TSTP Solution File: SEV157^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV157^5 : 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 : n006.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 18:05:08 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :  146
% Syntax   : Number of formulae    :  185 (  59 unt;  18 typ;   4 def)
%            Number of atoms       :  431 (   4 equ;   0 cnn)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 2748 ( 616   ~;  48   |;   0   &;1381   @)
%                                         (  48 <=>; 655  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  205 ( 205   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   68 (  66 usr;  61 con; 0-2 aty)
%            Number of variables   :  657 (   4   ^ 653   !;   0   ?; 657   :)

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

thf(ty_eigen__14,type,
    eigen__14: a ).

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 ).

thf(ty_eigen__25,type,
    eigen__25: a ).

thf(ty_eigen__7,type,
    eigen__7: a > a > $o ).

thf(ty_eigen__24,type,
    eigen__24: a ).

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

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

thf(ty_eigen__26,type,
    eigen__26: a > a > $o ).

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

thf(ty_eigen__5,type,
    eigen__5: a ).

thf(ty_eigen__19,type,
    eigen__19: a ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__10,type,
    eigen__10: a ).

thf(ty_eigen__8,type,
    eigen__8: a ).

thf(ty_eigen__23,type,
    eigen__23: a ).

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

thf(eigendef_eigen__14,definition,
    ( eigen__14
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( eigen__1 @ X1 @ X2 )
             => ( eigen__12 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__14])]) ).

thf(eigendef_eigen__10,definition,
    ( eigen__10
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__0 @ eigen__8 @ X1 )
           => ( eigen__7 @ eigen__8 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__10])]) ).

