TSTP Solution File: SEV150^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV150^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n002.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 : Thu Aug 31 19:32:45 EDT 2023

% Result   : Theorem 5.74s 5.89s
% Output   : Proof 5.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  300
% Syntax   : Number of formulae    :  337 (  56 unt;  25 typ;  18 def)
%            Number of atoms       :  950 (  27 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 2912 ( 761   ~; 156   |;   0   &;1131   @)
%                                         ( 129 <=>; 735  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  127 ( 127   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  157 ( 155 usr; 148 con; 0-2 aty)
%            Number of variables   :  512 (  42   ^; 470   !;   0   ?; 512   :)

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

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

thf(ty_eigen__5,type,
    eigen__5: a ).

thf(ty_eigen__113,type,
    eigen__113: a ).

thf(ty_eigen__112,type,
    eigen__112: a ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__51,type,
    eigen__51: a > $o ).

thf(ty_eigen__110,type,
    eigen__110: a ).

thf(ty_eigen__111,type,
    eigen__111: a ).

thf(ty_eigen__114,type,
    eigen__114: a ).

thf(ty_eigen__4,type,
    eigen__4: a > $o ).

thf(ty_eigen__115,type,
    eigen__115: a ).

thf(ty_eigen__17,type,
    eigen__17: a > $o ).

thf(ty_eigen__105,type,
    eigen__105: a ).

thf(ty_eigen__7,type,
    eigen__7: a ).

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

thf(ty_eigen__116,type,
    eigen__116: a ).

thf(ty_eigen__6,type,
    eigen__6: a ).

thf(ty_eigen__119,type,
    eigen__119: a ).

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

thf(ty_eigen__109,type,
    eigen__109: a ).

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(ty_eigen__50,type,
    eigen__50: a > $o ).

thf(ty_eigen__106,type,
    eigen__106: a ).

thf(ty_eigen__16,type,
    eigen__16: a > $o ).

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

thf(eigendef_eigen__106,definition,
    ( eigen__106
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__0 @ eigen__2 @ X1 )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__106])]) ).

thf(eigendef_eigen__110,definition,
    ( eigen__110
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ~ ( ( eigen__77 @ X1 )
                 => ~ ( eigen__0 @ X1 @ X2 ) )
             => ( eigen__77 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__110])]) ).

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

thf(eigendef_eigen__17,definition,
    ( eigen__17
    = ( eps__1
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: a] :
                    ( ( eigen__1 @ eigen__2 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__1 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__17])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ~ ( ( eigen__4 @ X1 )
                 => ~ ( ~ ( eigen__0 @ X1 @ X2 )
                     => ( eigen__1 @ X1 @ X2 ) ) )
             => ( eigen__4 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__119,definition,
    ( eigen__119
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__1 @ eigen__114 @ X1 )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__119])]) ).

thf(eigendef_eigen__116,definition,
    ( eigen__116
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__0 @ eigen__114 @ X1 )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__116])]) ).

thf(eigendef_eigen__114,definition,
    ( eigen__114
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ~ ( ( eigen__77 @ X1 )
                 => ~ ( ~ ! [X3: a > $o] :
                            ( ~ ( ! [X4: a] :
                                    ( ( eigen__0 @ X1 @ X4 )
                                   => ( X3 @ X4 ) )
                               => ~ ! [X4: a,X5: a] :
                                      ( ~ ( ( X3 @ X4 )
                                         => ~ ( eigen__0 @ X4 @ X5 ) )
                                     => ( X3 @ X5 ) ) )
                           => ( X3 @ X2 ) )
                     => ! [X3: a > $o] :
                          ( ~ ( ! [X4: a] :
                                  ( ( eigen__1 @ X1 @ X4 )
                                 => ( X3 @ X4 ) )
                             => ~ ! [X4: a,X5: a] :
                                    ( ~ ( ( X3 @ X4 )
                                       => ~ ( eigen__1 @ X4 @ X5 ) )
                                   => ( X3 @ X5 ) ) )
                         => ( X3 @ X2 ) ) ) )
             => ( eigen__77 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__114])]) ).

thf(eigendef_eigen__50,definition,
    ( eigen__50
    = ( eps__1
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: a] :
                    ( ( eigen__0 @ eigen__6 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__0 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__50])]) ).

thf(eigendef_eigen__109,definition,
    ( eigen__109
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ~ ( ( eigen__77 @ X1 )
                 => ~ ( eigen__1 @ X1 @ X2 ) )
             => ( eigen__77 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__109])]) ).

thf(eigendef_eigen__115,definition,
    ( eigen__115
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ~ ( ( eigen__77 @ eigen__114 )
               => ~ ( ~ ! [X2: a > $o] :
                          ( ~ ( ! [X3: a] :
                                  ( ( eigen__0 @ eigen__114 @ X3 )
                                 => ( X2 @ X3 ) )
                             => ~ ! [X3: a,X4: a] :
                                    ( ~ ( ( X2 @ X3 )
                                       => ~ ( eigen__0 @ X3 @ X4 ) )
                                   => ( X2 @ X4 ) ) )
                         => ( X2 @ X1 ) )
                   => ! [X2: a > $o] :
                        ( ~ ( ! [X3: a] :
                                ( ( eigen__1 @ eigen__114 @ X3 )
                               => ( X2 @ X3 ) )
                           => ~ ! [X3: a,X4: a] :
                                  ( ~ ( ( X2 @ X3 )
                                     => ~ ( eigen__1 @ X3 @ X4 ) )
                                 => ( X2 @ X4 ) ) )
                       => ( X2 @ X1 ) ) ) )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__115])]) ).

thf(eigendef_eigen__105,definition,
    ( eigen__105
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__1 @ eigen__2 @ X1 )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__105])]) ).

thf(eigendef_eigen__16,definition,
    ( eigen__16
    = ( eps__1
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: a] :
                    ( ( eigen__0 @ eigen__2 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__0 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__16])]) ).

thf(eigendef_eigen__112,definition,
    ( eigen__112
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ~ ( ( eigen__77 @ eigen__110 )
               => ~ ( eigen__0 @ eigen__110 @ X1 ) )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__112])]) ).

thf(eigendef_eigen__51,definition,
    ( eigen__51
    = ( eps__1
      @ ^ [X1: a > $o] :
          ~ ( ~ ( ! [X2: a] :
                    ( ( eigen__1 @ eigen__6 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__1 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__51])]) ).

thf(eigendef_eigen__113,definition,
    ( eigen__113
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ~ ! [X2: a > $o] :
                    ( ~ ( ! [X3: a] :
                            ( ( eigen__0 @ eigen__2 @ X3 )
                           => ( X2 @ X3 ) )
                       => ~ ! [X3: a,X4: a] :
                              ( ~ ( ( X2 @ X3 )
                                 => ~ ( eigen__0 @ X3 @ X4 ) )
                             => ( X2 @ X4 ) ) )
                   => ( X2 @ X1 ) )
             => ! [X2: a > $o] :
                  ( ~ ( ! [X3: a] :
                          ( ( eigen__1 @ eigen__2 @ X3 )
                         => ( X2 @ X3 ) )
                     => ~ ! [X3: a,X4: a] :
                            ( ~ ( ( X2 @ X3 )
                               => ~ ( eigen__1 @ X3 @ X4 ) )
                           => ( X2 @ X4 ) ) )
                 => ( X2 @ X1 ) ) )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__113])]) ).

