TSTP Solution File: SEV126^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV126^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 18:04:58 EDT 2022

% Result   : Theorem 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  101 (  22 unt;  11 typ;   4 def)
%            Number of atoms       :  245 (   4 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  839 ( 171   ~;  33   |;   0   &; 405   @)
%                                         (  30 <=>; 200  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  136 ( 136   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;  37 con; 0-2 aty)
%            Number of variables   :  185 (   4   ^ 181   !;   0   ?; 185   :)

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

thf(ty_eigen__6,type,
    eigen__6: a ).

thf(ty_eigen__12,type,
    eigen__12: a > a > $o ).

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

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

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

thf(ty_eigen__4,type,
    eigen__4: a ).

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

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__13,type,
    eigen__13: a > a > $o ).

thf(ty_eigen__9,type,
    eigen__9: a ).

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

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( ~ ( eigen__1 @ X1 @ X2 )
               => ( eigen__2 @ X1 @ X2 ) )
             => ( eigen__5 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

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

thf(eigendef_eigen__12,definition,
    ( eigen__12
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ~ ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__1 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__12])]) ).

thf(eigendef_eigen__13,definition,
    ( eigen__13
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ~ ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__2 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__13])]) ).

thf(eigendef_eigen__9,definition,
    ( eigen__9
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ~ ( eigen__1 @ eigen__6 @ X1 )
             => ( eigen__2 @ eigen__6 @ X1 ) )
           => ( eigen__5 @ eigen__6 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__9])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ! [X1: a > a > $o] :
            ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__1 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__6 @ eigen__9 ) )
     => ! [X1: a > a > $o] :
          ( ~ ( ! [X2: a,X3: a] :
                  ( ( eigen__2 @ X2 @ X3 )
                 => ( X1 @ X2 @ X3 ) )
             => ~ ( eigen__0 @ X1 ) )
         => ( X1 @ eigen__6 @ eigen__9 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( eigen__2 @ eigen__6 @ eigen__9 )
     => ( eigen__13 @ eigen__6 @ eigen__9 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__6 @ X1 )
       => ( eigen__12 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ ( ! [X1: a,X2: a] :
              ( ( ~ ( eigen__1 @ X1 @ X2 )
               => ( eigen__2 @ X1 @ X2 ) )
             => ( eigen__5 @ X1 @ X2 ) )
         => ~ sP1 )
     => ( eigen__5 @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ! [X1: a,X2: a] :
          ( ( eigen__2 @ X1 @ X2 )
         => ( eigen__13 @ X1 @ X2 ) )
     => ~ ( eigen__0 @ eigen__13 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a,X2: a] :
        ( ( eigen__2 @ X1 @ X2 )
       => ( eigen__13 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__13 @ eigen__6 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__2 @ eigen__6 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( eigen__5 @ eigen__6 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( eigen__1 @ eigen__6 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__2 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__6 @ eigen__9 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: a] :
        ( ( ~ ( eigen__1 @ eigen__6 @ X1 )
         => ( eigen__2 @ eigen__6 @ X1 ) )
       => ( eigen__5 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__12 @ eigen__6 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ! [X1: a,X2: a] :
          ( ( ~ ( eigen__1 @ X1 @ X2 )
           => ( eigen__2 @ X1 @ X2 ) )
         => ( eigen__5 @ X1 @ X2 ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ~ sP6
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ sP11
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP17
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: a,X2: a] :
        ( ( ~ ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( eigen__1 @ X4 @ X5 )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ( eigen__0 @ X3 ) )
               => ( X3 @ X1 @ X2 ) )
         => ! [X3: a > a > $o] :
              ( ~ ( ! [X4: a,X5: a] :
                      ( ( eigen__2 @ X4 @ X5 )
                     => ( X3 @ X4 @ X5 ) )
                 => ~ ( eigen__0 @ X3 ) )
             => ( X3 @ X1 @ X2 ) ) )
       => ( eigen__5 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: a,X2: a] :
        ( ( eigen__1 @ X1 @ X2 )
       => ( eigen__12 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( eigen__5 @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__1 @ X1 @ X2 )
         => ( eigen__2 @ X1 @ X2 ) )
       => ( eigen__5 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: a] :
        ( ( ~ ! [X2: a > a > $o] :
                ( ~ ( ! [X3: a,X4: a] :
                        ( ( eigen__1 @ X3 @ X4 )
                       => ( X2 @ X3 @ X4 ) )
                   => ~ ( eigen__0 @ X2 ) )
               => ( X2 @ eigen__6 @ X1 ) )
         => ! [X2: a > a > $o] :
              ( ~ ( ! [X3: a,X4: a] :
                      ( ( eigen__2 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) )
                 => ~ ( eigen__0 @ X2 ) )
             => ( X2 @ eigen__6 @ X1 ) ) )
       => ( eigen__5 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ ( sP20
         => ~ ( eigen__0 @ eigen__12 ) )
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: a] :
        ( ( eigen__2 @ eigen__6 @ X1 )
       => ( eigen__13 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP11
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( sP2
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP20
     => ~ ( eigen__0 @ eigen__12 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__1 @ X2 @ X3 )
                 => ( eigen__2 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__1 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__6 @ eigen__9 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(cTHM252B_pme,conjecture,
    ! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o,X4: a,X5: a] :
      ( ! [X6: a > a > $o] :
          ( ~ ( ! [X7: a,X8: a] :
                  ( ( ~ ( X2 @ X7 @ X8 )
                   => ( X3 @ X7 @ X8 ) )
                 => ( X6 @ X7 @ X8 ) )
             => ~ ( X1 @ X6 ) )
         => ( X6 @ X4 @ X5 ) )
     => ! [X6: a > a > $o] :
          ( ~ ( ! [X7: a,X8: a] :
                  ( ( ~ ! [X9: a > a > $o] :
                          ( ~ ( ! [X10: a,X11: a] :
                                  ( ( X2 @ X10 @ X11 )
                                 => ( X9 @ X10 @ X11 ) )
                             => ~ ( X1 @ X9 ) )
                         => ( X9 @ X7 @ X8 ) )
                   => ! [X9: a > a > $o] :
                        ( ~ ( ! [X10: a,X11: a] :
                                ( ( X3 @ X10 @ X11 )
                               => ( X9 @ X10 @ X11 ) )
                           => ~ ( X1 @ X9 ) )
                       => ( X9 @ X7 @ X8 ) ) )
                 => ( X6 @ X7 @ X8 ) )
             => ~ ( X1 @ X6 ) )
         => ( X6 @ X4 @ X5 ) ) ) ).