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( eigen__0 @ X1 @ X2 )
             => ( eigen__7 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(eigendef_eigen__19,definition,
    ( eigen__19
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__1 @ eigen__14 @ X1 )
           => ( eigen__12 @ eigen__14 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__19])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( eigen__7 @ X1 @ X2 )
           => ~ ( eigen__7 @ X2 @ X3 ) )
       => ( eigen__7 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( eigen__0 @ eigen__8 @ eigen__10 )
     => ( eigen__1 @ eigen__8 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__0 @ X1 @ X2 )
         => ( eigen__1 @ X1 @ X2 ) )
       => ( eigen__4 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( eigen__0 @ eigen__14 @ eigen__19 )
     => ( eigen__1 @ eigen__14 @ eigen__19 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__12 @ eigen__5 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__0 @ X2 @ X3 )
                 => ( eigen__1 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__24 @ eigen__25 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a] :
        ( ( ~ ( eigen__0 @ eigen__8 @ X1 )
         => ( eigen__1 @ eigen__8 @ X1 ) )
       => ( eigen__7 @ eigen__8 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__4 @ eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__0 @ X2 @ X3 )
                 => ( eigen__1 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__23 @ eigen__24 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( eigen__12 @ X1 @ X2 )
           => ~ ( eigen__12 @ X2 @ X3 ) )
       => ( eigen__12 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__14 @ X1 )
       => ( eigen__12 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( eigen__1 @ eigen__14 @ eigen__19 )
     => ( eigen__12 @ eigen__14 @ eigen__19 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__0 @ X1 @ X2 )
         => ( eigen__1 @ X1 @ X2 ) )
       => ( eigen__12 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__26 @ eigen__23 @ X1 )
           => ~ ( eigen__26 @ X1 @ X2 ) )
       => ( eigen__26 @ eigen__23 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: a] :
        ( ~ ( ( eigen__26 @ eigen__23 @ eigen__24 )
           => ~ ( eigen__26 @ eigen__24 @ X1 ) )
       => ( eigen__26 @ eigen__23 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ( eigen__0 @ eigen__8 @ eigen__10 )
     => ( eigen__7 @ eigen__8 @ eigen__10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( eigen__26 @ eigen__23 @ eigen__25 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ~ ( ! [X1: a,X2: a] :
              ( ( ~ ( eigen__0 @ X1 @ X2 )
               => ( eigen__1 @ X1 @ X2 ) )
             => ( eigen__26 @ X1 @ X2 ) )
         => ~ ! [X1: a,X2: a,X3: a] :
                ( ~ ( ( eigen__26 @ X1 @ X2 )
                   => ~ ( eigen__26 @ X2 @ X3 ) )
               => ( eigen__26 @ X1 @ X3 ) ) )
     => ( eigen__26 @ eigen__23 @ eigen__24 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( eigen__4 @ X1 @ X2 )
           => ~ ( eigen__4 @ X2 @ X3 ) )
       => ( eigen__4 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( eigen__26 @ eigen__23 @ eigen__24 )
     => ~ ( eigen__26 @ eigen__24 @ eigen__25 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ! [X1: a,X2: a] :
          ( ( ~ ( eigen__0 @ X1 @ X2 )
           => ( eigen__1 @ X1 @ X2 ) )
         => ( eigen__26 @ X1 @ X2 ) )
     => ~ ! [X1: a,X2: a,X3: a] :
            ( ~ ( ( eigen__26 @ X1 @ X2 )
               => ~ ( eigen__26 @ X2 @ X3 ) )
           => ( eigen__26 @ X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( eigen__26 @ X1 @ X2 )
           => ~ ( eigen__26 @ X2 @ X3 ) )
       => ( eigen__26 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: a,X2: a] :
        ( ( eigen__1 @ X1 @ X2 )
       => ( eigen__12 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: a] :
        ( ( ~ ( eigen__0 @ eigen__14 @ X1 )
         => ( eigen__1 @ eigen__14 @ X1 ) )
       => ( eigen__12 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eigen__7 @ eigen__8 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( eigen__26 @ eigen__23 @ eigen__24 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ~ ( ! [X1: a,X2: a] :
              ( ( eigen__0 @ X1 @ X2 )
             => ( eigen__7 @ X1 @ X2 ) )
         => ~ sP1 )
     => ( eigen__7 @ eigen__5 @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( sP3
     => ~ sP19 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: a,X2: a] :
        ( ( eigen__0 @ X1 @ X2 )
       => ( eigen__7 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ~ sP20
     => sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ~ ( sP23
         => ~ sP10 )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( eigen__26 @ eigen__24 @ eigen__25 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP2
     => sP25 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__0 @ X1 @ X2 )
         => ( eigen__1 @ X1 @ X2 ) )
       => ( eigen__7 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__0 @ X2 @ X3 )
                 => ( eigen__1 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__2 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( eigen__1 @ eigen__14 @ eigen__19 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: a] :
        ( ( eigen__0 @ eigen__8 @ X1 )
       => ( eigen__7 @ eigen__8 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( eigen__7 @ eigen__5 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__0 @ X1 @ X2 )
         => ( eigen__1 @ X1 @ X2 ) )
       => ( eigen__26 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( eigen__12 @ eigen__14 @ eigen__19 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( ~ sP28
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( sP29
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( eigen__0 @ eigen__8 @ eigen__10 ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( sP23
     => ~ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( sP4
     => sP40 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( ~ sP21
     => sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__0 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__5 @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__1 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__5 @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(cTHM250G_pme,conjecture,
    ! [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 ) )
               => ~ ! [X6: a,X7: a,X8: a] :
                      ( ~ ( ( X5 @ X6 @ X7 )
                         => ~ ( X5 @ X7 @ X8 ) )
                     => ( X5 @ X6 @ X8 ) ) )
           => ( X5 @ X3 @ X4 ) )
     => ~ ( ~ ( ! [X5: a,X6: a] :
                  ( ( ~ ! [X7: a > a > $o] :
                          ( ~ ( ! [X8: a,X9: a] :
                                  ( ( X1 @ X8 @ X9 )
                                 => ( X7 @ X8 @ X9 ) )
                             => ~ ! [X8: a,X9: a,X10: a] :
                                    ( ~ ( ( X7 @ X8 @ X9 )
                                       => ~ ( X7 @ X9 @ X10 ) )
                                   => ( X7 @ X8 @ X10 ) ) )
                         => ( X7 @ X5 @ X6 ) )
                   => ! [X7: a > a > $o] :
                        ( ~ ( ! [X8: a,X9: a] :
