TSTP Solution File: GRA027^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : GRA027^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% 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  : 600s
% DateTime : Sat Jul 16 07:21:39 EDT 2022

% Result   : Theorem 45.28s 45.57s
% Output   : Proof 45.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  188
% Syntax   : Number of formulae    :  209 (  28 unt;  15 typ;  15 def)
%            Number of atoms       :  906 ( 120 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 1134 ( 350   ~; 142   |;   0   &; 351   @)
%                                         (  76 <=>; 215  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  154 ( 154   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   96 (  94 usr;  83 con; 0-2 aty)
%            Number of variables   :   99 (  15   ^  84   !;   0   ?;  99   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__108,type,
    eigen__108: $o ).

thf(ty_eigen__109,type,
    eigen__109: $o > $o ).

thf(ty_eigen__112,type,
    eigen__112: ( $o > $o ) > $o ).

thf(ty_eigen__77,type,
    eigen__77: $o > $o ).

thf(ty_eigen__79,type,
    eigen__79: $o > $o ).

thf(ty_eigen__104,type,
    eigen__104: ( $o > $o ) > $o ).

thf(ty_eigen__103,type,
    eigen__103: ( $o > $o ) > $o ).

thf(ty_eigen__111,type,
    eigen__111: ( $o > $o ) > $o ).

thf(ty_eigen__107,type,
    eigen__107: $o ).

thf(ty_eigen__110,type,
    eigen__110: $o > $o ).

thf(ty_eigen__105,type,
    eigen__105: $o ).

thf(ty_eigen__100,type,
    eigen__100: $o > $o ).

thf(ty_eigen__101,type,
    eigen__101: $o > $o ).

thf(ty_eigen__78,type,
    eigen__78: $o > $o ).

thf(ty_eigen__102,type,
    eigen__102: $o > $o ).

thf(h0,assumption,
    ! [X1: ( $o > $o ) > $o,X2: $o > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__110,definition,
    ( eigen__110
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__77 )
                                 => ( X2 @ eigen__109 ) )
                             => ( X2 @ X1 ) )
                         => ( X3 @ eigen__77 ) )
                     => ~ ( X3 @ eigen__109 ) )
                 => ( X3 @ X1 ) )
             => ( ~ ( ( ( eigen__77 @ $false )
                     != ( eigen__109 @ $false ) )
                   => ( ( eigen__77 @ $false )
                      = ( X1 @ $false ) ) )
               => ( ( eigen__109 @ $false )
                  = ( X1 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__110])]) ).

thf(h1,assumption,
    ! [X1: $o > $o,X2: $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__108,definition,
    ( eigen__108
    = ( eps__1
      @ ^ [X1: $o] :
          ( ( eigen__78 @ X1 )
         != ( eigen__101 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__108])]) ).

thf(eigendef_eigen__109,definition,
    ( eigen__109
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__77 )
                                 => ( X3 @ X1 ) )
                             => ( X3 @ X2 ) )
                         => ( X4 @ eigen__77 ) )
                     => ~ ( X4 @ X1 ) )
                 => ( X4 @ X2 ) )
             => ( ~ ( ( ( eigen__77 @ $false )
                     != ( X1 @ $false ) )
                   => ( ( eigen__77 @ $false )
                      = ( X2 @ $false ) ) )
               => ( ( X1 @ $false )
                  = ( X2 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__109])]) ).

thf(eigendef_eigen__105,definition,
    ( eigen__105
    = ( eps__1
      @ ^ [X1: $o] :
          ( ( eigen__101 @ X1 )
         != ( eigen__102 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__105])]) ).

thf(eigendef_eigen__77,definition,
    ( eigen__77
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
                                 => ( X4 @ X2 ) )
                             => ( X4 @ X3 ) )
                         => ( X5 @ X1 ) )
                     => ~ ( X5 @ X2 ) )
                 => ( X5 @ X3 ) )
             => ( ~ ( ( ( X1 @ $false )
                     != ( X2 @ $false ) )
                   => ( ( X1 @ $false )
                      = ( X3 @ $false ) ) )
               => ( ( X2 @ $false )
                  = ( X3 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__77])]) ).