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ~ ( ( eigen__4 @ eigen__6 )
               => ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
                   => ( eigen__1 @ eigen__6 @ X1 ) ) )
           => ( eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
             => ( eigen__1 @ eigen__2 @ X1 ) )
           => ( eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(eigendef_eigen__111,definition,
    ( eigen__111
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ~ ( ( eigen__77 @ eigen__109 )
               => ~ ( eigen__1 @ eigen__109 @ X1 ) )
           => ( eigen__77 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__111])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__4 @ X1 )
           => ~ ( ~ ! [X3: a > $o] :
                      ( ~ ( ! [X4: a] :
                              ( ( eigen__0 @ X1 @ X4 )
                             => ( X3 @ X4 ) )
                         => ~ ! [X4: a,X5: a] :
                                ( ~ ( ( X3 @ X4 )
                                   => ~ ( eigen__0 @ X4 @ X5 ) )
                               => ( X3 @ X5 ) ) )
                     => ( X3 @ X2 ) )
               => ! [X3: a > $o] :
                    ( ~ ( ! [X4: a] :
                            ( ( eigen__1 @ X1 @ X4 )
                           => ( X3 @ X4 ) )
                       => ~ ! [X4: a,X5: a] :
                              ( ~ ( ( X3 @ X4 )
                                 => ~ ( eigen__1 @ X4 @ X5 ) )
                             => ( X3 @ X5 ) ) )
                   => ( X3 @ X2 ) ) ) )
       => ( eigen__4 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ( ! [X1: a] :
              ( ( ~ ! [X2: a > $o] :
                      ( ~ ( ! [X3: a] :
                              ( ( eigen__0 @ eigen__2 @ X3 )
                             => ( X2 @ X3 ) )
                         => ~ ! [X3: a,X4: a] :
                                ( ~ ( ( X2 @ X3 )
                                   => ~ ( eigen__0 @ X3 @ X4 ) )
                               => ( X2 @ X4 ) ) )
                     => ( X2 @ X1 ) )
               => ! [X2: a > $o] :
                    ( ~ ( ! [X3: a] :
                            ( ( eigen__1 @ eigen__2 @ X3 )
                           => ( X2 @ X3 ) )
                       => ~ ! [X3: a,X4: a] :
                              ( ~ ( ( X2 @ X3 )
                                 => ~ ( eigen__1 @ X3 @ X4 ) )
                             => ( X2 @ X4 ) ) )
                   => ( X2 @ X1 ) ) )
             => ( eigen__77 @ X1 ) )
         => ~ ! [X1: a,X2: a] :
                ( ~ ( ( eigen__77 @ X1 )
                   => ~ ( ~ ! [X3: a > $o] :
                              ( ~ ( ! [X4: a] :
                                      ( ( eigen__0 @ X1 @ X4 )
                                     => ( X3 @ X4 ) )
                                 => ~ ! [X4: a,X5: a] :
                                        ( ~ ( ( X3 @ X4 )
                                           => ~ ( eigen__0 @ X4 @ X5 ) )
                                       => ( X3 @ X5 ) ) )
                             => ( X3 @ X2 ) )
                       => ! [X3: a > $o] :
                            ( ~ ( ! [X4: a] :
                                    ( ( eigen__1 @ X1 @ X4 )
                                   => ( X3 @ X4 ) )
                               => ~ ! [X4: a,X5: a] :
                                      ( ~ ( ( X3 @ X4 )
                                         => ~ ( eigen__1 @ X4 @ X5 ) )
                                     => ( X3 @ X5 ) ) )
                           => ( X3 @ X2 ) ) ) )
               => ( eigen__77 @ X2 ) ) )
     => ( eigen__77 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__77 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__77 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__1 @ eigen__2 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a] :
        ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
         => ( eigen__1 @ eigen__2 @ X1 ) )
       => ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__16 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ! [X1: a] :
          ( ( eigen__0 @ eigen__2 @ X1 )
         => ( eigen__77 @ X1 ) )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__77 @ eigen__113 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ! [X1: a] :
          ( ( eigen__0 @ eigen__114 @ X1 )
         => ( eigen__77 @ X1 ) )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: a] :
        ( ~ ( ( eigen__4 @ eigen__6 )
           => ~ ( ~ ! [X2: a > $o] :
                      ( ~ ( ! [X3: a] :
                              ( ( eigen__0 @ eigen__6 @ X3 )
                             => ( X2 @ X3 ) )
                         => ~ ! [X3: a,X4: a] :
                                ( ~ ( ( X2 @ X3 )
                                   => ~ ( eigen__0 @ X3 @ X4 ) )
                               => ( X2 @ X4 ) ) )
                     => ( X2 @ X1 ) )
               => ! [X2: a > $o] :
                    ( ~ ( ! [X3: a] :
                            ( ( eigen__1 @ eigen__6 @ X3 )
                           => ( X2 @ X3 ) )
                       => ~ ! [X3: a,X4: a] :
                              ( ~ ( ( X2 @ X3 )
                                 => ~ ( eigen__1 @ X3 @ X4 ) )
                             => ( X2 @ X4 ) ) )
                   => ( X2 @ X1 ) ) ) )
       => ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ~ ( eigen__0 @ eigen__2 @ eigen__5 )
     => ( eigen__1 @ eigen__2 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( eigen__4 @ eigen__6 )
     => ~ ( ~ ! [X1: a > $o] :
                ( ~ ( ! [X2: a] :
                        ( ( eigen__0 @ eigen__6 @ X2 )
                       => ( X1 @ X2 ) )
                   => ~ ! [X2: a,X3: a] :
                          ( ~ ( ( X1 @ X2 )
                             => ~ ( eigen__0 @ X2 @ X3 ) )
                         => ( X1 @ X3 ) ) )
               => ( X1 @ eigen__7 ) )
         => ! [X1: a > $o] :
              ( ~ ( ! [X2: a] :
                      ( ( eigen__1 @ eigen__6 @ X2 )
                     => ( X1 @ X2 ) )
                 => ~ ! [X2: a,X3: a] :
                        ( ~ ( ( X1 @ X2 )
                           => ~ ( eigen__1 @ X2 @ X3 ) )
                       => ( X1 @ X3 ) ) )
             => ( X1 @ eigen__7 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a] :
        ( ~ ( ( eigen__77 @ eigen__109 )
           => ~ ( ~ ( eigen__0 @ eigen__109 @ X1 )
               => ( eigen__1 @ eigen__109 @ X1 ) ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__1 @ eigen__109 @ eigen__111 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: a] :
        ( ( eigen__0 @ eigen__6 @ X1 )
       => ( eigen__50 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: a] :
        ( ( eigen__0 @ eigen__114 @ X1 )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ! [X1: a] :
          ( ( ~ ! [X2: a > $o] :
                  ( ~ ( ! [X3: a] :
                          ( ( eigen__0 @ eigen__2 @ X3 )
                         => ( X2 @ X3 ) )
                     => ~ ! [X3: a,X4: a] :
                            ( ~ ( ( X2 @ X3 )
                               => ~ ( eigen__0 @ X3 @ X4 ) )
                           => ( X2 @ X4 ) ) )
                 => ( X2 @ X1 ) )
           => ! [X2: a > $o] :
                ( ~ ( ! [X3: a] :
                        ( ( eigen__1 @ eigen__2 @ X3 )
                       => ( X2 @ X3 ) )
                   => ~ ! [X3: a,X4: a] :
                          ( ~ ( ( X2 @ X3 )
                             => ~ ( eigen__1 @ X3 @ X4 ) )
                         => ( X2 @ X4 ) ) )
               => ( X2 @ X1 ) ) )
         => ( eigen__77 @ X1 ) )
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__77 @ X1 )
               => ~ ( ~ ! [X3: a > $o] :
                          ( ~ ( ! [X4: a] :
                                  ( ( eigen__0 @ X1 @ X4 )
                                 => ( X3 @ X4 ) )
                             => ~ ! [X4: a,X5: a] :
                                    ( ~ ( ( X3 @ X4 )
                                       => ~ ( eigen__0 @ X4 @ X5 ) )
                                   => ( X3 @ X5 ) ) )
                         => ( X3 @ X2 ) )
                   => ! [X3: a > $o] :
                        ( ~ ( ! [X4: a] :
                                ( ( eigen__1 @ X1 @ X4 )
                               => ( X3 @ X4 ) )
                           => ~ ! [X4: a,X5: a] :
                                  ( ~ ( ( X3 @ X4 )
                                     => ~ ( eigen__1 @ X4 @ X5 ) )
                                 => ( X3 @ X5 ) ) )
                       => ( X3 @ X2 ) ) ) )
           => ( eigen__77 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( eigen__0 @ eigen__114 @ eigen__116 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ~ ( ! [X1: a] :
              ( ( eigen__1 @ eigen__2 @ X1 )
             => ( eigen__17 @ X1 ) )
         => ~ ! [X1: a,X2: a] :
                ( ~ ( ( eigen__17 @ X1 )
                   => ~ ( eigen__1 @ X1 @ X2 ) )
               => ( eigen__17 @ X2 ) ) )
     => ( eigen__17 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__77 @ X1 )
           => ~ ( eigen__1 @ X1 @ X2 ) )
       => ( eigen__77 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( ~ ( eigen__0 @ eigen__2 @ eigen__106 )
       => ( eigen__1 @ eigen__2 @ eigen__106 ) )
     => ( eigen__77 @ eigen__106 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ~ ( eigen__0 @ eigen__2 @ eigen__105 )
     => ( eigen__1 @ eigen__2 @ eigen__105 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ ( ! [X1: a] :
              ( ( eigen__1 @ eigen__114 @ X1 )
             => ( eigen__77 @ X1 ) )
         => ~ sP21 )
     => ( eigen__77 @ eigen__115 ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eigen__1 @ eigen__2 @ eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: a] :
        ( ~ ( ( eigen__77 @ eigen__109 )
           => ~ ( eigen__1 @ eigen__109 @ X1 ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: a] :
        ( ~ ( ( eigen__77 @ eigen__114 )
           => ~ ( ~ ( eigen__0 @ eigen__114 @ X1 )
               => ( eigen__1 @ eigen__114 @ X1 ) ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: a] :
        ( ~ ( ( eigen__77 @ eigen__110 )
           => ~ ( eigen__0 @ eigen__110 @ X1 ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ~ ( sP6
         => ~ ! [X1: a,X2: a] :
                ( ~ ( ( eigen__4 @ X1 )
                   => ~ ( ~ ( eigen__0 @ X1 @ X2 )
                       => ( eigen__1 @ X1 @ X2 ) ) )
               => ( eigen__4 @ X2 ) ) )
     => ( eigen__4 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ( eigen__1 @ eigen__2 @ eigen__5 )
     => ( eigen__17 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ! [X1: a] :
          ( ( eigen__1 @ eigen__114 @ X1 )
         => ( eigen__77 @ X1 ) )
     => ~ sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__6 @ X1 )
       => ( eigen__51 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ( eigen__77 @ eigen__109 )
     => ~ sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__1 @ eigen__114 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__115 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ~ ! [X1: a > $o] :
            ( ~ ( ! [X2: a] :
                    ( ( eigen__0 @ eigen__2 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__0 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__5 ) )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( eigen__0 @ eigen__2 @ eigen__106 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( ~ sP10
     => ( eigen__77 @ eigen__115 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( ~ ( ( eigen__77 @ eigen__110 )
         => ~ ( ~ ( eigen__0 @ eigen__110 @ eigen__112 )
             => ( eigen__1 @ eigen__110 @ eigen__112 ) ) )
     => ( eigen__77 @ eigen__112 ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ( eigen__77 @ eigen__114 )
     => ~ ( ~ sP19
         => ( eigen__1 @ eigen__114 @ eigen__116 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__77 @ X1 )
           => ~ ( ~ ( eigen__0 @ X1 @ X2 )
               => ( eigen__1 @ X1 @ X2 ) ) )
       => ( eigen__77 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( eigen__17 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( sP6
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__4 @ X1 )
               => ~ ( ~ ( eigen__0 @ X1 @ X2 )
                   => ( eigen__1 @ X1 @ X2 ) ) )
           => ( eigen__4 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__0 @ eigen__6 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__0 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( ( eigen__77 @ eigen__109 )
     => ~ ( ~ ( eigen__0 @ eigen__109 @ eigen__111 )
         => sP15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( ~ sP44
     => ( eigen__77 @ eigen__111 ) ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( sP23
     => ( eigen__77 @ eigen__105 ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( ! [X1: a] :
          ( ( eigen__0 @ eigen__2 @ X1 )
         => ( eigen__16 @ X1 ) )
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__16 @ X1 )
               => ~ ( eigen__0 @ X1 @ X2 ) )
           => ( eigen__16 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( ( eigen__0 @ eigen__2 @ eigen__5 )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__1 @ eigen__6 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( eigen__51 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( ~ ( ( eigen__77 @ eigen__114 )
         => ~ ( ~ ! [X1: a > $o] :
                    ( ~ ( ! [X2: a] :
                            ( ( eigen__0 @ eigen__114 @ X2 )
                           => ( X1 @ X2 ) )
                       => ~ ! [X2: a,X3: a] :
                              ( ~ ( ( X1 @ X2 )
                                 => ~ ( eigen__0 @ X2 @ X3 ) )
                             => ( X1 @ X3 ) ) )
                   => ( X1 @ eigen__115 ) )
             => sP34 ) )
     => ( eigen__77 @ eigen__115 ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( eigen__77 @ eigen__116 ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( eigen__4 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( ~ ! [X1: a > $o] :
            ( ~ ( ! [X2: a] :
                    ( ( eigen__0 @ eigen__114 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__0 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__115 ) )
     => sP34 ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( ( eigen__1 @ eigen__114 @ eigen__119 )
     => ( eigen__77 @ eigen__119 ) ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( ~ sP2
     => ( eigen__1 @ eigen__6 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( ~ sP43
     => sP49 ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ( eigen__77 @ eigen__106 ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( ~ sP39
     => sP52 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( sP36
     => sP58 ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ( ~ ! [X1: a > $o] :
            ( ~ ( ! [X2: a] :
                    ( ( eigen__0 @ eigen__2 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ! [X2: a,X3: a] :
                      ( ~ ( ( X1 @ X2 )
                         => ~ ( eigen__0 @ X2 @ X3 ) )
                     => ( X1 @ X3 ) ) )
           => ( X1 @ eigen__113 ) )
     => ! [X1: a > $o] :
          ( ~ ( ! [X2: a] :
                  ( ( eigen__1 @ eigen__2 @ X2 )
                 => ( X1 @ X2 ) )
             => ~ ! [X2: a,X3: a] :
                    ( ~ ( ( X1 @ X2 )
                       => ~ ( eigen__1 @ X2 @ X3 ) )
                   => ( X1 @ X3 ) ) )
         => ( X1 @ eigen__113 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ( eigen__1 @ eigen__2 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( eigen__77 @ eigen__115 ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__0 @ eigen__2 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__0 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__113 ) ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ( sP12
     => ( eigen__4 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( ~ sP19
     => ( eigen__1 @ eigen__114 @ eigen__116 ) ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ( sP25
     => ( eigen__77 @ eigen__105 ) ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ! [X1: a] :
        ( ~ ( ( eigen__77 @ eigen__110 )
           => ~ ( ~ ( eigen__0 @ eigen__110 @ X1 )
               => ( eigen__1 @ eigen__110 @ X1 ) ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ( eigen__4 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ( eigen__77 @ eigen__105 ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__1 @ eigen__2 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__113 ) ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ( ~ ( eigen__0 @ eigen__114 @ eigen__119 )
     => ( eigen__1 @ eigen__114 @ eigen__119 ) ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ! [X1: a] :
        ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
         => ( eigen__1 @ eigen__2 @ X1 ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ( ~ sP8
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ( eigen__77 @ eigen__109 ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ( eigen__0 @ eigen__110 @ eigen__112 ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
    ( sP77
  <=> ( ~ sP13
     => sP53 ) ),
    introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(sP78,plain,
    ( sP78
  <=> ( eigen__1 @ eigen__6 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP78])]) ).

