20/0.54  # Current number of unprocessed clauses: 740
% 0.20/0.54  # ...number of literals in the above   : 2700
% 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) : 3325
% 0.20/0.54  # Rec. Clause-clause subsumption calls : 1698
% 0.20/0.54  # Non-unit clause-clause subsumptions  : 12
% 0.20/0.54  # Unit Clause-clause subsumption calls : 122
% 0.20/0.54  # Rewrite failures with RHS unbound    : 0
% 0.20/0.54  # BW rewrite match attempts            : 5
% 0.20/0.54  # BW rewrite match successes           : 1
% 0.20/0.54  # Condensation attempts                : 179
% 0.20/0.54  # Condensation successes               : 3
% 0.20/0.54  # Termbank termtop insertions          : 29042
% 0.20/0.54  # Search garbage collected termcells   : 2620
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.042 s
% 0.20/0.54  # System time              : 0.006 s
% 0.20/0.54  # Total time               : 0.048 s
% 0.20/0.54  # Maximum resident set size: 2312 pages
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.044 s
% 0.20/0.54  # System time              : 0.009 s
% 0.20/0.54  # Total time               : 0.053 s
% 0.20/0.54  # Maximum resident set size: 1788 pages
% 0.20/0.54  % E---3.1 exiting
% 0.20/0.54  % E exiting
%------------------------------------------------------------------------------