                                ( ( X2 @ X8 @ X9 )
                               => ( X7 @ X8 @ X9 ) )
                           => ~ ! [X8: a,X9: a,X10: a] :
                                  ( ~ ( ( X7 @ X8 @ X9 )
                                     => ~ ( X7 @ X9 @ X10 ) )
                                 => ( X7 @ X8 @ X10 ) ) )
                       => ( X7 @ X5 @ X6 ) ) )
                 => ! [X7: a > a > $o] :
                      ( ~ ( ! [X8: a,X9: a] :
                              ( ( ~ ( X1 @ X8 @ X9 )
                               => ( X2 @ X8 @ X9 ) )
                             => ( X7 @ X8 @ X9 ) )
                         => ~ ! [X8: a,X9: a,X10: a] :
                                ( ~ ( ( X7 @ X8 @ X9 )
                                   => ~ ( X7 @ X9 @ X10 ) )
                               => ( X7 @ X8 @ X10 ) ) )
                     => ( X7 @ X5 @ X6 ) ) )
             => ~ ! [X5: a,X6: a,X7: a] :
                    ( ~ ( ! [X8: a > a > $o] :
                            ( ~ ( ! [X9: a,X10: a] :
                                    ( ( ~ ( X1 @ X9 @ X10 )
                                     => ( X2 @ X9 @ X10 ) )
                                   => ( X8 @ X9 @ X10 ) )
                               => ~ ! [X9: a,X10: a,X11: a] :
                                      ( ~ ( ( X8 @ X9 @ X10 )
                                         => ~ ( X8 @ X10 @ X11 ) )
                                     => ( X8 @ X9 @ X11 ) ) )
                           => ( X8 @ X5 @ X6 ) )
                       => ~ ! [X8: a > a > $o] :
                              ( ~ ( ! [X9: a,X10: a] :
                                      ( ( ~ ( X1 @ X9 @ X10 )
                                       => ( X2 @ X9 @ X10 ) )
                                     => ( X8 @ X9 @ X10 ) )
                                 => ~ ! [X9: a,X10: a,X11: a] :
                                        ( ~ ( ( X8 @ X9 @ X10 )
                                           => ~ ( X8 @ X10 @ X11 ) )
                                       => ( X8 @ X9 @ X11 ) ) )
                             => ( X8 @ X6 @ X7 ) ) )
                   => ! [X8: a > a > $o] :
                        ( ~ ( ! [X9: a,X10: a] :
                                ( ( ~ ( X1 @ X9 @ X10 )
                                 => ( X2 @ X9 @ X10 ) )
                               => ( X8 @ X9 @ X10 ) )
                           => ~ ! [X9: a,X10: a,X11: a] :
                                  ( ~ ( ( X8 @ X9 @ X10 )
                                     => ~ ( X8 @ X10 @ X11 ) )
                                 => ( X8 @ X9 @ X11 ) ) )
                       => ( X8 @ X5 @ X7 ) ) ) )
         => ! [X5: a > a > $o] :
              ( ~ ( ! [X6: a,X7: a] :
                      ( ( ~ ( X1 @ X6 @ X7 )
                       => ( X2 @ X6 @ X7 ) )
                     => ( X5 @ X6 @ X7 ) )
                 => ~ ! [X6: a,X7: a,X8: a] :
                        ( ~ ( ( X5 @ X6 @ X7 )
                           => ~ ( X5 @ X7 @ X8 ) )
                       => ( X5 @ X6 @ X8 ) ) )
             => ( X5 @ X3 @ X4 ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ! [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 ) )
                 => ~ ! [X6: a,X7: a,X8: a] :
                        ( ~ ( ( X5 @ X6 @ X7 )
                           => ~ ( X5 @ X7 @ X8 ) )
                       => ( X5 @ X6 @ X8 ) ) )
             => ( X5 @ X3 @ X4 ) )
       => ~ ( ~ ( ! [X5: a,X6: a] :
                    ( ( ~ ! [X7: a > a > $o] :
                            ( ~ ( ! [X8: a,X9: a] :
                                    ( ( X1 @ X8 @ X9 )
                                   => ( X7 @ X8 @ X9 ) )
                               => ~ ! [X8: a,X9: a,X10: a] :
                                      ( ~ ( ( X7 @ X8 @ X9 )
                                         => ~ ( X7 @ X9 @ X10 ) )
                                     => ( X7 @ X8 @ X10 ) ) )
                           => ( X7 @ X5 @ X6 ) )
                     => ! [X7: a > a > $o] :
                          ( ~ ( ! [X8: a,X9: a] :
                                  ( ( X2 @ X8 @ X9 )
                                 => ( X7 @ X8 @ X9 ) )
                             => ~ ! [X8: a,X9: a,X10: a] :
                                    ( ~ ( ( X7 @ X8 @ X9 )
                                       => ~ ( X7 @ X9 @ X10 ) )
                                   => ( X7 @ X8 @ X10 ) ) )
                         => ( X7 @ X5 @ X6 ) ) )
                   => ! [X7: a > a > $o] :
                        ( ~ ( ! [X8: a,X9: a] :
                                ( ( ~ ( X1 @ X8 @ X9 )
                                 => ( X2 @ X8 @ X9 ) )
                               => ( X7 @ X8 @ X9 ) )
                           => ~ ! [X8: a,X9: a,X10: a] :
                                  ( ~ ( ( X7 @ X8 @ X9 )
                                     => ~ ( X7 @ X9 @ X10 ) )
                                 => ( X7 @ X8 @ X10 ) ) )
                       => ( X7 @ X5 @ X6 ) ) )
               => ~ ! [X5: a,X6: a,X7: a] :
                      ( ~ ( ! [X8: a > a > $o] :
                              ( ~ ( ! [X9: a,X10: a] :
                                      ( ( ~ ( X1 @ X9 @ X10 )
                                       => ( X2 @ X9 @ X10 ) )
                                     => ( X8 @ X9 @ X10 ) )
                                 => ~ ! [X9: a,X10: a,X11: a] :
                                        ( ~ ( ( X8 @ X9 @ X10 )
                                           => ~ ( X8 @ X10 @ X11 ) )
                                       => ( X8 @ X9 @ X11 ) ) )
                             => ( X8 @ X5 @ X6 ) )
                         => ~ ! [X8: a > a > $o] :
                                ( ~ ( ! [X9: a,X10: a] :
                                        ( ( ~ ( X1 @ X9 @ X10 )
                                         => ( X2 @ X9 @ X10 ) )
                                       => ( X8 @ X9 @ X10 ) )
                                   => ~ ! [X9: a,X10: a,X11: a] :
                                          ( ~ ( ( X8 @ X9 @ X10 )
                                             => ~ ( X8 @ X10 @ X11 ) )
                                         => ( X8 @ X9 @ X11 ) ) )
                               => ( X8 @ X6 @ X7 ) ) )
                     => ! [X8: a > a > $o] :
                          ( ~ ( ! [X9: a,X10: a] :
                                  ( ( ~ ( X1 @ X9 @ X10 )
                                   => ( X2 @ X9 @ X10 ) )
                                 => ( X8 @ X9 @ X10 ) )
                             => ~ ! [X9: a,X10: a,X11: a] :
                                    ( ~ ( ( X8 @ X9 @ X10 )
                                       => ~ ( X8 @ X10 @ X11 ) )
                                   => ( X8 @ X9 @ X11 ) ) )
                         => ( X8 @ X5 @ X7 ) ) ) )
           => ! [X5: a > a > $o] :
                ( ~ ( ! [X6: a,X7: a] :
                        ( ( ~ ( X1 @ X6 @ X7 )
                         => ( X2 @ X6 @ X7 ) )
                       => ( X5 @ X6 @ X7 ) )
                   => ~ ! [X6: a,X7: a,X8: a] :
                          ( ~ ( ( X5 @ X6 @ X7 )
                             => ~ ( X5 @ X7 @ X8 ) )
                         => ( X5 @ X6 @ X8 ) ) )
               => ( X5 @ X3 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM250G_pme]) ).