thf(sP79,plain,
    ( sP79
  <=> ( ( eigen__4 @ eigen__6 )
     => ~ sP56 ) ),
    introduced(definition,[new_symbols(definition,[sP79])]) ).

thf(sP80,plain,
    ( sP80
  <=> ! [X1: a] :
        ( ( ~ ! [X2: a > $o] :
                ( ~ ( ! [X3: a] :
                        ( ( eigen__0 @ eigen__2 @ X3 )
                       => ( X2 @ X3 ) )
                   => ~ ! [X3: a,X4: a] :
                          ( ~ ( ( X2 @ X3 )
                             => ~ ( eigen__0 @ X3 @ X4 ) )
                         => ( X2 @ X4 ) ) )
               => ( X2 @ X1 ) )
         => ! [X2: a > $o] :
              ( ~ ( ! [X3: a] :
                      ( ( eigen__1 @ eigen__2 @ X3 )
                     => ( X2 @ X3 ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ~ ( ( X2 @ X3 )
                           => ~ ( eigen__1 @ X3 @ X4 ) )
                       => ( X2 @ X4 ) ) )
             => ( X2 @ X1 ) ) )
       => ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP80])]) ).

thf(sP81,plain,
    ( sP81
  <=> ( ~ sP47
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP81])]) ).

thf(sP82,plain,
    ( sP82
  <=> ! [X1: a] :
        ( ( eigen__0 @ eigen__2 @ X1 )
       => ( eigen__16 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP82])]) ).

thf(sP83,plain,
    ( sP83
  <=> ( ( eigen__77 @ eigen__114 )
     => ~ sP72 ) ),
    introduced(definition,[new_symbols(definition,[sP83])]) ).

thf(sP84,plain,
    ( sP84
  <=> ( ( eigen__77 @ eigen__114 )
     => ~ sP54 ) ),
    introduced(definition,[new_symbols(definition,[sP84])]) ).

thf(sP85,plain,
    ( sP85
  <=> ( eigen__4 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP85])]) ).

thf(sP86,plain,
    ( sP86
  <=> ( sP16
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__50 @ X1 )
               => ~ ( eigen__0 @ X1 @ X2 ) )
           => ( eigen__50 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP86])]) ).

thf(sP87,plain,
    ( sP87
  <=> ( eigen__77 @ eigen__119 ) ),
    introduced(definition,[new_symbols(definition,[sP87])]) ).

thf(sP88,plain,
    ( sP88
  <=> ( sP2
     => ( eigen__50 @ eigen__7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP88])]) ).

thf(sP89,plain,
    ( sP89
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__2 @ X1 )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP89])]) ).

thf(sP90,plain,
    ( sP90
  <=> ( ~ sP36
     => ( eigen__1 @ eigen__2 @ eigen__106 ) ) ),
    introduced(definition,[new_symbols(definition,[sP90])]) ).