thf(h2,negated_conjecture,
    ~ ! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o,X4: a,X5: a] :
        ( ! [X6: a > a > $o] :
            ( ~ ( ! [X7: a,X8: a] :
                    ( ( ~ ( X2 @ X7 @ X8 )
                     => ( X3 @ X7 @ X8 ) )
                   => ( X6 @ X7 @ X8 ) )
               => ~ ( X1 @ X6 ) )
           => ( X6 @ X4 @ X5 ) )
       => ! [X6: a > a > $o] :
            ( ~ ( ! [X7: a,X8: a] :
                    ( ( ~ ! [X9: a > a > $o] :
                            ( ~ ( ! [X10: a,X11: a] :
                                    ( ( X2 @ X10 @ X11 )
                                   => ( X9 @ X10 @ X11 ) )
                               => ~ ( X1 @ X9 ) )
                           => ( X9 @ X7 @ X8 ) )
                     => ! [X9: a > a > $o] :
                          ( ~ ( ! [X10: a,X11: a] :
                                  ( ( X3 @ X10 @ X11 )
                                 => ( X9 @ X10 @ X11 ) )
                             => ~ ( X1 @ X9 ) )
                         => ( X9 @ X7 @ X8 ) ) )
                   => ( X6 @ X7 @ X8 ) )
               => ~ ( X1 @ X6 ) )
           => ( X6 @ X4 @ X5 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM252B_pme]) ).