thf(h2,assumption,
    ~ ! [X1: a > a > $o,X2: a,X3: a] :
        ( ~ ! [X4: a > a > $o] :
              ( ~ ( ! [X5: a,X6: a] :
                      ( ( ~ ( eigen__0 @ X5 @ X6 )
                       => ( X1 @ X5 @ X6 ) )
                     => ( X4 @ X5 @ X6 ) )
                 => ~ ! [X5: a,X6: a,X7: a] :
                        ( ~ ( ( X4 @ X5 @ X6 )
                           => ~ ( X4 @ X6 @ X7 ) )
                       => ( X4 @ X5 @ X7 ) ) )
             => ( X4 @ X2 @ X3 ) )
       => ~ ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ! [X6: a > a > $o] :
                            ( ~ ( ! [X7: a,X8: a] :
                                    ( ( eigen__0 @ X7 @ X8 )
                                   => ( X6 @ X7 @ X8 ) )
                               => ~ ! [X7: a,X8: a,X9: a] :
                                      ( ~ ( ( X6 @ X7 @ X8 )
                                         => ~ ( X6 @ X8 @ X9 ) )
                                     => ( X6 @ X7 @ X9 ) ) )
                           => ( X6 @ X4 @ X5 ) )
                     => ! [X6: a > a > $o] :
                          ( ~ ( ! [X7: a,X8: a] :
                                  ( ( X1 @ X7 @ X8 )
                                 => ( X6 @ X7 @ X8 ) )
                             => ~ ! [X7: a,X8: a,X9: a] :
                                    ( ~ ( ( X6 @ X7 @ X8 )
                                       => ~ ( X6 @ X8 @ X9 ) )
                                   => ( X6 @ X7 @ X9 ) ) )
                         => ( X6 @ X4 @ X5 ) ) )
                   => ! [X6: a > a > $o] :
                        ( ~ ( ! [X7: a,X8: a] :
                                ( ( ~ ( eigen__0 @ X7 @ X8 )
                                 => ( X1 @ X7 @ X8 ) )
                               => ( X6 @ X7 @ X8 ) )
                           => ~ ! [X7: a,X8: a,X9: a] :
                                  ( ~ ( ( X6 @ X7 @ X8 )
                                     => ~ ( X6 @ X8 @ X9 ) )
                                 => ( X6 @ X7 @ X9 ) ) )
                       => ( X6 @ X4 @ X5 ) ) )
               => ~ ! [X4: a,X5: a,X6: a] :
                      ( ~ ( ! [X7: a > a > $o] :
                              ( ~ ( ! [X8: a,X9: a] :
                                      ( ( ~ ( eigen__0 @ X8 @ X9 )
                                       => ( X1 @ X8 @ X9 ) )
                                     => ( X7 @ X8 @ X9 ) )
                                 => ~ ! [X8: a,X9: a,X10: a] :
                                        ( ~ ( ( X7 @ X8 @ X9 )
                                           => ~ ( X7 @ X9 @ X10 ) )
                                       => ( X7 @ X8 @ X10 ) ) )
                             => ( X7 @ X4 @ X5 ) )
                         => ~ ! [X7: a > a > $o] :
                                ( ~ ( ! [X8: a,X9: a] :
                                        ( ( ~ ( eigen__0 @ X8 @ X9 )
                                         => ( X1 @ X8 @ X9 ) )
                                       => ( X7 @ X8 @ X9 ) )
                                   => ~ ! [X8: a,X9: a,X10: a] :
                                          ( ~ ( ( X7 @ X8 @ X9 )
                                             => ~ ( X7 @ X9 @ X10 ) )
                                         => ( X7 @ X8 @ X10 ) ) )
                               => ( X7 @ X5 @ X6 ) ) )
                     => ! [X7: a > a > $o] :
                          ( ~ ( ! [X8: a,X9: a] :
                                  ( ( ~ ( eigen__0 @ X8 @ X9 )
                                   => ( X1 @ X8 @ X9 ) )
                                 => ( X7 @ X8 @ X9 ) )
                             => ~ ! [X8: a,X9: a,X10: a] :
                                    ( ~ ( ( X7 @ X8 @ X9 )
                                       => ~ ( X7 @ X9 @ X10 ) )
                                   => ( X7 @ X8 @ X10 ) ) )
                         => ( X7 @ X4 @ X6 ) ) ) )
           => ! [X4: a > a > $o] :
                ( ~ ( ! [X5: a,X6: a] :
                        ( ( ~ ( eigen__0 @ X5 @ X6 )
                         => ( X1 @ X5 @ X6 ) )
                       => ( X4 @ X5 @ X6 ) )
                   => ~ ! [X5: a,X6: a,X7: a] :
                          ( ~ ( ( X4 @ X5 @ X6 )
                             => ~ ( X4 @ X6 @ X7 ) )
                         => ( X4 @ X5 @ X7 ) ) )
               => ( X4 @ X2 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: a,X2: a] :
        ( ~ ! [X3: a > a > $o] :
              ( ~ ( ! [X4: a,X5: a] :
                      ( ( ~ ( eigen__0 @ X4 @ X5 )
                       => ( eigen__1 @ X4 @ X5 ) )
                     => ( X3 @ X4 @ X5 ) )
                 => ~ ! [X4: a,X5: a,X6: a] :
                        ( ~ ( ( X3 @ X4 @ X5 )
                           => ~ ( X3 @ X5 @ X6 ) )
                       => ( X3 @ X4 @ X6 ) ) )
             => ( X3 @ X1 @ X2 ) )
       => ~ ( ~ ( ! [X3: a,X4: a] :
                    ( ( ~ ! [X5: a > a > $o] :
                            ( ~ ( ! [X6: a,X7: a] :
                                    ( ( eigen__0 @ X6 @ X7 )
                                   => ( X5 @ X6 @ X7 ) )
                               => ~ ! [X6: a,X7: a,X8: a] :
                                      ( ~ ( ( X5 @ X6 @ X7 )
                                         => ~ ( X5 @ X7 @ X8 ) )
                                     => ( X5 @ X6 @ X8 ) ) )
                           => ( X5 @ X3 @ X4 ) )
                     => ! [X5: a > a > $o] :
                          ( ~ ( ! [X6: a,X7: a] :
                                  ( ( eigen__1 @ X6 @ X7 )
                                 => ( X5 @ X6 @ X7 ) )
                             => ~ ! [X6: a,X7: a,X8: a] :
                                    ( ~ ( ( X5 @ X6 @ X7 )
                                       => ~ ( X5 @ X7 @ X8 ) )
                                   => ( X5 @ X6 @ X8 ) ) )
                         => ( X5 @ X3 @ X4 ) ) )
                   => ! [X5: a > a > $o] :
                        ( ~ ( ! [X6: a,X7: a] :
                                ( ( ~ ( eigen__0 @ X6 @ X7 )
                                 => ( eigen__1 @ X6 @ X7 ) )
                               => ( X5 @ X6 @ X7 ) )
                           => ~ ! [X6: a,X7: a,X8: a] :
                                  ( ~ ( ( X5 @ X6 @ X7 )
                                     => ~ ( X5 @ X7 @ X8 ) )
                                 => ( X5 @ X6 @ X8 ) ) )
                       => ( X5 @ X3 @ X4 ) ) )
               => ~ ! [X3: a,X4: a,X5: a] :
                      ( ~ ( ! [X6: a > a > $o] :
                              ( ~ ( ! [X7: a,X8: a] :
                                      ( ( ~ ( eigen__0 @ X7 @ X8 )
                                       => ( eigen__1 @ X7 @ X8 ) )
                                     => ( X6 @ X7 @ X8 ) )