thf(sP91,plain,
    ( sP91
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__77 @ X1 )
           => ~ ( ~ ! [X3: a > $o] :
                      ( ~ ( ! [X4: a] :
                              ( ( eigen__0 @ X1 @ X4 )
                             => ( X3 @ X4 ) )
                         => ~ ! [X4: a,X5: a] :
                                ( ~ ( ( X3 @ X4 )
                                   => ~ ( eigen__0 @ X4 @ X5 ) )
                               => ( X3 @ X5 ) ) )
                     => ( X3 @ X2 ) )
               => ! [X3: a > $o] :
                    ( ~ ( ! [X4: a] :
                            ( ( eigen__1 @ X1 @ X4 )
                           => ( X3 @ X4 ) )
                       => ~ ! [X4: a,X5: a] :
                              ( ~ ( ( X3 @ X4 )
                                 => ~ ( eigen__1 @ X4 @ X5 ) )
                             => ( X3 @ X5 ) ) )
                   => ( X3 @ X2 ) ) ) )
       => ( eigen__77 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP91])]) ).

thf(sP92,plain,
    ( sP92
  <=> ( ~ ( eigen__0 @ eigen__109 @ eigen__111 )
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP92])]) ).

thf(sP93,plain,
    ( sP93
  <=> ( eigen__77 @ eigen__112 ) ),
    introduced(definition,[new_symbols(definition,[sP93])]) ).

thf(sP94,plain,
    ( sP94
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__0 @ eigen__2 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__0 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP94])]) ).

thf(sP95,plain,
    ( sP95
  <=> ( sP35
     => sP69 ) ),
    introduced(definition,[new_symbols(definition,[sP95])]) ).

thf(sP96,plain,
    ( sP96
  <=> ( eigen__50 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP96])]) ).

thf(sP97,plain,
    ( sP97
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__4 @ X1 )
           => ~ ( ~ ( eigen__0 @ X1 @ X2 )
               => ( eigen__1 @ X1 @ X2 ) ) )
       => ( eigen__4 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP97])]) ).

thf(sP98,plain,
    ( sP98
  <=> ( sP61
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP98])]) ).

thf(sP99,plain,
    ( sP99
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( eigen__0 @ eigen__114 @ X2 )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( eigen__0 @ X2 @ X3 ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__115 ) ) ),
    introduced(definition,[new_symbols(definition,[sP99])]) ).

thf(sP100,plain,
    ( sP100
  <=> ( eigen__0 @ eigen__2 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP100])]) ).

thf(sP101,plain,
    ( sP101
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( ~ ! [X3: a > $o] :
                        ( ~ ( ! [X4: a] :
                                ( ( eigen__0 @ eigen__2 @ X4 )
                               => ( X3 @ X4 ) )
                           => ~ ! [X4: a,X5: a] :
                                  ( ~ ( ( X3 @ X4 )
                                     => ~ ( eigen__0 @ X4 @ X5 ) )
                                 => ( X3 @ X5 ) ) )
                       => ( X3 @ X2 ) )
                 => ! [X3: a > $o] :
                      ( ~ ( ! [X4: a] :
                              ( ( eigen__1 @ eigen__2 @ X4 )
                             => ( X3 @ X4 ) )
                         => ~ ! [X4: a,X5: a] :
                                ( ~ ( ( X3 @ X4 )
                                   => ~ ( eigen__1 @ X4 @ X5 ) )
                               => ( X3 @ X5 ) ) )
                     => ( X3 @ X2 ) ) )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( ~ ! [X4: a > $o] :
                                ( ~ ( ! [X5: a] :
                                        ( ( eigen__0 @ X2 @ X5 )
                                       => ( X4 @ X5 ) )
                                   => ~ ! [X5: a,X6: a] :
                                          ( ~ ( ( X4 @ X5 )
                                             => ~ ( eigen__0 @ X5 @ X6 ) )
                                         => ( X4 @ X6 ) ) )
                               => ( X4 @ X3 ) )
                         => ! [X4: a > $o] :
                              ( ~ ( ! [X5: a] :
                                      ( ( eigen__1 @ X2 @ X5 )
                                     => ( X4 @ X5 ) )
                                 => ~ ! [X5: a,X6: a] :
                                        ( ~ ( ( X4 @ X5 )
                                           => ~ ( eigen__1 @ X5 @ X6 ) )
                                       => ( X4 @ X6 ) ) )
                             => ( X4 @ X3 ) ) ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP101])]) ).

thf(sP102,plain,
    ( sP102
  <=> ( ! [X1: a] :
          ( ( eigen__1 @ eigen__2 @ X1 )
         => ( eigen__17 @ X1 ) )
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__17 @ X1 )
               => ~ ( eigen__1 @ X1 @ X2 ) )
           => ( eigen__17 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP102])]) ).

thf(sP103,plain,
    ( sP103
  <=> ( eigen__77 @ eigen__110 ) ),
    introduced(definition,[new_symbols(definition,[sP103])]) ).

thf(sP104,plain,
    ( sP104
  <=> ( eigen__77 @ eigen__114 ) ),
    introduced(definition,[new_symbols(definition,[sP104])]) ).

thf(sP105,plain,
    ( sP105
  <=> ! [X1: a] :
        ( ( ~ ! [X2: a > $o] :
                ( ~ ( ! [X3: a] :
                        ( ( eigen__0 @ eigen__2 @ X3 )
                       => ( X2 @ X3 ) )
                   => ~ ! [X3: a,X4: a] :
                          ( ~ ( ( X2 @ X3 )
                             => ~ ( eigen__0 @ X3 @ X4 ) )
                         => ( X2 @ X4 ) ) )
               => ( X2 @ X1 ) )
         => ! [X2: a > $o] :
              ( ~ ( ! [X3: a] :
                      ( ( eigen__1 @ eigen__2 @ X3 )
                     => ( X2 @ X3 ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ~ ( ( X2 @ X3 )
                           => ~ ( eigen__1 @ X3 @ X4 ) )
                       => ( X2 @ X4 ) ) )
             => ( X2 @ X1 ) ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP105])]) ).

thf(sP106,plain,
    ( sP106
  <=> ( ~ sP79
     => sP53 ) ),
    introduced(definition,[new_symbols(definition,[sP106])]) ).

thf(sP107,plain,
    ( sP107
  <=> ( ~ sP86
     => sP96 ) ),
    introduced(definition,[new_symbols(definition,[sP107])]) ).

thf(sP108,plain,
    ( sP108
  <=> ( eigen__77 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP108])]) ).

thf(sP109,plain,
    ( sP109
  <=> ! [X1: a] :
        ( ~ ( sP104
           => ~ ( ~ ! [X2: a > $o] :
                      ( ~ ( ! [X3: a] :
                              ( ( eigen__0 @ eigen__114 @ X3 )
                             => ( X2 @ X3 ) )
                         => ~ ! [X3: a,X4: a] :
                                ( ~ ( ( X2 @ X3 )
                                   => ~ ( eigen__0 @ X3 @ X4 ) )
                               => ( X2 @ X4 ) ) )
                     => ( X2 @ X1 ) )
               => ! [X2: a > $o] :
                    ( ~ ( ! [X3: a] :
                            ( ( eigen__1 @ eigen__114 @ X3 )
                           => ( X2 @ X3 ) )
                       => ~ ! [X3: a,X4: a] :
                              ( ~ ( ( X2 @ X3 )
                                 => ~ ( eigen__1 @ X3 @ X4 ) )
                             => ( X2 @ X4 ) ) )
                   => ( X2 @ X1 ) ) ) )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP109])]) ).

thf(sP110,plain,
    ( sP110
  <=> ( ~ sP83
     => sP87 ) ),
    introduced(definition,[new_symbols(definition,[sP110])]) ).

thf(sP111,plain,
    ( sP111
  <=> ! [X1: a] :
        ( ~ ( ( eigen__4 @ eigen__6 )
           => ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
               => ( eigen__1 @ eigen__6 @ X1 ) ) )
       => ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP111])]) ).

thf(sP112,plain,
    ( sP112
  <=> ( sP103
     => ~ ( ~ sP76
         => ( eigen__1 @ eigen__110 @ eigen__112 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP112])]) ).

thf(sP113,plain,
    ( sP113
  <=> ( sP78
     => sP50 ) ),
    introduced(definition,[new_symbols(definition,[sP113])]) ).

thf(sP114,plain,
    ( sP114
  <=> ( ~ sP33
     => ( eigen__77 @ eigen__111 ) ) ),
    introduced(definition,[new_symbols(definition,[sP114])]) ).

thf(sP115,plain,
    ( sP115
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__114 @ X1 )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP115])]) ).