thf(h2,assumption,
    ! [X1: ( ( $o > $o ) > $o ) > $o,X2: ( $o > $o ) > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__112,definition,
    ( eigen__112
    = ( eps__2
      @ ^ [X1: ( $o > $o ) > $o] :
          ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__111 @ eigen__77 )
                               => ( eigen__111 @ eigen__109 ) )
                           => ( eigen__111 @ eigen__110 ) )
                       => ( X1 @ eigen__77 ) )
                   => ~ ( X1 @ eigen__109 ) )
               => ( X1 @ eigen__110 ) )
           => ( ~ ( ( ( eigen__77 @ $false )
                   != ( eigen__109 @ $false ) )
                 => ( ( eigen__77 @ $false )
                    = ( eigen__110 @ $false ) ) )
             => ( ( eigen__109 @ $false )
                = ( eigen__110 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__112])]) ).

thf(eigendef_eigen__100,definition,
    ( eigen__100
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ( ( ( X1 @ $false )
              = ( eigen__79 @ $false ) )
           => ( ( eigen__79 @ $false )
              = ( X1 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__100])]) ).

thf(eigendef_eigen__101,definition,
    ( eigen__101
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__78 )
                                 => ( X3 @ X1 ) )
                             => ( X3 @ X2 ) )
                         => ( X4 @ eigen__78 ) )
                     => ~ ( X4 @ X1 ) )
                 => ( X4 @ X2 ) )
             => ( ~ ( ( ( eigen__78 @ $false )
                      = ( X1 @ $false ) )
                   => ( ( eigen__78 @ $false )
                     != ( X2 @ $false ) ) )
               => ( ( X1 @ $false )
                 != ( X2 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__101])]) ).

thf(eigendef_eigen__78,definition,
    ( eigen__78
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
                                 => ( X4 @ X2 ) )
                             => ( X4 @ X3 ) )
                         => ( X5 @ X1 ) )
                     => ~ ( X5 @ X2 ) )
                 => ( X5 @ X3 ) )
             => ( ~ ( ( ( X1 @ $false )
                      = ( X2 @ $false ) )
                   => ( ( X1 @ $false )
                     != ( X3 @ $false ) ) )
               => ( ( X2 @ $false )
                 != ( X3 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__78])]) ).

thf(eigendef_eigen__102,definition,
    ( eigen__102
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__78 )
                                 => ( X2 @ eigen__101 ) )
                             => ( X2 @ X1 ) )
                         => ( X3 @ eigen__78 ) )
                     => ~ ( X3 @ eigen__101 ) )
                 => ( X3 @ X1 ) )
             => ( ~ ( ( ( eigen__78 @ $false )
                      = ( eigen__101 @ $false ) )
                   => ( ( eigen__78 @ $false )
                     != ( X1 @ $false ) ) )
               => ( ( eigen__101 @ $false )
                 != ( X1 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__102])]) ).

thf(eigendef_eigen__103,definition,
    ( eigen__103
    = ( eps__2
      @ ^ [X1: ( $o > $o ) > $o] :
          ~ ! [X2: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__78 )
                                 => ( X1 @ eigen__101 ) )
                             => ( X1 @ eigen__102 ) )
                         => ( X2 @ eigen__78 ) )
                     => ~ ( X2 @ eigen__101 ) )
                 => ( X2 @ eigen__102 ) )
             => ( ~ ( ( ( eigen__78 @ $false )
                      = ( eigen__101 @ $false ) )
                   => ( ( eigen__78 @ $false )
                     != ( eigen__102 @ $false ) ) )
               => ( ( eigen__101 @ $false )
                 != ( eigen__102 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__103])]) ).

thf(eigendef_eigen__104,definition,
    ( eigen__104
    = ( eps__2
      @ ^ [X1: ( $o > $o ) > $o] :
          ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__103 @ eigen__78 )
                               => ( eigen__103 @ eigen__101 ) )
                           => ( eigen__103 @ eigen__102 ) )
                       => ( X1 @ eigen__78 ) )
                   => ~ ( X1 @ eigen__101 ) )
               => ( X1 @ eigen__102 ) )
           => ( ~ ( ( ( eigen__78 @ $false )
                    = ( eigen__101 @ $false ) )
                 => ( ( eigen__78 @ $false )
                   != ( eigen__102 @ $false ) ) )
             => ( ( eigen__101 @ $false )
               != ( eigen__102 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__104])]) ).