                                 => ~ ! [X7: a,X8: a,X9: a] :
                                        ( ~ ( ( X6 @ X7 @ X8 )
                                           => ~ ( X6 @ X8 @ X9 ) )
                                       => ( X6 @ X7 @ X9 ) ) )
                             => ( X6 @ X3 @ X4 ) )
                         => ~ ! [X6: a > a > $o] :
                                ( ~ ( ! [X7: a,X8: a] :
                                        ( ( ~ ( eigen__0 @ X7 @ X8 )
                                         => ( eigen__1 @ X7 @ X8 ) )
                                       => ( X6 @ X7 @ X8 ) )
                                   => ~ ! [X7: a,X8: a,X9: a] :
                                          ( ~ ( ( X6 @ X7 @ X8 )
                                             => ~ ( X6 @ X8 @ X9 ) )
                                         => ( X6 @ X7 @ X9 ) ) )
                               => ( X6 @ X4 @ X5 ) ) )
                     => ! [X6: a > a > $o] :
                          ( ~ ( ! [X7: a,X8: a] :
                                  ( ( ~ ( eigen__0 @ X7 @ X8 )
                                   => ( eigen__1 @ X7 @ X8 ) )
                                 => ( X6 @ X7 @ X8 ) )
                             => ~ ! [X7: a,X8: a,X9: a] :
                                    ( ~ ( ( X6 @ X7 @ X8 )
                                       => ~ ( X6 @ X8 @ X9 ) )
                                   => ( X6 @ X7 @ X9 ) ) )
                         => ( X6 @ X3 @ X5 ) ) ) )
           => ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( ~ ( eigen__0 @ X4 @ X5 )
                         => ( eigen__1 @ X4 @ X5 ) )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ! [X4: a,X5: a,X6: a] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) ) )
               => ( X3 @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: a] :
        ( ~ ! [X2: a > a > $o] :
              ( ~ ( ! [X3: a,X4: a] :
                      ( ( ~ ( eigen__0 @ X3 @ X4 )
                       => ( eigen__1 @ X3 @ X4 ) )
                     => ( X2 @ X3 @ X4 ) )
                 => ~ ! [X3: a,X4: a,X5: a] :
                        ( ~ ( ( X2 @ X3 @ X4 )
                           => ~ ( X2 @ X4 @ X5 ) )
                       => ( X2 @ X3 @ X5 ) ) )
             => ( X2 @ eigen__2 @ X1 ) )
       => ~ ( ~ ( ! [X2: a,X3: a] :
                    ( ( ~ ! [X4: a > a > $o] :
                            ( ~ ( ! [X5: a,X6: a] :
                                    ( ( eigen__0 @ X5 @ X6 )
                                   => ( X4 @ X5 @ X6 ) )
                               => ~ ! [X5: a,X6: a,X7: a] :
                                      ( ~ ( ( X4 @ X5 @ X6 )
                                         => ~ ( X4 @ X6 @ X7 ) )
                                     => ( X4 @ X5 @ X7 ) ) )
                           => ( X4 @ X2 @ X3 ) )
                     => ! [X4: a > a > $o] :
                          ( ~ ( ! [X5: a,X6: a] :
                                  ( ( eigen__1 @ X5 @ X6 )
                                 => ( X4 @ X5 @ X6 ) )
                             => ~ ! [X5: a,X6: a,X7: a] :
                                    ( ~ ( ( X4 @ X5 @ X6 )
                                       => ~ ( X4 @ X6 @ X7 ) )
                                   => ( X4 @ X5 @ X7 ) ) )
                         => ( X4 @ X2 @ X3 ) ) )
                   => ! [X4: a > a > $o] :
                        ( ~ ( ! [X5: a,X6: a] :
                                ( ( ~ ( eigen__0 @ X5 @ X6 )
                                 => ( eigen__1 @ X5 @ X6 ) )
                               => ( X4 @ X5 @ X6 ) )
                           => ~ ! [X5: a,X6: a,X7: a] :
                                  ( ~ ( ( X4 @ X5 @ X6 )
                                     => ~ ( X4 @ X6 @ X7 ) )
                                 => ( X4 @ X5 @ X7 ) ) )
                       => ( X4 @ X2 @ X3 ) ) )
               => ~ ! [X2: a,X3: a,X4: a] :
                      ( ~ ( ! [X5: a > a > $o] :
                              ( ~ ( ! [X6: a,X7: a] :
                                      ( ( ~ ( eigen__0 @ X6 @ X7 )
                                       => ( eigen__1 @ X6 @ X7 ) )
                                     => ( X5 @ X6 @ X7 ) )
                                 => ~ ! [X6: a,X7: a,X8: a] :
                                        ( ~ ( ( X5 @ X6 @ X7 )
                                           => ~ ( X5 @ X7 @ X8 ) )
                                       => ( X5 @ X6 @ X8 ) ) )
                             => ( X5 @ X2 @ X3 ) )
                         => ~ ! [X5: a > a > $o] :
                                ( ~ ( ! [X6: a,X7: a] :
                                        ( ( ~ ( eigen__0 @ X6 @ X7 )
                                         => ( eigen__1 @ X6 @ X7 ) )
                                       => ( X5 @ X6 @ X7 ) )
                                   => ~ ! [X6: a,X7: a,X8: a] :
                                          ( ~ ( ( X5 @ X6 @ X7 )
                                             => ~ ( X5 @ X7 @ X8 ) )
                                         => ( X5 @ X6 @ X8 ) ) )
                               => ( X5 @ X3 @ X4 ) ) )
                     => ! [X5: a > a > $o] :
                          ( ~ ( ! [X6: a,X7: a] :
                                  ( ( ~ ( eigen__0 @ X6 @ X7 )
                                   => ( eigen__1 @ X6 @ X7 ) )
                                 => ( X5 @ X6 @ X7 ) )
                             => ~ ! [X6: a,X7: a,X8: a] :
                                    ( ~ ( ( X5 @ X6 @ X7 )
                                       => ~ ( X5 @ X7 @ X8 ) )
                                   => ( X5 @ X6 @ X8 ) ) )
                         => ( X5 @ X2 @ X4 ) ) ) )
           => ! [X2: a > a > $o] :
                ( ~ ( ! [X3: a,X4: a] :
                        ( ( ~ ( eigen__0 @ X3 @ X4 )
                         => ( eigen__1 @ X3 @ X4 ) )
                       => ( X2 @ X3 @ X4 ) )
                   => ~ ! [X3: a,X4: a,X5: a] :
                          ( ~ ( ( X2 @ X3 @ X4 )
                             => ~ ( X2 @ X4 @ X5 ) )
                         => ( X2 @ X3 @ X5 ) ) )
               => ( X2 @ eigen__2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ~ sP35
     => ~ ( ~ ( ! [X1: a,X2: a] :
                  ( ( ~ ! [X3: a > a > $o] :
                          ( ~ ( ! [X4: a,X5: a] :
                                  ( ( eigen__0 @ X4 @ X5 )
                                 => ( X3 @ X4 @ X5 ) )
                             => ~ ! [X4: a,X5: a,X6: a] :
                                    ( ~ ( ( X3 @ X4 @ X5 )
                                       => ~ ( X3 @ X5 @ X6 ) )
                                   => ( X3 @ X4 @ X6 ) ) )