thf(h3,assumption,
    ~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
        ( ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ( ~ ( X1 @ X6 @ X7 )
                     => ( X2 @ X6 @ X7 ) )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( eigen__0 @ X5 ) )
           => ( X5 @ X3 @ X4 ) )
       => ! [X5: a > a > $o] :
            ( ~ ( ! [X6: a,X7: a] :
                    ( ( ~ ! [X8: a > a > $o] :
                            ( ~ ( ! [X9: a,X10: a] :
                                    ( ( X1 @ X9 @ X10 )
                                   => ( X8 @ X9 @ X10 ) )
                               => ~ ( eigen__0 @ X8 ) )
                           => ( X8 @ X6 @ X7 ) )
                     => ! [X8: a > a > $o] :
                          ( ~ ( ! [X9: a,X10: a] :
                                  ( ( X2 @ X9 @ X10 )
                                 => ( X8 @ X9 @ X10 ) )
                             => ~ ( eigen__0 @ X8 ) )
                         => ( X8 @ X6 @ X7 ) ) )
                   => ( X5 @ X6 @ X7 ) )
               => ~ ( eigen__0 @ X5 ) )
           => ( X5 @ X3 @ X4 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: a > a > $o,X2: a,X3: a] :
        ( ! [X4: a > a > $o] :
            ( ~ ( ! [X5: a,X6: a] :
                    ( ( ~ ( eigen__1 @ X5 @ X6 )
                     => ( X1 @ X5 @ X6 ) )
                   => ( X4 @ X5 @ X6 ) )
               => ~ ( eigen__0 @ X4 ) )
           => ( X4 @ X2 @ X3 ) )
       => ! [X4: a > a > $o] :
            ( ~ ( ! [X5: a,X6: a] :
                    ( ( ~ ! [X7: a > a > $o] :
                            ( ~ ( ! [X8: a,X9: a] :
                                    ( ( eigen__1 @ X8 @ X9 )
                                   => ( X7 @ X8 @ X9 ) )
                               => ~ ( eigen__0 @ X7 ) )
                           => ( X7 @ X5 @ X6 ) )
                     => ! [X7: a > a > $o] :
                          ( ~ ( ! [X8: a,X9: a] :
                                  ( ( X1 @ X8 @ X9 )
                                 => ( X7 @ X8 @ X9 ) )
                             => ~ ( eigen__0 @ X7 ) )
                         => ( X7 @ X5 @ X6 ) ) )
                   => ( X4 @ X5 @ X6 ) )
               => ~ ( eigen__0 @ X4 ) )
           => ( X4 @ X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: a,X2: a] :
        ( ! [X3: a > a > $o] :
            ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ( eigen__1 @ X4 @ X5 )
                     => ( eigen__2 @ X4 @ X5 ) )
                   => ( X3 @ X4 @ X5 ) )
               => ~ ( eigen__0 @ X3 ) )
           => ( X3 @ X1 @ X2 ) )
       => ! [X3: a > a > $o] :
            ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ! [X6: a > a > $o] :
                            ( ~ ( ! [X7: a,X8: a] :
                                    ( ( eigen__1 @ X7 @ X8 )
                                   => ( X6 @ X7 @ X8 ) )
                               => ~ ( eigen__0 @ X6 ) )
                           => ( X6 @ X4 @ X5 ) )
                     => ! [X6: a > a > $o] :
                          ( ~ ( ! [X7: a,X8: a] :
                                  ( ( eigen__2 @ X7 @ X8 )
                                 => ( X6 @ X7 @ X8 ) )
                             => ~ ( eigen__0 @ X6 ) )
                         => ( X6 @ X4 @ X5 ) ) )
                   => ( X3 @ X4 @ X5 ) )
               => ~ ( eigen__0 @ X3 ) )
           => ( X3 @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: a] :
        ( ! [X2: a > a > $o] :
            ( ~ ( ! [X3: a,X4: a] :
                    ( ( ~ ( eigen__1 @ X3 @ X4 )
                     => ( eigen__2 @ X3 @ X4 ) )
                   => ( X2 @ X3 @ X4 ) )
               => ~ ( eigen__0 @ X2 ) )
           => ( X2 @ eigen__3 @ X1 ) )
       => ! [X2: a > a > $o] :
            ( ~ ( ! [X3: a,X4: a] :
                    ( ( ~ ! [X5: a > a > $o] :
                            ( ~ ( ! [X6: a,X7: a] :
                                    ( ( eigen__1 @ X6 @ X7 )
                                   => ( X5 @ X6 @ X7 ) )
                               => ~ ( eigen__0 @ X5 ) )
                           => ( X5 @ X3 @ X4 ) )
                     => ! [X5: a > a > $o] :
                          ( ~ ( ! [X6: a,X7: a] :
                                  ( ( eigen__2 @ X6 @ X7 )
                                 => ( X5 @ X6 @ X7 ) )
                             => ~ ( eigen__0 @ X5 ) )
                         => ( X5 @ X3 @ X4 ) ) )
                   => ( X2 @ X3 @ X4 ) )
               => ~ ( eigen__0 @ X2 ) )
           => ( X2 @ eigen__3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP29
     => ! [X1: a > a > $o] :
          ( ~ ( ! [X2: a,X3: a] :
                  ( ( ~ ! [X4: a > a > $o] :
                          ( ~ ( ! [X5: a,X6: a] :
                                  ( ( eigen__1 @ X5 @ X6 )
                                 => ( X4 @ X5 @ X6 ) )
                             => ~ ( eigen__0 @ X4 ) )
                         => ( X4 @ X2 @ X3 ) )
                   => ! [X4: a > a > $o] :
                        ( ~ ( ! [X5: a,X6: a] :
                                ( ( eigen__2 @ X5 @ X6 )
                               => ( X4 @ X5 @ X6 ) )
                           => ~ ( eigen__0 @ X4 ) )
                       => ( X4 @ X2 @ X3 ) ) )
                 => ( X1 @ X2 @ X3 ) )
             => ~ ( eigen__0 @ X1 ) )
         => ( X1 @ eigen__3 @ eigen__4 ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP29,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ! [X4: a > a > $o] :
                        ( ~ ( ! [X5: a,X6: a] :
                                ( ( eigen__1 @ X5 @ X6 )
                               => ( X4 @ X5 @ X6 ) )
                           => ~ ( eigen__0 @ X4 ) )
                       => ( X4 @ X2 @ X3 ) )
                 => ! [X4: a > a > $o] :
                      ( ~ ( ! [X5: a,X6: a] :
                              ( ( eigen__2 @ X5 @ X6 )
                             => ( X4 @ X5 @ X6 ) )
                         => ~ ( eigen__0 @ X4 ) )
                     => ( X4 @ X2 @ X3 ) ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__3 @ eigen__4 ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( ~ ( sP19
         => ~ sP1 )
     => sP21 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( sP19
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP21,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP19,
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP25
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | ~ sP9
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP20
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP26
    | ~ sP11
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP6
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP28
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP16
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP16
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP24
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP24
    | ~ sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP12
    | ~ sP16 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__13]) ).