thf(sP116,plain,
    ( sP116
  <=> ! [X1: a > $o] :
        ( ~ ( ! [X2: a] :
                ( ( ~ ( eigen__0 @ eigen__2 @ X2 )
                 => ( eigen__1 @ eigen__2 @ X2 ) )
               => ( X1 @ X2 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ~ ( ( X1 @ X2 )
                     => ~ ( ~ ( eigen__0 @ X2 @ X3 )
                         => ( eigen__1 @ X2 @ X3 ) ) )
                 => ( X1 @ X3 ) ) )
       => ( X1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP116])]) ).

thf(sP117,plain,
    ( sP117
  <=> ! [X1: a] :
        ( ( eigen__0 @ eigen__2 @ X1 )
       => ( eigen__77 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP117])]) ).

thf(sP118,plain,
    ( sP118
  <=> ( sP19
     => sP52 ) ),
    introduced(definition,[new_symbols(definition,[sP118])]) ).

thf(sP119,plain,
    ( sP119
  <=> ( eigen__77 @ eigen__111 ) ),
    introduced(definition,[new_symbols(definition,[sP119])]) ).

thf(sP120,plain,
    ( sP120
  <=> ( ~ ( sP32
         => ~ ! [X1: a,X2: a] :
                ( ~ ( ( eigen__51 @ X1 )
                   => ~ ( eigen__1 @ X1 @ X2 ) )
               => ( eigen__51 @ X2 ) ) )
     => sP50 ) ),
    introduced(definition,[new_symbols(definition,[sP120])]) ).

thf(sP121,plain,
    ( sP121
  <=> ( sP32
     => ~ ! [X1: a,X2: a] :
            ( ~ ( ( eigen__51 @ X1 )
               => ~ ( eigen__1 @ X1 @ X2 ) )
           => ( eigen__51 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP121])]) ).

thf(sP122,plain,
    ( sP122
  <=> ( eigen__1 @ eigen__114 @ eigen__119 ) ),
    introduced(definition,[new_symbols(definition,[sP122])]) ).

thf(sP123,plain,
    ( sP123
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__2 @ X1 )
       => ( eigen__17 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP123])]) ).

thf(sP124,plain,
    ( sP124
  <=> ( ~ ( sP89
         => ~ sP21 )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP124])]) ).

thf(sP125,plain,
    ( sP125
  <=> ( ~ sP76
     => ( eigen__1 @ eigen__110 @ eigen__112 ) ) ),
    introduced(definition,[new_symbols(definition,[sP125])]) ).

thf(sP126,plain,
    ( sP126
  <=> ( eigen__4 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP126])]) ).

thf(sP127,plain,
    ( sP127
  <=> ( ~ ( sP103
         => ~ sP76 )
     => sP93 ) ),
    introduced(definition,[new_symbols(definition,[sP127])]) ).

thf(sP128,plain,
    ( sP128
  <=> ( sP89
     => ~ sP21 ) ),
    introduced(definition,[new_symbols(definition,[sP128])]) ).

thf(sP129,plain,
    ( sP129
  <=> ( sP103
     => ~ sP76 ) ),
    introduced(definition,[new_symbols(definition,[sP129])]) ).

thf(cTHM251A_pme,conjecture,
    ! [X1: a > a > $o,X2: a > a > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > $o] :
            ( ~ ( ! [X6: a] :
                    ( ( ~ ( X1 @ X3 @ X6 )
                     => ( X2 @ X3 @ X6 ) )
                   => ( X5 @ X6 ) )
               => ~ ! [X6: a,X7: a] :
                      ( ~ ( ( X5 @ X6 )
                         => ~ ( ~ ( X1 @ X6 @ X7 )
                             => ( X2 @ X6 @ X7 ) ) )
                     => ( X5 @ X7 ) ) )
           => ( X5 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > $o] :
            ( ~ ( ! [X6: a] :
                    ( ( ~ ! [X7: a > $o] :
                            ( ~ ( ! [X8: a] :
                                    ( ( X1 @ X3 @ X8 )
                                   => ( X7 @ X8 ) )
                               => ~ ! [X8: a,X9: a] :
                                      ( ~ ( ( X7 @ X8 )
                                         => ~ ( X1 @ X8 @ X9 ) )
                                     => ( X7 @ X9 ) ) )
                           => ( X7 @ X6 ) )
                     => ! [X7: a > $o] :
                          ( ~ ( ! [X8: a] :
                                  ( ( X2 @ X3 @ X8 )
                                 => ( X7 @ X8 ) )
                             => ~ ! [X8: a,X9: a] :
                                    ( ~ ( ( X7 @ X8 )
                                       => ~ ( X2 @ X8 @ X9 ) )
                                   => ( X7 @ X9 ) ) )
                         => ( X7 @ X6 ) ) )
                   => ( X5 @ X6 ) )
               => ~ ! [X6: a,X7: a] :
                      ( ~ ( ( X5 @ X6 )
                         => ~ ( ~ ! [X8: a > $o] :
                                    ( ~ ( ! [X9: a] :
                                            ( ( X1 @ X6 @ X9 )
                                           => ( X8 @ X9 ) )
                                       => ~ ! [X9: a,X10: a] :
                                              ( ~ ( ( X8 @ X9 )
                                                 => ~ ( X1 @ X9 @ X10 ) )
                                             => ( X8 @ X10 ) ) )
                                   => ( X8 @ X7 ) )
                             => ! [X8: a > $o] :
                                  ( ~ ( ! [X9: a] :
                                          ( ( X2 @ X6 @ X9 )
                                         => ( X8 @ X9 ) )
                                     => ~ ! [X9: a,X10: a] :
                                            ( ~ ( ( X8 @ X9 )
                                               => ~ ( X2 @ X9 @ X10 ) )
                                           => ( X8 @ X10 ) ) )
                                 => ( X8 @ X7 ) ) ) )
                     => ( X5 @ X7 ) ) )
           => ( X5 @ X4 ) ) ) ) ).

thf(h2,negated_conjecture,
    ~ ! [X1: a > a > $o,X2: a > a > $o] :
        ( ( ^ [X3: a,X4: a] :
            ! [X5: a > $o] :
              ( ~ ( ! [X6: a] :
                      ( ( ~ ( X1 @ X3 @ X6 )
                       => ( X2 @ X3 @ X6 ) )
                     => ( X5 @ X6 ) )
                 => ~ ! [X6: a,X7: a] :
                        ( ~ ( ( X5 @ X6 )
                           => ~ ( ~ ( X1 @ X6 @ X7 )
                               => ( X2 @ X6 @ X7 ) ) )
                       => ( X5 @ X7 ) ) )
             => ( X5 @ X4 ) ) )
        = ( ^ [X3: a,X4: a] :
            ! [X5: a > $o] :
              ( ~ ( ! [X6: a] :
                      ( ( ~ ! [X7: a > $o] :
                              ( ~ ( ! [X8: a] :
                                      ( ( X1 @ X3 @ X8 )
                                     => ( X7 @ X8 ) )
                                 => ~ ! [X8: a,X9: a] :
                                        ( ~ ( ( X7 @ X8 )
                                           => ~ ( X1 @ X8 @ X9 ) )
                                       => ( X7 @ X9 ) ) )
                             => ( X7 @ X6 ) )
                       => ! [X7: a > $o] :
                            ( ~ ( ! [X8: a] :
                                    ( ( X2 @ X3 @ X8 )
                                   => ( X7 @ X8 ) )
                               => ~ ! [X8: a,X9: a] :
                                      ( ~ ( ( X7 @ X8 )
                                         => ~ ( X2 @ X8 @ X9 ) )
                                     => ( X7 @ X9 ) ) )
                           => ( X7 @ X6 ) ) )
                     => ( X5 @ X6 ) )
                 => ~ ! [X6: a,X7: a] :
                        ( ~ ( ( X5 @ X6 )
                           => ~ ( ~ ! [X8: a > $o] :
                                      ( ~ ( ! [X9: a] :
                                              ( ( X1 @ X6 @ X9 )
                                             => ( X8 @ X9 ) )
                                         => ~ ! [X9: a,X10: a] :
                                                ( ~ ( ( X8 @ X9 )
                                                   => ~ ( X1 @ X9 @ X10 ) )
                                               => ( X8 @ X10 ) ) )
                                     => ( X8 @ X7 ) )
                               => ! [X8: a > $o] :
                                    ( ~ ( ! [X9: a] :
                                            ( ( X2 @ X6 @ X9 )
                                           => ( X8 @ X9 ) )
                                       => ~ ! [X9: a,X10: a] :
                                              ( ~ ( ( X8 @ X9 )
                                                 => ~ ( X2 @ X9 @ X10 ) )
                                             => ( X8 @ X10 ) ) )
                                   => ( X8 @ X7 ) ) ) )
                       => ( X5 @ X7 ) ) )
             => ( X5 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM251A_pme]) ).