thf(eigendef_eigen__111,definition,
    ( eigen__111
    = ( eps__2
      @ ^ [X1: ( $o > $o ) > $o] :
          ~ ! [X2: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__77 )
                                 => ( X1 @ eigen__109 ) )
                             => ( X1 @ eigen__110 ) )
                         => ( X2 @ eigen__77 ) )
                     => ~ ( X2 @ eigen__109 ) )
                 => ( X2 @ eigen__110 ) )
             => ( ~ ( ( ( eigen__77 @ $false )
                     != ( eigen__109 @ $false ) )
                   => ( ( eigen__77 @ $false )
                      = ( eigen__110 @ $false ) ) )
               => ( ( eigen__109 @ $false )
                  = ( eigen__110 @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__111])]) ).

thf(eigendef_eigen__79,definition,
    ( eigen__79
    = ( eps__0
      @ ^ [X1: $o > $o] :
          ~ ! [X2: $o > $o] :
              ( ( ( X2 @ $false )
                = ( X1 @ $false ) )
             => ( ( X1 @ $false )
                = ( X2 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__79])]) ).

thf(eigendef_eigen__107,definition,
    ( eigen__107
    = ( eps__1
      @ ^ [X1: $o] :
          ( ( eigen__78 @ X1 )
         != ( eigen__102 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__107])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
                           => ( X4 @ X2 ) )
                       => ( X4 @ X3 ) )
                   => ( X5 @ X1 ) )
               => ~ ( X5 @ X2 ) )
           => ( X5 @ X3 ) )
       => ( ~ ( ( ( X1 @ $false )
               != ( X2 @ $false ) )
             => ( ( X1 @ $false )
                = ( X3 @ $false ) ) )
         => ( ( X2 @ $false )
            = ( X3 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eigen__78 @ eigen__107 )
      = ( eigen__102 @ eigen__107 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__78 )
                           => ( X3 @ X1 ) )
                       => ( X3 @ X2 ) )
                   => ( X4 @ eigen__78 ) )
               => ~ ( X4 @ X1 ) )
           => ( X4 @ X2 ) )
       => ( ~ ( ( ( eigen__78 @ $false )
                = ( X1 @ $false ) )
             => ( ( eigen__78 @ $false )
               != ( X2 @ $false ) ) )
         => ( ( X1 @ $false )
           != ( X2 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__107 = eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__105 = eigen__108 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__101 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( eigen__78 @ eigen__108 )
      = ( eigen__101 @ eigen__108 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__102 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__102 @ eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> eigen__107 ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( $false = sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $o] :
        ( ( eigen__101 @ X1 )
        = ( eigen__102 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__77 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__108 = eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__104 @ eigen__101 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( eigen__101 @ eigen__108 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ ( ~ ( ~ ( ( eigen__103 @ eigen__78 )
                 => ( eigen__103 @ eigen__101 ) )
             => ( eigen__103 @ eigen__102 ) )
         => ( eigen__104 @ eigen__78 ) )
     => ~ sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( eigen__102 @ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__77 )
                           => ( X1 @ eigen__109 ) )
                       => ( X1 @ eigen__110 ) )
                   => ( X2 @ eigen__77 ) )
               => ~ ( X2 @ eigen__109 ) )
           => ( X2 @ eigen__110 ) )
       => ( ~ ( ( sP13
               != ( eigen__109 @ $false ) )
             => ( sP13
                = ( eigen__110 @ $false ) ) )
         => ( ( eigen__109 @ $false )
            = ( eigen__110 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( $false = eigen__108 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ( eigen__109 @ $false )
      = ( eigen__110 @ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( eigen__78 @ eigen__108 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ~ ( ( sP13
           != ( eigen__109 @ $false ) )
         => ( sP13
            = ( eigen__110 @ $false ) ) )
     => sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ( sP13
       != ( eigen__109 @ $false ) )
     => ( sP13
        = ( eigen__110 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eigen__108 = sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( $false = eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $o] :
        ( ( ( eigen__100 @ $false )
          = X1 )
       => ( X1
          = ( eigen__100 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( ( eigen__103 @ eigen__78 )
     => ( eigen__103 @ eigen__101 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( eigen__78 = eigen__102 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__111 @ eigen__77 )
                         => ( eigen__111 @ eigen__109 ) )
                     => ( eigen__111 @ eigen__110 ) )
                 => ( eigen__112 @ eigen__77 ) )
             => ~ ( eigen__112 @ eigen__109 ) )
         => ( eigen__112 @ eigen__110 ) )
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ( ( eigen__100 @ $false )
        = ( eigen__79 @ $false ) )
     => ( ( eigen__79 @ $false )
        = ( eigen__100 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ~ ( ( ( eigen__78 @ $false )
            = sP6 )
         => ( ( eigen__78 @ $false )
           != sP8 ) )
     => ( sP6 != sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $o > $o,X2: $o > $o] :
        ( ( ( X2 @ $false )
          = ( X1 @ $false ) )
       => ( ( X1 @ $false )
          = ( X2 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( eigen__78 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ sP28
                       => ( eigen__103 @ eigen__102 ) )
                   => ( X1 @ eigen__78 ) )
               => ~ ( X1 @ eigen__101 ) )
           => ( X1 @ eigen__102 ) )
       => sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( sP10 = eigen__108 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> eigen__105 ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ! [X1: $o] :
        ( ( eigen__78 @ X1 )
        = ( eigen__101 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( sP10 = $false ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> eigen__108 ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( sP13