                         => ( X3 @ X1 @ X2 ) )
                   => ! [X3: a > a > $o] :
                        ( ~ ( ! [X4: a,X5: a] :
                                ( ( eigen__1 @ X4 @ X5 )
                               => ( X3 @ X4 @ X5 ) )
                           => ~ ! [X4: a,X5: a,X6: a] :
                                  ( ~ ( ( X3 @ X4 @ X5 )
                                     => ~ ( X3 @ X5 @ X6 ) )
                                 => ( X3 @ X4 @ X6 ) ) )
                       => ( X3 @ X1 @ X2 ) ) )
                 => ! [X3: a > a > $o] :
                      ( ~ ( ! [X4: a,X5: a] :
                              ( ( ~ ( eigen__0 @ X4 @ X5 )
                               => ( eigen__1 @ X4 @ X5 ) )
                             => ( X3 @ X4 @ X5 ) )
                         => ~ ! [X4: a,X5: a,X6: a] :
                                ( ~ ( ( X3 @ X4 @ X5 )
                                   => ~ ( X3 @ X5 @ X6 ) )
                               => ( X3 @ X4 @ X6 ) ) )
                     => ( X3 @ X1 @ X2 ) ) )
             => ~ ! [X1: a,X2: a,X3: a] :
                    ( ~ ( ! [X4: a > a > $o] :
                            ( ~ ( ! [X5: a,X6: a] :
                                    ( ( ~ ( eigen__0 @ X5 @ X6 )
                                     => ( eigen__1 @ X5 @ X6 ) )
                                   => ( X4 @ X5 @ X6 ) )
                               => ~ ! [X5: a,X6: a,X7: a] :
                                      ( ~ ( ( X4 @ X5 @ X6 )
                                         => ~ ( X4 @ X6 @ X7 ) )
                                     => ( X4 @ X5 @ X7 ) ) )
                           => ( X4 @ X1 @ X2 ) )
                       => ~ ! [X4: a > a > $o] :
                              ( ~ ( ! [X5: a,X6: a] :
                                      ( ( ~ ( eigen__0 @ X5 @ X6 )
                                       => ( eigen__1 @ X5 @ X6 ) )
                                     => ( X4 @ X5 @ X6 ) )
                                 => ~ ! [X5: a,X6: a,X7: a] :
                                        ( ~ ( ( X4 @ X5 @ X6 )
                                           => ~ ( X4 @ X6 @ X7 ) )
                                       => ( X4 @ X5 @ X7 ) ) )
                             => ( X4 @ X2 @ X3 ) ) )
                   => ! [X4: a > a > $o] :
                        ( ~ ( ! [X5: a,X6: a] :
                                ( ( ~ ( eigen__0 @ X5 @ X6 )
                                 => ( eigen__1 @ X5 @ X6 ) )
                               => ( X4 @ X5 @ X6 ) )
                           => ~ ! [X5: a,X6: a,X7: a] :
                                  ( ~ ( ( X4 @ X5 @ X6 )
                                     => ~ ( X4 @ X6 @ X7 ) )
                                 => ( X4 @ X5 @ X7 ) ) )
                       => ( X4 @ X1 @ X3 ) ) ) )
         => sP35 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP35,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ( ~ ( ! [X1: a,X2: a] :
            ( ( ~ ! [X3: a > a > $o] :
                    ( ~ ( ! [X4: a,X5: a] :
                            ( ( eigen__0 @ X4 @ X5 )
                           => ( X3 @ X4 @ X5 ) )
                       => ~ ! [X4: a,X5: a,X6: a] :
                              ( ~ ( ( X3 @ X4 @ X5 )
                                 => ~ ( X3 @ X5 @ X6 ) )
                             => ( X3 @ X4 @ X6 ) ) )
                   => ( X3 @ X1 @ X2 ) )
             => ! [X3: a > a > $o] :
                  ( ~ ( ! [X4: a,X5: a] :
                          ( ( eigen__1 @ X4 @ X5 )
                         => ( X3 @ X4 @ X5 ) )
                     => ~ ! [X4: a,X5: a,X6: a] :
                            ( ~ ( ( X3 @ X4 @ X5 )
                               => ~ ( X3 @ X5 @ X6 ) )
                           => ( X3 @ X4 @ X6 ) ) )
                 => ( X3 @ X1 @ X2 ) ) )
           => ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( ~ ( eigen__0 @ X4 @ X5 )
                         => ( eigen__1 @ X4 @ X5 ) )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ! [X4: a,X5: a,X6: a] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) ) )
               => ( X3 @ X1 @ X2 ) ) )
       => ~ ! [X1: a,X2: a,X3: a] :
              ( ~ ( ! [X4: a > a > $o] :
                      ( ~ ( ! [X5: a,X6: a] :
                              ( ( ~ ( eigen__0 @ X5 @ X6 )
                               => ( eigen__1 @ X5 @ X6 ) )
                             => ( X4 @ X5 @ X6 ) )
                         => ~ ! [X5: a,X6: a,X7: a] :
                                ( ~ ( ( X4 @ X5 @ X6 )
                                   => ~ ( X4 @ X6 @ X7 ) )
                               => ( X4 @ X5 @ X7 ) ) )
                     => ( X4 @ X1 @ X2 ) )
                 => ~ ! [X4: a > a > $o] :
                        ( ~ ( ! [X5: a,X6: a] :
                                ( ( ~ ( eigen__0 @ X5 @ X6 )
                                 => ( eigen__1 @ X5 @ X6 ) )
                               => ( X4 @ X5 @ X6 ) )
                           => ~ ! [X5: a,X6: a,X7: a] :
                                  ( ~ ( ( X4 @ X5 @ X6 )
                                     => ~ ( X4 @ X6 @ X7 ) )
                                 => ( X4 @ X5 @ X7 ) ) )
                       => ( X4 @ X2 @ X3 ) ) )
             => ! [X4: a > a > $o] :
                  ( ~ ( ! [X5: a,X6: a] :
                          ( ( ~ ( eigen__0 @ X5 @ X6 )
                           => ( eigen__1 @ X5 @ X6 ) )
                         => ( X4 @ X5 @ X6 ) )
                     => ~ ! [X5: a,X6: a,X7: a] :
                            ( ~ ( ( X4 @ X5 @ X6 )
                               => ~ ( X4 @ X6 @ X7 ) )
                           => ( X4 @ X5 @ X7 ) ) )
                 => ( X4 @ X1 @ X3 ) ) ) )
   => sP35 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP41,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP28,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP19,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ( ! [X1: a,X2: a] :
        ( ( ~ ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( eigen__0 @ X4 @ X5 )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ! [X4: a,X5: a,X6: a] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) ) )
               => ( X3 @ X1 @ X2 ) )
         => ! [X3: a > a > $o] :
              ( ~ ( ! [X4: a,X5: a] :
                      ( ( eigen__1 @ X4 @ X5 )
                     => ( X3 @ X4 @ X5 ) )
                 => ~ ! [X4: a,X5: a,X6: a] :
                        ( ~ ( ( X3 @ X4 @ X5 )
                           => ~ ( X3 @ X5 @ X6 ) )
                       => ( X3 @ X4 @ X6 ) ) )
             => ( X3 @ X1 @ X2 ) ) )
       => ! [X3: a > a > $o] :
            ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ( eigen__0 @ X4 @ X5 )