thf(h3,assumption,
    ~ ! [X1: a > a > $o] :
        ( ( ^ [X2: a,X3: a] :
            ! [X4: a > $o] :
              ( ~ ( ! [X5: a] :
                      ( ( ~ ( eigen__0 @ X2 @ X5 )
                       => ( X1 @ X2 @ X5 ) )
                     => ( X4 @ X5 ) )
                 => ~ ! [X5: a,X6: a] :
                        ( ~ ( ( X4 @ X5 )
                           => ~ ( ~ ( eigen__0 @ X5 @ X6 )
                               => ( X1 @ X5 @ X6 ) ) )
                       => ( X4 @ X6 ) ) )
             => ( X4 @ X3 ) ) )
        = ( ^ [X2: a,X3: a] :
            ! [X4: a > $o] :
              ( ~ ( ! [X5: a] :
                      ( ( ~ ! [X6: a > $o] :
                              ( ~ ( ! [X7: a] :
                                      ( ( eigen__0 @ X2 @ X7 )
                                     => ( X6 @ X7 ) )
                                 => ~ ! [X7: a,X8: a] :
                                        ( ~ ( ( X6 @ X7 )
                                           => ~ ( eigen__0 @ X7 @ X8 ) )
                                       => ( X6 @ X8 ) ) )
                             => ( X6 @ X5 ) )
                       => ! [X6: a > $o] :
                            ( ~ ( ! [X7: a] :
                                    ( ( X1 @ X2 @ X7 )
                                   => ( X6 @ X7 ) )
                               => ~ ! [X7: a,X8: a] :
                                      ( ~ ( ( X6 @ X7 )
                                         => ~ ( X1 @ X7 @ X8 ) )
                                     => ( X6 @ X8 ) ) )
                           => ( X6 @ X5 ) ) )
                     => ( X4 @ X5 ) )
                 => ~ ! [X5: a,X6: a] :
                        ( ~ ( ( X4 @ X5 )
                           => ~ ( ~ ! [X7: a > $o] :
                                      ( ~ ( ! [X8: a] :
                                              ( ( eigen__0 @ X5 @ X8 )
                                             => ( X7 @ X8 ) )
                                         => ~ ! [X8: a,X9: a] :
                                                ( ~ ( ( X7 @ X8 )
                                                   => ~ ( eigen__0 @ X8 @ X9 ) )
                                               => ( X7 @ X9 ) ) )
                                     => ( X7 @ X6 ) )
                               => ! [X7: a > $o] :
                                    ( ~ ( ! [X8: a] :
                                            ( ( X1 @ X5 @ X8 )
                                           => ( X7 @ X8 ) )
                                       => ~ ! [X8: a,X9: a] :
                                              ( ~ ( ( X7 @ X8 )
                                                 => ~ ( X1 @ X8 @ X9 ) )
                                             => ( X7 @ X9 ) ) )
                                   => ( X7 @ X6 ) ) ) )
                       => ( X4 @ X6 ) ) )
             => ( X4 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ( ( ^ [X1: a,X2: a] :
        ! [X3: a > $o] :
          ( ~ ( ! [X4: a] :
                  ( ( ~ ( eigen__0 @ X1 @ X4 )
                   => ( eigen__1 @ X1 @ X4 ) )
                 => ( X3 @ X4 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ~ ( ( X3 @ X4 )
                       => ~ ( ~ ( eigen__0 @ X4 @ X5 )
                           => ( eigen__1 @ X4 @ X5 ) ) )
                   => ( X3 @ X5 ) ) )
         => ( X3 @ X2 ) ) )
   != ( ^ [X1: a,X2: a] :
        ! [X3: a > $o] :
          ( ~ ( ! [X4: a] :
                  ( ( ~ ! [X5: a > $o] :
                          ( ~ ( ! [X6: a] :
                                  ( ( eigen__0 @ X1 @ X6 )
                                 => ( X5 @ X6 ) )
                             => ~ ! [X6: a,X7: a] :
                                    ( ~ ( ( X5 @ X6 )
                                       => ~ ( eigen__0 @ X6 @ X7 ) )
                                   => ( X5 @ X7 ) ) )
                         => ( X5 @ X4 ) )
                   => ! [X5: a > $o] :
                        ( ~ ( ! [X6: a] :
                                ( ( eigen__1 @ X1 @ X6 )
                               => ( X5 @ X6 ) )
                           => ~ ! [X6: a,X7: a] :
                                  ( ~ ( ( X5 @ X6 )
                                     => ~ ( eigen__1 @ X6 @ X7 ) )
                                 => ( X5 @ X7 ) ) )
                       => ( X5 @ X4 ) ) )
                 => ( X3 @ X4 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ~ ( ( X3 @ X4 )
                       => ~ ( ~ ! [X6: a > $o] :
                                  ( ~ ( ! [X7: a] :
                                          ( ( eigen__0 @ X4 @ X7 )
                                         => ( X6 @ X7 ) )
                                     => ~ ! [X7: a,X8: a] :
                                            ( ~ ( ( X6 @ X7 )
                                               => ~ ( eigen__0 @ X7 @ X8 ) )
                                           => ( X6 @ X8 ) ) )
                                 => ( X6 @ X5 ) )
                           => ! [X6: a > $o] :
                                ( ~ ( ! [X7: a] :
                                        ( ( eigen__1 @ X4 @ X7 )
                                       => ( X6 @ X7 ) )
                                   => ~ ! [X7: a,X8: a] :
                                          ( ~ ( ( X6 @ X7 )
                                             => ~ ( eigen__1 @ X7 @ X8 ) )
                                         => ( X6 @ X8 ) ) )
                               => ( X6 @ X5 ) ) ) )
                   => ( X3 @ X5 ) ) )
         => ( X3 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: a] :
        ( ( ^ [X2: a] :
            ! [X3: a > $o] :
              ( ~ ( ! [X4: a] :
                      ( ( ~ ( eigen__0 @ X1 @ X4 )
                       => ( eigen__1 @ X1 @ X4 ) )
                     => ( X3 @ X4 ) )
                 => ~ ! [X4: a,X5: a] :
                        ( ~ ( ( X3 @ X4 )
                           => ~ ( ~ ( eigen__0 @ X4 @ X5 )
                               => ( eigen__1 @ X4 @ X5 ) ) )
                       => ( X3 @ X5 ) ) )
             => ( X3 @ X2 ) ) )
        = ( ^ [X2: a] :
            ! [X3: a > $o] :
              ( ~ ( ! [X4: a] :
                      ( ( ~ ! [X5: a > $o] :
                              ( ~ ( ! [X6: a] :
                                      ( ( eigen__0 @ X1 @ X6 )
                                     => ( X5 @ X6 ) )
                                 => ~ ! [X6: a,X7: a] :
                                        ( ~ ( ( X5 @ X6 )
                                           => ~ ( eigen__0 @ X6 @ X7 ) )
                                       => ( X5 @ X7 ) ) )
                             => ( X5 @ X4 ) )
                       => ! [X5: a > $o] :
                            ( ~ ( ! [X6: a] :
                                    ( ( eigen__1 @ X1 @ X6 )
                                   => ( X5 @ X6 ) )
                               => ~ ! [X6: a,X7: a] :
                                      ( ~ ( ( X5 @ X6 )
                                         => ~ ( eigen__1 @ X6 @ X7 ) )
                                     => ( X5 @ X7 ) ) )
                           => ( X5 @ X4 ) ) )
                     => ( X3 @ X4 ) )
                 => ~ ! [X4: a,X5: a] :
                        ( ~ ( ( X3 @ X4 )
                           => ~ ( ~ ! [X6: a > $o] :
                                      ( ~ ( ! [X7: a] :
                                              ( ( eigen__0 @ X4 @ X7 )
                                             => ( X6 @ X7 ) )
                                         => ~ ! [X7: a,X8: a] :
                                                ( ~ ( ( X6 @ X7 )
                                                   => ~ ( eigen__0 @ X7 @ X8 ) )
                                               => ( X6 @ X8 ) ) )
                                     => ( X6 @ X5 ) )
                               => ! [X6: a > $o] :
                                    ( ~ ( ! [X7: a] :
                                            ( ( eigen__1 @ X4 @ X7 )
                                           => ( X6 @ X7 ) )
                                       => ~ ! [X7: a,X8: a] :
                                              ( ~ ( ( X6 @ X7 )
                                                 => ~ ( eigen__1 @ X7 @ X8 ) )
                                             => ( X6 @ X8 ) ) )
                                   => ( X6 @ X5 ) ) ) )
                       => ( X3 @ X5 ) ) )
             => ( X3 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( ( ^ [X1: a] :
        ! [X2: a > $o] :
          ( ~ ( ! [X3: a] :
                  ( ( ~ ( eigen__0 @ eigen__2 @ X3 )
                   => ( eigen__1 @ eigen__2 @ X3 ) )
                 => ( X2 @ X3 ) )
             => ~ ! [X3: a,X4: a] :
                    ( ~ ( ( X2 @ X3 )
                       => ~ ( ~ ( eigen__0 @ X3 @ X4 )
                           => ( eigen__1 @ X3 @ X4 ) ) )
                   => ( X2 @ X4 ) ) )
         => ( X2 @ X1 ) ) )
   != ( ^ [X1: a] :
        ! [X2: a > $o] :
          ( ~ ( ! [X3: a] :
                  ( ( ~ ! [X4: a > $o] :
                          ( ~ ( ! [X5: a] :
                                  ( ( eigen__0 @ eigen__2 @ X5 )
                                 => ( X4 @ X5 ) )
                             => ~ ! [X5: a,X6: a] :
                                    ( ~ ( ( X4 @ X5 )
                                       => ~ ( eigen__0 @ X5 @ X6 ) )
                                   => ( X4 @ X6 ) ) )
                         => ( X4 @ X3 ) )
                   => ! [X4: a > $o] :
                        ( ~ ( ! [X5: a] :
                                ( ( eigen__1 @ eigen__2 @ X5 )
                               => ( X4 @ X5 ) )
                           => ~ ! [X5: a,X6: a] :
                                  ( ~ ( ( X4 @ X5 )
                                     => ~ ( eigen__1 @ X5 @ X6 ) )
                                 => ( X4 @ X6 ) ) )
                       => ( X4 @ X3 ) ) )
                 => ( X2 @ X3 ) )
             => ~ ! [X3: a,X4: a] :
                    ( ~ ( ( X2 @ X3 )
                       => ~ ( ~ ! [X5: a > $o] :
                                  ( ~ ( ! [X6: a] :
                                          ( ( eigen__0 @ X3 @ X6 )
                                         => ( X5 @ X6 ) )
                                     => ~ ! [X6: a,X7: a] :
                                            ( ~ ( ( X5 @ X6 )
                                               => ~ ( eigen__0 @ X6 @ X7 ) )
                                           => ( X5 @ X7 ) ) )
                                 => ( X5 @ X4 ) )
                           => ! [X5: a > $o] :
                                ( ~ ( ! [X6: a] :
                                        ( ( eigen__1 @ X3 @ X6 )
                                       => ( X5 @ X6 ) )
                                   => ~ ! [X6: a,X7: a] :
                                          ( ~ ( ( X5 @ X6 )
                                             => ~ ( eigen__1 @ X6 @ X7 ) )
                                         => ( X5 @ X7 ) ) )
                               => ( X5 @ X4 ) ) ) )
                   => ( X2 @ X4 ) ) )
         => ( X2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: a] :
        ( ( ! [X2: a > $o] :
              ( ~ ( ! [X3: a] :
                      ( ( ~ ( eigen__0 @ eigen__2 @ X3 )
                       => ( eigen__1 @ eigen__2 @ X3 ) )
                     => ( X2 @ X3 ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ~ ( ( X2 @ X3 )
                           => ~ ( ~ ( eigen__0 @ X3 @ X4 )
                               => ( eigen__1 @ X3 @ X4 ) ) )
                       => ( X2 @ X4 ) ) )
             => ( X2 @ X1 ) ) )
        = ( ! [X2: a > $o] :
              ( ~ ( ! [X3: a] :
                      ( ( ~ ! [X4: a > $o] :
                              ( ~ ( ! [X5: a] :
                                      ( ( eigen__0 @ eigen__2 @ X5 )
                                     => ( X4 @ X5 ) )
                                 => ~ ! [X5: a,X6: a] :
                                        ( ~ ( ( X4 @ X5 )
                                           => ~ ( eigen__0 @ X5 @ X6 ) )
                                       => ( X4 @ X6 ) ) )
                             => ( X4 @ X3 ) )
                       => ! [X4: a > $o] :
                            ( ~ ( ! [X5: a] :
                                    ( ( eigen__1 @ eigen__2 @ X5 )
                                   => ( X4 @ X5 ) )
                               => ~ ! [X5: a,X6: a] :
                                      ( ~ ( ( X4 @ X5 )
                                         => ~ ( eigen__1 @ X5 @ X6 ) )
                                     => ( X4 @ X6 ) ) )
                           => ( X4 @ X3 ) ) )
                     => ( X2 @ X3 ) )
                 => ~ ! [X3: a,X4: a] :
                        ( ~ ( ( X2 @ X3 )
                           => ~ ( ~ ! [X5: a > $o] :
                                      ( ~ ( ! [X6: a] :
                                              ( ( eigen__0 @ X3 @ X6 )
                                             => ( X5 @ X6 ) )
                                         => ~ ! [X6: a,X7: a] :
                                                ( ~ ( ( X5 @ X6 )
                                                   => ~ ( eigen__0 @ X6 @ X7 ) )
                                               => ( X5 @ X7 ) ) )
                                     => ( X5 @ X4 ) )
                               => ! [X5: a > $o] :
                                    ( ~ ( ! [X6: a] :
                                            ( ( eigen__1 @ X3 @ X6 )
                                           => ( X5 @ X6 ) )
                                       => ~ ! [X6: a,X7: a] :
                                              ( ~ ( ( X5 @ X6 )
                                                 => ~ ( eigen__1 @ X6 @ X7 ) )
                                             => ( X5 @ X7 ) ) )
                                   => ( X5 @ X4 ) ) ) )
                       => ( X2 @ X4 ) ) )
             => ( X2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP116 != sP101,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP116,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP101,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP116,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP101,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( ~ ( sP80
         => ~ sP1 )
     => sP85 ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP80
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ sP85,
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP80,
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP113
    | ~ sP78
    | sP50 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP32
    | sP113 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP121
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP88
    | ~ sP2
    | sP96 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP16
    | sP88 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP86
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP120
    | ~ sP50 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP120
    | ~ sP121 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP107
    | ~ sP96 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP107
    | ~ sP86 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP49
    | ~ sP120 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__51]) ).