      = ( eigen__110 @ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: $o > $o] :
        ( ( ( X1 @ $false )
          = ( eigen__79 @ $false ) )
       => ( ( eigen__79 @ $false )
          = ( X1 @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ! [X1: $o > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__78 )
                           => ( X2 @ eigen__101 ) )
                       => ( X2 @ X1 ) )
                   => ( X3 @ eigen__78 ) )
               => ~ ( X3 @ eigen__101 ) )
           => ( X3 @ X1 ) )
       => ( ~ ( ( sP34 = sP6 )
             => ( sP34
               != ( X1 @ $false ) ) )
         => ( sP6
           != ( X1 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( sP34 = sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( eigen__110 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__77 )
                           => ( X3 @ X1 ) )
                       => ( X3 @ X2 ) )
                   => ( X4 @ eigen__77 ) )
               => ~ ( X4 @ X1 ) )
           => ( X4 @ X2 ) )
       => ( ~ ( ( sP13
               != ( X1 @ $false ) )
             => ( sP13
                = ( X2 @ $false ) ) )
         => ( ( X1 @ $false )
            = ( X2 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( sP37 = $false ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( eigen__109 @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ! [X1: $o > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__77 )
                           => ( X2 @ eigen__109 ) )
                       => ( X2 @ X1 ) )
                   => ( X3 @ eigen__77 ) )
               => ~ ( X3 @ eigen__109 ) )
           => ( X3 @ X1 ) )
       => ( ~ ( ( sP13 != sP48 )
             => ( sP13
                = ( X1 @ $false ) ) )
         => ( sP48
            = ( X1 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( ~ ( sP33
         => ~ ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
                ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
                                   => ( X4 @ X2 ) )
                               => ( X4 @ X3 ) )
                           => ( X5 @ X1 ) )
                       => ~ ( X5 @ X2 ) )
                   => ( X5 @ X3 ) )
               => ( ~ ( ( ( X1 @ $false )
                        = ( X2 @ $false ) )
                     => ( ( X1 @ $false )
                       != ( X3 @ $false ) ) )
                 => ( ( X2 @ $false )
                   != ( X3 @ $false ) ) ) ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( ~ ( ~ sP17
         => ( eigen__104 @ eigen__102 ) )
     => sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( sP37 = sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( ~ sP17
     => ( eigen__104 @ eigen__102 ) ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( eigen__103 @ eigen__78 ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__78 )
                           => ( X1 @ eigen__101 ) )
                       => ( X1 @ eigen__102 ) )
                   => ( X2 @ eigen__78 ) )
               => ~ ( X2 @ eigen__101 ) )
           => ( X2 @ eigen__102 ) )
       => sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( eigen__104 @ eigen__102 ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ! [X1: ( $o > $o ) > ( $o > $o ) > $o] :
        ( ~ ( ! [X2: $o > $o,X3: $o > $o] :
                ( ( X1 @ X2 @ X3 )
               => ( X1 @ X3 @ X2 ) )
           => ~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
                  ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ X2 )
                                     => ( X5 @ X3 ) )
                                 => ( X5 @ X4 ) )
                             => ( X6 @ X2 ) )
                         => ~ ( X6 @ X3 ) )
                     => ( X6 @ X4 ) )
                 => ( ~ ( ( X1 @ X3 @ X2 )
                       => ~ ( X1 @ X4 @ X2 ) )
                   => ~ ( X1 @ X4 @ X3 ) ) ) )
       => ~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
              ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ X2 )
                                 => ( X5 @ X3 ) )
                             => ( X5 @ X4 ) )
                         => ( X6 @ X2 ) )
                     => ~ ( X6 @ X3 ) )
                 => ( X6 @ X4 ) )
             => ( ~ ( ~ ( X1 @ X3 @ X2 )
                   => ( X1 @ X4 @ X2 ) )
               => ( X1 @ X4 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ( eigen__78 = eigen__101 ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( eigen__101 @ sP37 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( eigen__78 @ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ! [X1: $o,X2: $o] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ( sP6 = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
                           => ( X4 @ X2 ) )
                       => ( X4 @ X3 ) )
                   => ( X5 @ X1 ) )
               => ~ ( X5 @ X2 ) )
           => ( X5 @ X3 ) )
       => ( ~ ( ( ( X1 @ $false )
                = ( X2 @ $false ) )
             => ( ( X1 @ $false )
               != ( X3 @ $false ) ) )
         => ( ( X2 @ $false )
           != ( X3 @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ( eigen__101 = eigen__102 ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ( sP40 = $false ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ! [X1: ( $o > $o ) > $o] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__111 @ eigen__77 )
                           => ( eigen__111 @ eigen__109 ) )
                       => ( eigen__111 @ eigen__110 ) )
                   => ( X1 @ eigen__77 ) )
               => ~ ( X1 @ eigen__109 ) )
           => ( X1 @ eigen__110 ) )
       => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ( sP59 = sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ( eigen__103 @ eigen__101 ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ( sP44
     => ( sP34 != sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ( eigen__103 @ eigen__102 ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ! [X1: $o] :
        ( ( eigen__78 @ X1 )
        = ( eigen__102 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( sP13 = sP48 ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ( ~ sP28
     => sP71 ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ( sP33
     => ~ sP63 ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ( ~ sP74
     => ( eigen__104 @ eigen__78 ) ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(ramsey_l_3_3_4,conjecture,
    ~ sP57 ).

