TSTP Solution File: SEV261^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV261^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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
% DateTime : Tue Mar 30 22:05:13 EDT 2021

% Result   : Theorem 26.02s
% Output   : Proof 26.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  179
% Syntax   : Number of formulae    :  197 (  23 unt;  13 typ;  12 def)
%            Number of atoms       :  713 ( 154 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  722 ( 301   ~; 102   |;   0   &; 104   @)
%                                         (  81 <=>; 134  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  96 usr;  89 con; 0-2 aty)
%            Number of variables   :  182 ( 127   ^  55   !;   0   ?; 182   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_eigen__14,type,
    eigen__14: a > $o ).

thf(ty_eigen__6,type,
    eigen__6: a > $o ).

thf(ty_eigen__2,type,
    eigen__2: a > $o ).

thf(ty_eigen__7,type,
    eigen__7: a ).

thf(ty_eigen__1,type,
    eigen__1: a > $o ).

thf(ty_eigen__0,type,
    eigen__0: a > $o ).

thf(ty_eigen__4,type,
    eigen__4: a ).

thf(ty_eigen__5,type,
    eigen__5: ( a > $o ) > $o ).

thf(ty_eigen__11,type,
    eigen__11: a > $o ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__8,type,
    eigen__8: a ).

thf(ty_eigen__18,type,
    eigen__18: a > $o ).

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

thf(eigendef_eigen__11,definition,
    ( eigen__11
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( X1
              = ( ^ [X2: a] : $false ) )
           => ( ( X1
               != ( ^ [X2: a] : $false ) )
             => ( X1
                = ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__11])]) ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__1
      @ ^ [X1: a] :
          ( ( eigen__2 @ X1 )
         != $false ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ! [X2: a > $o] :
              ( ~ ( ~ ( ( ( eigen__0
                         != ( ^ [X3: a] : $false ) )
                       => ( eigen__0
                          = ( ^ [X3: a] : ~ $false ) ) )
                     => ~ ( ( X1
                           != ( ^ [X3: a] : $false ) )
                         => ( X1
                            = ( ^ [X3: a] : ~ $false ) ) ) )
                 => ( X2
                   != ( ^ [X3: a] :
                          ~ ( ( eigen__0 @ X3 )
                           => ~ ( X1 @ X3 ) ) ) ) )
             => ( ( X2
                 != ( ^ [X3: a] : $false ) )
               => ( X2
                  = ( ^ [X3: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: a > $o] :
                    ( ( eigen__5 @ X2 )
                   => ( ( X2
                       != ( ^ [X3: a] : $false ) )
                     => ( X2
                        = ( ^ [X3: a] : ~ $false ) ) ) )
               => ( X1
                 != ( ^ [X2: a] :
                        ~ ! [X3: a > $o] :
                            ( ( eigen__5 @ X3 )
                           => ~ ( X3 @ X2 ) ) ) ) )
           => ( ( X1
               != ( ^ [X2: a] : $false ) )
             => ( X1
                = ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__14,definition,
    ( eigen__14
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( X1
              = ( ^ [X2: a] : ~ $false ) )
           => ( ( X1
               != ( ^ [X2: a] : $false ) )
             => ( X1
                = ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__14])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ! [X2: a > $o,X3: a > $o] :
              ( ~ ( ~ ( ( ( X1
                         != ( ^ [X4: a] : $false ) )
                       => ( X1
                          = ( ^ [X4: a] : ~ $false ) ) )
                     => ~ ( ( X2
                           != ( ^ [X4: a] : $false ) )
                         => ( X2
                            = ( ^ [X4: a] : ~ $false ) ) ) )
                 => ( X3
                   != ( ^ [X4: a] :
                          ~ ( ( X1 @ X4 )
                           => ~ ( X2 @ X4 ) ) ) ) )
             => ( ( X3
                 != ( ^ [X4: a] : $false ) )
               => ( X3
                  = ( ^ [X4: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__18,definition,
    ( eigen__18
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( eigen__5 @ X1 )
           => ~ ( X1 @ eigen__7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__18])]) ).