thf(12,plain,
    ( sP43
    | ~ sP107 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__50]) ).

thf(13,plain,
    ( sP57
    | ~ sP49 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP57
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP13
    | ~ sP126
    | ~ sP57 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP77
    | sP13
    | sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP11
    | sP77 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP1
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP30
    | ~ sP62
    | sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP123
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP102
    | sP123 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP48
    | ~ sP100
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP82
    | sP48 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP47
    | sP82 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP20
    | ~ sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP20
    | ~ sP102 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( sP81
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP81
    | ~ sP47 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( sP5
    | ~ sP20 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__17]) ).

thf(30,plain,
    ( sP94
    | ~ sP81 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16]) ).

thf(31,plain,
    ( sP35
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( sP35
    | ~ sP94 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP95
    | ~ sP35
    | sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP80
    | sP95 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP56
    | sP2
    | sP78 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( sP79
    | sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP79
    | sP126 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( sP106
    | ~ sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( sP106
    | ~ sP79 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP111
    | ~ sP106 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).

thf(41,plain,
    ( sP97
    | ~ sP111 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(42,plain,
    ( ~ sP12
    | sP100
    | sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( sP65
    | ~ sP69 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP65
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP6
    | ~ sP65 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(46,plain,
    ( ~ sP42
    | ~ sP6
    | ~ sP97 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP29
    | sP42
    | sP85 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( ~ sP116
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(49,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h9,h10,h8,h7,h6,h5,h4,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,h9,h16,h17,h15]) ).

thf(50,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,49,h16,h17]) ).

thf(51,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,50,h14,h15]) ).

thf(52,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h10,51,h13]) ).

thf(h18,assumption,
    ~ ( ~ ( sP73
         => ~ sP40 )
     => sP108 ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( sP73
     => ~ sP40 ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ sP108,
    introduced(assumption,[]) ).

thf(h21,assumption,
    sP73,
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP40,
    introduced(assumption,[]) ).

thf(53,plain,
    ( sP72
    | ~ sP122 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( ~ sP83
    | ~ sP104
    | ~ sP72 ),
    inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
    ( ~ sP110
    | sP83
    | sP87 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( ~ sP27
    | sP110 ),
    inference(all_rule,[status(thm)],]) ).

thf(57,plain,
    ( sP66
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    ( ~ sP39
    | ~ sP104
    | ~ sP66 ),
    inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
    ( ~ sP59
    | sP39
    | sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
    ( ~ sP27
    | sP59 ),
    inference(all_rule,[status(thm)],]) ).

thf(61,plain,
    ( ~ sP40
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(62,plain,
    ( sP125
    | ~ sP76 ),
    inference(prop_rule,[status(thm)],]) ).

thf(63,plain,
    ( ~ sP112
    | ~ sP103
    | ~ sP125 ),
    inference(prop_rule,[status(thm)],]) ).

thf(64,plain,
    ( ~ sP38
    | sP112
    | sP93 ),
    inference(prop_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP68
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(66,plain,
    ( ~ sP40
    | sP68 ),
    inference(all_rule,[status(thm)],]) ).