thf(h3,negated_conjecture,
    sP57,
    inference(assume_negation,[status(cth)],[ramsey_l_3_3_4]) ).

thf(1,plain,
    ( sP73
    | ~ sP13
    | ~ sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP73
    | sP13
    | sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP41
    | ~ sP13
    | ~ sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP41
    | sP13
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP24
    | ~ sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP24
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP21
    | ~ sP48
    | ~ sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP21
    | sP48
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP23
    | ~ sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP23
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP30
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP66
    | ~ sP30 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__112]) ).

thf(13,plain,
    ( sP19
    | ~ sP66 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__111]) ).

thf(14,plain,
    ( sP49
    | ~ sP19 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__110]) ).

thf(15,plain,
    ( sP46
    | ~ sP49 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__109]) ).

thf(16,plain,
    ( sP5
    | ~ sP37
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP59
    | sP16
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP59
    | sP6
    | ~ sP47 ),
    inference(mating_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP52
    | ~ sP37
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP9
    | sP18
    | ~ sP52 ),
    inference(mating_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP47
    | sP37
    | sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP9
    | sP8
    | ~ sP47 ),
    inference(mating_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP14
    | ~ sP40
    | ~ sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP16
    | sP59
    | ~ sP14 ),
    inference(mating_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP6
    | sP59
    | ~ sP26 ),
    inference(mating_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP4
    | ~ sP10
    | ~ sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP18
    | sP9
    | ~ sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP26
    | sP69
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP8
    | sP9
    | ~ sP26 ),
    inference(mating_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP67
    | ~ sP59
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( sP67
    | sP59
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( sP36
    | ~ sP10
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP60
    | sP22
    | ~ sP36 ),
    inference(mating_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP60
    | sP34
    | ~ sP39 ),
    inference(mating_rule,[status(thm)],]) ).