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__1
      @ ^ [X1: a] :
          ( ( eigen__6 @ X1 )
         != ( ~ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ~ ( ( ( eigen__0
                       != ( ^ [X2: a] : $false ) )
                     => ( eigen__0
                        = ( ^ [X2: a] : ~ $false ) ) )
                   => ~ ( ( eigen__1
                         != ( ^ [X2: a] : $false ) )
                       => ( eigen__1
                          = ( ^ [X2: a] : ~ $false ) ) ) )
               => ( X1
                 != ( ^ [X2: a] :
                        ~ ( ( eigen__0 @ X2 )
                         => ~ ( eigen__1 @ X2 ) ) ) ) )
           => ( ( X1
               != ( ^ [X2: a] : $false ) )
             => ( X1
                = ( ^ [X2: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__1
      @ ^ [X1: a] :
          ( ( eigen__2 @ X1 )
         != ( ~ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__1
      @ ^ [X1: a] :
          ( ( eigen__6 @ X1 )
         != $false ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

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

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__2
      @ ^ [X1: ( a > $o ) > $o] :
          ~ ! [X2: a > $o] :
              ( ~ ( ! [X3: a > $o] :
                      ( ( X1 @ X3 )
                     => ( ( X3
                         != ( ^ [X4: a] : $false ) )
                       => ( X3
                          = ( ^ [X4: a] : ~ $false ) ) ) )
                 => ( X2
                   != ( ^ [X3: a] :
                          ~ ! [X4: a > $o] :
                              ( ( X1 @ X4 )
                             => ~ ( X4 @ X3 ) ) ) ) )
             => ( ( X2
                 != ( ^ [X3: a] : $false ) )
               => ( X2
                  = ( ^ [X3: a] : ~ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a > $o] :
        ( ( eigen__5 @ X1 )
       => ~ ( X1 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( eigen__6 @ eigen__7 )
      = $false ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__18
      = ( ^ [X1: a] : ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__0
      = ( ^ [X1: a] : ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a > $o] :
        ( ~ ( ~ ( ( ( eigen__0
                   != ( ^ [X2: a] : $false ) )
                 => sP5 )
               => ~ ( ( eigen__1
                     != ( ^ [X2: a] : $false ) )
                   => ( eigen__1
                      = ( ^ [X2: a] : ~ $false ) ) ) )
           => ( X1
             != ( ^ [X2: a] :
                    ~ ( ( eigen__0 @ X2 )
                     => ~ ( eigen__1 @ X2 ) ) ) ) )
       => ( ( X1
           != ( ^ [X2: a] : $false ) )
         => ( X1
            = ( ^ [X2: a] : ~ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( eigen__2 @ eigen__4 )
      = ( ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( eigen__2
       != ( ^ [X1: a] : $false ) )
     => ( eigen__2
        = ( ^ [X1: a] : ~ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( eigen__0 @ eigen__3 )
     => ~ ( eigen__1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( eigen__11
      = ( ^ [X1: a] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__6 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__1 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__5 @ eigen__18 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: a] :
        ( ( eigen__2 @ X1 )
        = ( ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( eigen__6
      = ( ^ [X1: a] : $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( eigen__1
      = ( ^ [X1: a] : ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: a > $o] :
        ( ( eigen__5 @ X1 )
       => ~ ( X1 @ eigen__8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( eigen__6 @ eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: ( a > $o ) > $o,X2: a > $o] :
        ( ~ ( ! [X3: a > $o] :
                ( ( X1 @ X3 )
               => ( ( X3
                   != ( ^ [X4: a] : $false ) )
                 => ( X3
                    = ( ^ [X4: a] : ~ $false ) ) ) )
           => ( X2
             != ( ^ [X3: a] :
                    ~ ! [X4: a > $o] :
                        ( ( X1 @ X4 )
                       => ~ ( X4 @ X3 ) ) ) ) )
       => ( ( X2
           != ( ^ [X3: a] : $false ) )
         => ( X2
            = ( ^ [X3: a] : ~ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