                     => ( eigen__1 @ X4 @ X5 ) )
                   => ( X3 @ X4 @ X5 ) )
               => ~ ! [X4: a,X5: a,X6: a] :
                      ( ~ ( ( X3 @ X4 @ X5 )
                         => ~ ( X3 @ X5 @ X6 ) )
                     => ( X3 @ X4 @ X6 ) ) )
           => ( X3 @ X1 @ X2 ) ) )
   => ~ ! [X1: a,X2: a,X3: a] :
          ( ~ ( ! [X4: a > a > $o] :
                  ( ~ ( ! [X5: a,X6: a] :
                          ( ( ~ ( eigen__0 @ X5 @ X6 )
                           => ( eigen__1 @ X5 @ X6 ) )
                         => ( X4 @ X5 @ X6 ) )
                     => ~ ! [X5: a,X6: a,X7: a] :
                            ( ~ ( ( X4 @ X5 @ X6 )
                               => ~ ( X4 @ X6 @ X7 ) )
                           => ( X4 @ X5 @ X7 ) ) )
                 => ( X4 @ X1 @ X2 ) )
             => ~ ! [X4: a > a > $o] :
                    ( ~ ( ! [X5: a,X6: a] :
                            ( ( ~ ( eigen__0 @ X5 @ X6 )
                             => ( eigen__1 @ X5 @ X6 ) )
                           => ( X4 @ X5 @ X6 ) )
                       => ~ ! [X5: a,X6: a,X7: a] :
                              ( ~ ( ( X4 @ X5 @ X6 )
                                 => ~ ( X4 @ X6 @ X7 ) )
                             => ( X4 @ X5 @ X7 ) ) )
                   => ( X4 @ X2 @ X3 ) ) )
         => ! [X4: a > a > $o] :
              ( ~ ( ! [X5: a,X6: a] :
                      ( ( ~ ( eigen__0 @ X5 @ X6 )
                       => ( eigen__1 @ X5 @ X6 ) )
                     => ( X4 @ X5 @ X6 ) )
                 => ~ ! [X5: a,X6: a,X7: a] :
                        ( ~ ( ( X4 @ X5 @ X6 )
                           => ~ ( X4 @ X6 @ X7 ) )
                       => ( X4 @ X5 @ X7 ) ) )
             => ( X4 @ X1 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP35,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ! [X1: a,X2: a] :
        ( ( ~ ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( eigen__0 @ X4 @ X5 )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ! [X4: a,X5: a,X6: a] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) ) )
               => ( X3 @ X1 @ X2 ) )
         => ! [X3: a > a > $o] :
              ( ~ ( ! [X4: a,X5: a] :
                      ( ( eigen__1 @ X4 @ X5 )
                     => ( X3 @ X4 @ X5 ) )
                 => ~ ! [X4: a,X5: a,X6: a] :
                        ( ~ ( ( X3 @ X4 @ X5 )
                           => ~ ( X3 @ X5 @ X6 ) )
                       => ( X3 @ X4 @ X6 ) ) )
             => ( X3 @ X1 @ X2 ) ) )
       => ! [X3: a > a > $o] :
            ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ( eigen__0 @ X4 @ X5 )
                     => ( eigen__1 @ X4 @ X5 ) )
                   => ( X3 @ X4 @ X5 ) )
               => ~ ! [X4: a,X5: a,X6: a] :
                      ( ~ ( ( X3 @ X4 @ X5 )
                         => ~ ( X3 @ X5 @ X6 ) )
                     => ( X3 @ X4 @ X6 ) ) )
           => ( X3 @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ! [X1: a,X2: a,X3: a] :
        ( ~ ( ! [X4: a > a > $o] :
                ( ~ ( ! [X5: a,X6: a] :
                        ( ( ~ ( eigen__0 @ X5 @ X6 )
                         => ( eigen__1 @ X5 @ X6 ) )
                       => ( X4 @ X5 @ X6 ) )
                   => ~ ! [X5: a,X6: a,X7: a] :
                          ( ~ ( ( X4 @ X5 @ X6 )
                             => ~ ( X4 @ X6 @ X7 ) )
                         => ( X4 @ X5 @ X7 ) ) )
               => ( X4 @ X1 @ X2 ) )
           => ~ ! [X4: a > a > $o] :
                  ( ~ ( ! [X5: a,X6: a] :
                          ( ( ~ ( eigen__0 @ X5 @ X6 )
                           => ( eigen__1 @ X5 @ X6 ) )
                         => ( X4 @ X5 @ X6 ) )
                     => ~ ! [X5: a,X6: a,X7: a] :
                            ( ~ ( ( X4 @ X5 @ X6 )
                               => ~ ( X4 @ X6 @ X7 ) )
                           => ( X4 @ X5 @ X7 ) ) )
                 => ( X4 @ X2 @ X3 ) ) )
       => ! [X4: a > a > $o] :
            ( ~ ( ! [X5: a,X6: a] :
                    ( ( ~ ( eigen__0 @ X5 @ X6 )
                     => ( eigen__1 @ X5 @ X6 ) )
                   => ( X4 @ X5 @ X6 ) )
               => ~ ! [X5: a,X6: a,X7: a] :
                      ( ~ ( ( X4 @ X5 @ X6 )
                         => ~ ( X4 @ X6 @ X7 ) )
                     => ( X4 @ X5 @ X7 ) ) )
           => ( X4 @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ! [X1: a] :
        ( ( ~ ! [X2: a > a > $o] :
                ( ~ ( ! [X3: a,X4: a] :
                        ( ( eigen__0 @ X3 @ X4 )
                       => ( X2 @ X3 @ X4 ) )
                   => ~ ! [X3: a,X4: a,X5: a] :
                          ( ~ ( ( X2 @ X3 @ X4 )
                             => ~ ( X2 @ X4 @ X5 ) )
                         => ( X2 @ X3 @ X5 ) ) )
               => ( X2 @ eigen__5 @ X1 ) )
         => ! [X2: a > a > $o] :
              ( ~ ( ! [X3: a,X4: a] :
                      ( ( eigen__1 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) )
                 => ~ ! [X3: a,X4: a,X5: a] :
                        ( ~ ( ( X2 @ X3 @ X4 )
                           => ~ ( X2 @ X4 @ X5 ) )
                       => ( X2 @ X3 @ X5 ) ) )
             => ( X2 @ eigen__5 @ X1 ) ) )
       => ! [X2: a > a > $o] :
            ( ~ ( ! [X3: a,X4: a] :
                    ( ( ~ ( eigen__0 @ X3 @ X4 )
                     => ( eigen__1 @ X3 @ X4 ) )
                   => ( X2 @ X3 @ X4 ) )
               => ~ ! [X3: a,X4: a,X5: a] :
                      ( ~ ( ( X2 @ X3 @ X4 )
                         => ~ ( X2 @ X4 @ X5 ) )
                     => ( X2 @ X3 @ X5 ) ) )
           => ( X2 @ eigen__5 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ( ( ~ sP47
       => sP48 )
     => ! [X1: a > a > $o] :
          ( ~ ( ! [X2: a,X3: a] :
                  ( ( ~ ( eigen__0 @ X2 @ X3 )
                   => ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X2 @ X3 ) )
             => ~ ! [X2: a,X3: a,X4: a] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X3 @ X4 ) )
                   => ( X1 @ X2 @ X4 ) ) )
         => ( X1 @ eigen__5 @ eigen__6 ) ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ( ~ sP47
   => sP48 ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__0 @ X2 @ X3 )
                 => ( eigen__1 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__5 @ eigen__6 ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    sP47,
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP48,
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( ~ ( sP34
         => ~ sP1 )
     => sP38 ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    ~ ( sP34
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h25,assumption,
    ~ sP38,
    introduced(assumption,[]) ).