thf(14,plain,
    ( sP30
    | ~ sP24 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).

thf(15,plain,
    ( sP2
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP2
    | ~ sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP19
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP23
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP27
    | ~ sP2
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP17
    | sP11
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP18
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP18
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP13
    | ~ sP18 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).

thf(24,plain,
    ( sP22
    | ~ sP13 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(25,plain,
    ( ~ sP29
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP5
    | sP15
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP15
    | ~ sP22
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,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,h8,h13,h14,h12]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,28,h13,h14]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,29,h11,h12]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[h9,30,h10]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,31,h8,h9]) ).

thf(33,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__4)],[h6,32,h7]) ).

thf(34,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,33,h6]) ).

thf(35,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,34,h5]) ).

thf(36,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,35,h4]) ).

thf(37,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,36,h3]) ).

thf(38,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[37,h1]) ).

thf(39,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[38,h0]) ).

thf(0,theorem,
    ! [X1: ( a > a > $o ) > $o,X2: a > a > $o,X3: a > a > $o,X4: a,X5: a] :
      ( ! [X6: a > a > $o] :
          ( ~ ( ! [X7: a,X8: a] :
                  ( ( ~ ( X2 @ X7 @ X8 )
                   => ( X3 @ X7 @ X8 ) )
                 => ( X6 @ X7 @ X8 ) )
             => ~ ( X1 @ X6 ) )
         => ( X6 @ X4 @ X5 ) )
     => ! [X6: a > a > $o] :
          ( ~ ( ! [X7: a,X8: a] :
                  ( ( ~ ! [X9: a > a > $o] :
                          ( ~ ( ! [X10: a,X11: a] :
                                  ( ( X2 @ X10 @ X11 )
                                 => ( X9 @ X10 @ X11 ) )
                             => ~ ( X1 @ X9 ) )
                         => ( X9 @ X7 @ X8 ) )
                   => ! [X9: a > a > $o] :
                        ( ~ ( ! [X10: a,X11: a] :
                                ( ( X3 @ X10 @ X11 )
                               => ( X9 @ X10 @ X11 ) )
                           => ~ ( X1 @ X9 ) )
                       => ( X9 @ X7 @ X8 ) ) )
                 => ( X6 @ X7 @ X8 ) )
             => ~ ( X1 @ X6 ) )
         => ( X6 @ X4 @ X5 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h2])],[37,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV126^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n009.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 : Mon Jun 27 22:08:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.38  % SZS status Theorem
% 0.19/0.38  % Mode: mode213
% 0.19/0.38  % Inferences: 65
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------