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

thf(sP22,plain,
    ( sP22
  <=> ( eigen__6
      = ( ^ [X1: a] : ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: a] :
        ( ( eigen__2 @ X1 )
        = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__2 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP13
      = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ( eigen__0 @ eigen__3 )
      = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: a] :
        ( ( eigen__6 @ X1 )
        = ( ~ ! [X2: a > $o] :
                ( ( eigen__5 @ X2 )
               => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( eigen__0
      = ( ^ [X1: a] : sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
        = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a > $o] :
                ( ( eigen__5 @ X2 )
               => ( ( X2
                   != ( ^ [X3: a] : sP21 ) )
                 => ( X2
                    = ( ^ [X3: a] : ~ sP21 ) ) ) )
           => ( X1
             != ( ^ [X2: a] :
                    ~ ! [X3: a > $o] :
                        ( ( eigen__5 @ X3 )
                       => ~ ( X3 @ X2 ) ) ) ) )
       => ( ( X1
           != ( ^ [X2: a] : sP21 ) )
         => ( X1
            = ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( sP19
      = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: a] :
        ( ( eigen__18 @ X1 )
        = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP8 = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( ~ sP16
     => sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( eigen__0 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ( eigen__1 @ eigen__3 )
      = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( sP8
      = ( ~ sP10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ! [X1: a > $o,X2: a > $o] :
        ( ~ ( ~ ( ( ~ sP28
                 => sP5 )
               => ~ ( ( X1
                     != ( ^ [X3: a] : sP21 ) )
                   => ( X1
                      = ( ^ [X3: a] : ~ sP21 ) ) ) )
           => ( X2
             != ( ^ [X3: a] :
                    ~ ( ( eigen__0 @ X3 )
                     => ~ ( X1 @ X3 ) ) ) ) )
       => ( ( X2
           != ( ^ [X3: a] : sP21 ) )
         => ( X2
            = ( ^ [X3: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( sP11
     => ( ~ sP11
       => ( eigen__11
          = ( ^ [X1: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( sP12
      = ( ~ sP2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( ( eigen__18 @ eigen__7 )
      = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( ~ ( ! [X1: a > $o] :
              ( ( eigen__5 @ X1 )
             => ( ( X1
                 != ( ^ [X2: a] : sP21 ) )
               => ( X1
                  = ( ^ [X2: a] : ~ sP21 ) ) ) )
         => ( eigen__6
           != ( ^ [X1: a] :
                  ~ ! [X2: a > $o] :
                      ( ( eigen__5 @ X2 )
                     => ~ ( X2 @ X1 ) ) ) ) )
     => sP34 ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( ! [X1: a > $o] :
          ( ( eigen__5 @ X1 )
         => ( ( X1
             != ( ^ [X2: a] : sP21 ) )
           => ( X1
              = ( ^ [X2: a] : ~ sP21 ) ) ) )
     => ( eigen__6
       != ( ^ [X1: a] :
              ~ ! [X2: a > $o] :
                  ( ( eigen__5 @ X2 )
                 => ~ ( X2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( ( eigen__18
       != ( ^ [X1: a] : sP21 ) )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( eigen__18 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( eigen__2
      = ( ^ [X1: a] : sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( eigen__6
      = ( ^ [X1: a] :
            ~ ! [X2: a > $o] :
                ( ( eigen__5 @ X2 )
               => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( sP24
      = ( ~ ( sP35
           => ~ sP13 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( sP14
     => sP44 ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( ~ ( ( ~ sP28
           => sP5 )
         => ~ ( ( eigen__1
               != ( ^ [X1: a] : sP21 ) )
             => sP17 ) )
     => ( eigen__2
       != ( ^ [X1: a] :
              ~ ( ( eigen__0 @ X1 )
               => ~ ( eigen__1 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( ( ~ sP28
       => sP5 )
     => ~ ( ( eigen__1
           != ( ^ [X1: a] : sP21 ) )
         => sP17 ) ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( eigen__5
      @ ^ [X1: a] : ~ sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ! [X1: a] :
        ( ( eigen__6 @ X1 )
        = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( sP14
     => ~ sP47 ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ! [X1: a > $o] :
        ( ( X1
          = ( ^ [X2: a] : ~ sP21 ) )
       => ( ( X1
           != ( ^ [X2: a] : sP21 ) )
         => ( X1
            = ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( sP35
     => ~ sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( eigen__1
      = ( ^ [X1: a] : sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ( ~ sP60
     => sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ! [X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ~ ( ~ ( ( ( X1
                   != ( ^ [X4: a] : sP21 ) )
                 => ( X1
                    = ( ^ [X4: a] : ~ sP21 ) ) )
               => ~ ( ( X2
                     != ( ^ [X4: a] : sP21 ) )
                   => ( X2
                      = ( ^ [X4: a] : ~ sP21 ) ) ) )
           => ( X3
             != ( ^ [X4: a] :
                    ~ ( ( X1 @ X4 )
                     => ~ ( X2 @ X4 ) ) ) ) )
       => ( ( X3
           != ( ^ [X4: a] : sP21 ) )
         => ( X3
            = ( ^ [X4: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( sP19
      = ( ~ sP18 ) ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ( eigen__18
      = ( ^ [X1: a] : sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ! [X1: a] :
        ( ( eigen__2 @ X1 )
        = ( ~ ( ( eigen__0 @ X1 )
             => ~ ( eigen__1 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( ~ sP1
     => ~ sP62 ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ! [X1: a] :
        ( ( eigen__6 @ X1 )
        = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ( eigen__14
      = ( ^ [X1: a] : ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ( ~ sP52
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ( eigen__2
      = ( ^ [X1: a] :
            ~ ( ( eigen__0 @ X1 )
             => ~ ( eigen__1 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ! [X1: a > $o] :
        ( ( X1
          = ( ^ [X2: a] : sP21 ) )
       => ( ( X1
           != ( ^ [X2: a] : sP21 ) )
         => ( X1
            = ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( ~ sP28
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ( eigen__2
      = ( ^ [X1: a] : ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ! [X1: a > $o] :
        ( ( eigen__5 @ X1 )
       => ( ( X1
           != ( ^ [X2: a] : sP21 ) )
         => ( X1
            = ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ( sP72
     => ~ sP58 ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
    ( sP77
  <=> ( sP68
     => ( ( eigen__14
         != ( ^ [X1: a] : sP21 ) )
       => sP68 ) ) ),
    introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(sP78,plain,
    ( sP78
  <=> ( ~ sP11
     => ( eigen__11
        = ( ^ [X1: a] : ~ sP21 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP78])]) ).