thf(67,plain,
    ( sP92
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
    ( ~ sP44
    | ~ sP75
    | ~ sP92 ),
    inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
    ( ~ sP45
    | sP44
    | sP119 ),
    inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
    ( ~ sP14
    | sP45 ),
    inference(all_rule,[status(thm)],]) ).

thf(71,plain,
    ( ~ sP40
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP90
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( ~ sP22
    | ~ sP90
    | sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( ~ sP73
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(75,plain,
    ( sP23
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(76,plain,
    ( ~ sP46
    | ~ sP23
    | sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
    ( ~ sP73
    | sP46 ),
    inference(all_rule,[status(thm)],]) ).

thf(78,plain,
    ( sP55
    | ~ sP87 ),
    inference(prop_rule,[status(thm)],]) ).

thf(79,plain,
    ( sP55
    | sP122 ),
    inference(prop_rule,[status(thm)],]) ).

thf(80,plain,
    ( sP115
    | ~ sP55 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__119]) ).

thf(81,plain,
    ( ~ sP31
    | ~ sP115
    | ~ sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(82,plain,
    ( sP118
    | ~ sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(83,plain,
    ( sP118
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(84,plain,
    ( sP17
    | ~ sP118 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__116]) ).

thf(85,plain,
    ( ~ sP10
    | ~ sP17
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(86,plain,
    ( ~ sP24
    | sP31
    | sP63 ),
    inference(prop_rule,[status(thm)],]) ).

thf(87,plain,
    ( ~ sP37
    | sP10
    | sP63 ),
    inference(prop_rule,[status(thm)],]) ).

thf(88,plain,
    ( ~ sP34
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(89,plain,
    ( ~ sP99
    | sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(90,plain,
    ( ~ sP54
    | sP99
    | sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(91,plain,
    ( sP84
    | sP54 ),
    inference(prop_rule,[status(thm)],]) ).

thf(92,plain,
    ( sP84
    | sP104 ),
    inference(prop_rule,[status(thm)],]) ).

thf(93,plain,
    ( sP51
    | ~ sP63 ),
    inference(prop_rule,[status(thm)],]) ).

thf(94,plain,
    ( sP51
    | ~ sP84 ),
    inference(prop_rule,[status(thm)],]) ).

thf(95,plain,
    ( ~ sP124
    | sP128
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(96,plain,
    ( ~ sP74
    | sP8
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(97,plain,
    ( ~ sP71
    | sP124 ),
    inference(all_rule,[status(thm)],]) ).

thf(98,plain,
    ( ~ sP64
    | sP74 ),
    inference(all_rule,[status(thm)],]) ).

thf(99,plain,
    ( ~ sP61
    | sP64
    | sP71 ),
    inference(prop_rule,[status(thm)],]) ).

thf(100,plain,
    ( sP109
    | ~ sP51 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__115]) ).

thf(101,plain,
    ( sP98
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(102,plain,
    ( sP98
    | sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(103,plain,
    ( sP91
    | ~ sP109 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__114]) ).

thf(104,plain,
    ( sP105
    | ~ sP98 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__113]) ).

thf(105,plain,
    ( ~ sP18
    | ~ sP105
    | ~ sP91 ),
    inference(prop_rule,[status(thm)],]) ).

thf(106,plain,
    ( ~ sP3
    | sP18
    | sP108 ),
    inference(prop_rule,[status(thm)],]) ).

thf(107,plain,
    ( sP129
    | sP76 ),
    inference(prop_rule,[status(thm)],]) ).

thf(108,plain,
    ( sP129
    | sP103 ),
    inference(prop_rule,[status(thm)],]) ).

thf(109,plain,
    ( sP127
    | ~ sP93 ),
    inference(prop_rule,[status(thm)],]) ).

thf(110,plain,
    ( sP127
    | ~ sP129 ),
    inference(prop_rule,[status(thm)],]) ).

thf(111,plain,
    ( sP28
    | ~ sP127 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__112]) ).

thf(112,plain,
    ( sP33
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(113,plain,
    ( sP33
    | sP75 ),
    inference(prop_rule,[status(thm)],]) ).

thf(114,plain,
    ( sP114
    | ~ sP119 ),
    inference(prop_rule,[status(thm)],]) ).

thf(115,plain,
    ( sP114
    | ~ sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(116,plain,
    ( sP26
    | ~ sP114 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__111]) ).

thf(117,plain,
    ( sP4
    | ~ sP28 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__110]) ).

thf(118,plain,
    ( sP21
    | ~ sP26 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__109]) ).

thf(119,plain,
    ( sP60
    | ~ sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(120,plain,
    ( sP60
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(121,plain,
    ( sP117
    | ~ sP60 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__106]) ).

thf(122,plain,
    ( ~ sP8
    | ~ sP117
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(123,plain,
    ( sP67
    | ~ sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(124,plain,
    ( sP67
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(125,plain,
    ( sP89
    | ~ sP67 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__105]) ).

thf(126,plain,
    ( ~ sP128
    | ~ sP89
    | ~ sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(127,plain,
    ( ~ sP101
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(128,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,h21,h22,h20,h12]) ).

thf(129,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,128,h21,h22]) ).

thf(130,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,129,h19,h20]) ).

thf(131,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__77)],[h11,130,h18]) ).

thf(132,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,52,131,h9,h10,h11,h12]) ).

thf(133,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,132,h8]) ).

thf(134,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h7])],[h6,133,h7]) ).

thf(135,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,134,h6]) ).

thf(136,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,135,h5]) ).

thf(137,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,136,h4]) ).

thf(138,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,137,h3]) ).

thf(139,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[138,h1]) ).

thf(140,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[139,h0]) ).

thf(0,theorem,
    ! [X1: a > a > $o,X2: a > a > $o] :
      ( ( ^ [X3: a,X4: a] :
          ! [X5: a > $o] :
            ( ~ ( ! [X6: a] :
                    ( ( ~ ( X1 @ X3 @ X6 )
                     => ( X2 @ X3 @ X6 ) )
                   => ( X5 @ X6 ) )
               => ~ ! [X6: a,X7: a] :
                      ( ~ ( ( X5 @ X6 )
                         => ~ ( ~ ( X1 @ X6 @ X7 )
                             => ( X2 @ X6 @ X7 ) ) )
                     => ( X5 @ X7 ) ) )
           => ( X5 @ X4 ) ) )
      = ( ^ [X3: a,X4: a] :
          ! [X5: a > $o] :
            ( ~ ( ! [X6: a] :
                    ( ( ~ ! [X7: a > $o] :
                            ( ~ ( ! [X8: a] :
                                    ( ( X1 @ X3 @ X8 )
                                   => ( X7 @ X8 ) )
                               => ~ ! [X8: a,X9: a] :
                                      ( ~ ( ( X7 @ X8 )
                                         => ~ ( X1 @ X8 @ X9 ) )
                                     => ( X7 @ X9 ) ) )
                           => ( X7 @ X6 ) )
                     => ! [X7: a > $o] :
                          ( ~ ( ! [X8: a] :
                                  ( ( X2 @ X3 @ X8 )
                                 => ( X7 @ X8 ) )
                             => ~ ! [X8: a,X9: a] :
                                    ( ~ ( ( X7 @ X8 )
                                       => ~ ( X2 @ X8 @ X9 ) )
                                   => ( X7 @ X9 ) ) )
                         => ( X7 @ X6 ) ) )
                   => ( X5 @ X6 ) )
               => ~ ! [X6: a,X7: a] :
                      ( ~ ( ( X5 @ X6 )
                         => ~ ( ~ ! [X8: a > $o] :
                                    ( ~ ( ! [X9: a] :
                                            ( ( X1 @ X6 @ X9 )
                                           => ( X8 @ X9 ) )
                                       => ~ ! [X9: a,X10: a] :
                                              ( ~ ( ( X8 @ X9 )
                                                 => ~ ( X1 @ X9 @ X10 ) )
                                             => ( X8 @ X10 ) ) )
                                   => ( X8 @ X7 ) )
                             => ! [X8: a > $o] :
                                  ( ~ ( ! [X9: a] :
                                          ( ( X2 @ X6 @ X9 )
                                         => ( X8 @ X9 ) )
                                     => ~ ! [X9: a,X10: a] :
                                            ( ~ ( ( X8 @ X9 )
                                               => ~ ( X2 @ X9 @ X10 ) )
                                           => ( X8 @ X10 ) ) )
                                 => ( X8 @ X7 ) ) ) )
                     => ( X5 @ X7 ) ) )
           => ( X5 @ X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h2])],[138,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEV150^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug 24 02:10:01 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 5.74/5.89  % SZS status Theorem
% 5.74/5.89  % Mode: cade22grackle2xfee4
% 5.74/5.89  % Steps: 65503
% 5.74/5.89  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------