thf(35,plain,
    ( sP39
    | sP10
    | sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP18
    | sP8
    | ~ sP39 ),
    inference(mating_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP25
    | ~ sP40
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP22
    | sP60
    | ~ sP25 ),
    inference(mating_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP34
    | sP60
    | ~ sP11 ),
    inference(mating_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP11
    | sP69
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP8
    | sP18
    | ~ sP11 ),
    inference(mating_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP2
    | ~ sP60
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( sP2
    | sP60
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP22
    | sP34
    | ~ sP65 ),
    inference(mating_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP65
    | sP40
    | sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP16
    | sP6
    | ~ sP65 ),
    inference(mating_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP34
    | sP22
    | ~ sP20 ),
    inference(mating_rule,[status(thm)],]) ).

thf(48,plain,
    ( sP20
    | sP69
    | sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( ~ sP6
    | sP16
    | ~ sP20 ),
    inference(mating_rule,[status(thm)],]) ).

thf(50,plain,
    ( sP7
    | ~ sP22
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( sP7
    | sP22
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( sP38
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__108]) ).

thf(53,plain,
    ( sP58
    | ~ sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( ~ sP54
    | sP68
    | ~ sP58 ),
    inference(mating_rule,[status(thm)],]) ).

thf(55,plain,
    ( sP72
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__107]) ).

thf(56,plain,
    ( sP29
    | ~ sP72 ),
    inference(prop_rule,[status(thm)],]) ).

thf(57,plain,
    ( ~ sP54
    | sP71
    | ~ sP29 ),
    inference(mating_rule,[status(thm)],]) ).

thf(58,plain,
    ( sP28
    | ~ sP68 ),
    inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
    ( sP28
    | sP54 ),
    inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
    ( sP74
    | ~ sP71 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( sP74
    | ~ sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
    ( sP76
    | ~ sP74 ),
    inference(prop_rule,[status(thm)],]) ).

thf(63,plain,
    ( sP12
    | ~ sP67 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__105]) ).

thf(64,plain,
    ( sP64
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP15
    | sP56
    | ~ sP64 ),
    inference(mating_rule,[status(thm)],]) ).

thf(66,plain,
    ( sP17
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(67,plain,
    ( sP17
    | ~ sP76 ),
    inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
    ( sP53
    | ~ sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
    ( sP53
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
    ( ~ sP44
    | ~ sP34
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
    ( ~ sP44
    | sP34
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP70
    | sP44 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( ~ sP62
    | ~ sP6
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( ~ sP62
    | sP6
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
    ( sP32
    | sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(76,plain,
    ( sP32
    | ~ sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
    ( sP51
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(78,plain,
    ( sP51
    | ~ sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(79,plain,
    ( sP35
    | ~ sP51 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__104]) ).

thf(80,plain,
    ( sP55
    | ~ sP35 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__103]) ).

thf(81,plain,
    ( sP43
    | ~ sP55 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__102]) ).

thf(82,plain,
    ( sP3
    | ~ sP43 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__101]) ).

thf(83,plain,
    ( ~ sP27
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(84,plain,
    ( ~ sP61
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(85,plain,
    ( sP42
    | ~ sP31 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__100]) ).

thf(86,plain,
    ( sP33
    | ~ sP42 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__79]) ).

thf(87,plain,
    ( sP63
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__78]) ).

thf(88,plain,
    ( ~ sP75
    | ~ sP33
    | ~ sP63 ),
    inference(prop_rule,[status(thm)],]) ).

thf(89,plain,
    ( sP1
    | ~ sP46 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__77]) ).

thf(90,plain,
    ( ~ sP50
    | sP75
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(91,plain,
    ~ sP69,
    inference(prop_rule,[status(thm)],]) ).

thf(92,plain,
    sP61,
    inference(eq_sym,[status(thm)],]) ).

thf(93,plain,
    ( ~ sP57
    | sP50 ),
    inference(all_rule,[status(thm)],]) ).

thf(94,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,h3]) ).

thf(95,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[94,h2]) ).

thf(96,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[95,h1]) ).

thf(97,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[96,h0]) ).

thf(0,theorem,
    ~ sP57,
    inference(contra,[status(thm),contra(discharge,[h3])],[94,h3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRA027^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon May 30 23:40:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 45.28/45.57  % SZS status Theorem
% 45.28/45.57  % Mode: mode456
% 45.28/45.57  % Inferences: 1582
% 45.28/45.57  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------