thf(sP79,plain,
    ( sP79
  <=> ( ( eigen__14
       != ( ^ [X1: a] : sP21 ) )
     => sP68 ) ),
    introduced(definition,[new_symbols(definition,[sP79])]) ).

thf(sP80,plain,
    ( sP80
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
        = sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP80])]) ).

thf(sP81,plain,
    ( sP81
  <=> ( sP35
      = ( ~ sP21 ) ) ),
    introduced(definition,[new_symbols(definition,[sP81])]) ).

thf(cINDISCRETE_TOPOLOGY_pme,conjecture,
    ~ sP66 ).

thf(h3,negated_conjecture,
    sP66,
    inference(assume_negation,[status(cth)],[cINDISCRETE_TOPOLOGY_pme]) ).

thf(1,plain,
    ( ~ sP41
    | ~ sP47
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP32
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP64
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP14
    | sP55
    | ~ sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP75
    | sP51 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP51
    | ~ sP14
    | sP44 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP44
    | sP64
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP57
    | sP47 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP57
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP2
    | ~ sP57 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).

thf(11,plain,
    ( ~ sP40
    | ~ sP12
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP18
    | ~ sP55 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP63
    | sP19
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP27
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP27
    | sP63 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP79
    | ~ sP68 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( sP77
    | ~ sP79 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP77
    | sP68 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP58
    | ~ sP77 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).

thf(20,plain,
    ( sP78
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP39
    | ~ sP78 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP39
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP72
    | ~ sP39 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(24,plain,
    ( sP10
    | sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP10
    | sP46 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP37
    | ~ sP8
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP26
    | ~ sP46
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP36
    | ~ sP53
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP59
    | ~ sP35
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP50
    | sP24
    | sP59 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP81
    | sP35
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP25
    | sP13
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP65
    | sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP80
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP45
    | sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP65
    | sP50 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP29
    | sP81 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP71
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP17
    | sP71 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP60
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP5
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP28
    | sP80 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( sP31
    | ~ sP19
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP3
    | sP12
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP56
    | ~ sP31 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).

thf(46,plain,
    ( sP67
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).

thf(47,plain,
    ( sP22
    | ~ sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( sP16
    | ~ sP67 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( ~ sP49
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
    ( sP34
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( sP34
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( sP43
    | sP49 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    ( sP43
    | sP75 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( sP42
    | ~ sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
    ( sP42
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( sP30
    | ~ sP42 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(57,plain,
    ( sP20
    | ~ sP30 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).

thf(58,plain,
    ( ~ sP76
    | ~ sP72
    | ~ sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
    ~ sP21,
    inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
    ( sP7
    | ~ sP24
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( sP33
    | sP8
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
    ( sP15
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).

thf(63,plain,
    ( sP23
    | ~ sP33 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).

thf(64,plain,
    ( ~ sP61
    | sP60
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP73
    | sP28
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(66,plain,
    ( sP74
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(67,plain,
    ( sP48
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
    ( ~ sP70
    | sP65 ),
    inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
    ( sP54
    | sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
    ( sP54
    | sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
    ( sP9
    | ~ sP74 ),
    inference(prop_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP9
    | ~ sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( sP52
    | sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( sP52
    | ~ sP54 ),
    inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
    ( sP69
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(76,plain,
    ( sP69
    | ~ sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
    ( sP6
    | ~ sP69 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(78,plain,
    ( sP38
    | ~ sP6 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(79,plain,
    ( sP62
    | ~ sP38 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(80,plain,
    ( ~ sP1
    | sP76
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(81,plain,
    ( ~ sP66
    | sP1
    | ~ sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(82,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,h3]) ).

thf(83,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[82,h2]) ).

thf(84,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[83,h1]) ).

thf(85,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[84,h0]) ).

thf(0,theorem,
    ~ sP66,
    inference(contra,[status(thm),contra(discharge,[h3])],[82,h3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV261^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Mar 26 14:44:31 EDT 2021
% 0.13/0.34  % CPUTime  : 
% 26.02/26.34  % SZS status Theorem
% 26.02/26.34  % Mode: mode454
% 26.02/26.34  % Inferences: 790
% 26.02/26.34  % SZS output start Proof
% See solution above
% 26.02/26.34  % SZS output end Proof
%------------------------------------------------------------------------------