thf(h26,assumption,
    sP34,
    introduced(assumption,[]) ).

thf(h27,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP2
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP34
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP33
    | ~ sP2
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP16
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP16
    | sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP37
    | ~ sP16 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).

thf(8,plain,
    ( sP29
    | ~ sP37 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).

thf(9,plain,
    ( ~ sP47
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP27
    | sP42
    | sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP42
    | ~ sP29
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h21,h26,h27,h25]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,12,h26,h27]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,13,h24,h25]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__7)],[h20,14,h23]) ).

thf(h28,assumption,
    ~ ( ~ ( sP13
         => ~ sP10 )
     => sP5 ),
    introduced(assumption,[]) ).

thf(h29,assumption,
    ~ ( sP13
     => ~ sP10 ),
    introduced(assumption,[]) ).

thf(h30,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h31,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h32,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(16,plain,
    ( sP4
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP13
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP24
    | sP45 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP45
    | ~ sP4
    | sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP12
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP12
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP11
    | ~ sP12 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).

thf(23,plain,
    ( sP23
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).

thf(24,plain,
    ( ~ sP48
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP31
    | sP44
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP44
    | ~ sP23
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h31,h32,h29,h30,h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[16,17,18,19,20,21,22,23,24,25,26,h22,h31,h32,h30]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,27,h31,h32]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,28,h29,h30]) ).

thf(30,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__12)],[h20,29,h28]) ).

thf(31,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h19,15,30,h21,h22]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,31,h19,h20]) ).

thf(33,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__6)],[h17,32,h18]) ).

thf(34,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__5)],[h15,33,h17]) ).

thf(h33,assumption,
    ~ ! [X1: a,X2: a] :
        ( ~ ( ! [X3: a > a > $o] :
                ( ~ ( ! [X4: a,X5: a] :
                        ( ( ~ ( eigen__0 @ X4 @ X5 )
                         => ( eigen__1 @ X4 @ X5 ) )
                       => ( X3 @ X4 @ X5 ) )
                   => ~ ! [X4: a,X5: a,X6: a] :
                          ( ~ ( ( X3 @ X4 @ X5 )
                             => ~ ( X3 @ X5 @ X6 ) )
                         => ( X3 @ X4 @ X6 ) ) )
               => ( X3 @ eigen__23 @ X1 ) )
           => ~ ! [X3: a > a > $o] :
                  ( ~ ( ! [X4: a,X5: a] :
                          ( ( ~ ( eigen__0 @ X4 @ X5 )
                           => ( eigen__1 @ X4 @ X5 ) )
                         => ( X3 @ X4 @ X5 ) )
                     => ~ ! [X4: a,X5: a,X6: a] :
                            ( ~ ( ( X3 @ X4 @ X5 )
                               => ~ ( X3 @ X5 @ X6 ) )
                           => ( X3 @ X4 @ X6 ) ) )
                 => ( X3 @ X1 @ X2 ) ) )
       => ! [X3: a > a > $o] :
            ( ~ ( ! [X4: a,X5: a] :
                    ( ( ~ ( eigen__0 @ X4 @ X5 )
                     => ( eigen__1 @ X4 @ X5 ) )
                   => ( X3 @ X4 @ X5 ) )
               => ~ ! [X4: a,X5: a,X6: a] :
                      ( ~ ( ( X3 @ X4 @ X5 )
                         => ~ ( X3 @ X5 @ X6 ) )
                     => ( X3 @ X4 @ X6 ) ) )
           => ( X3 @ eigen__23 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h34,assumption,
    ~ ! [X1: a] :
        ( ~ ( sP9
           => ~ ! [X2: a > a > $o] :
                  ( ~ ( ! [X3: a,X4: a] :
                          ( ( ~ ( eigen__0 @ X3 @ X4 )
                           => ( eigen__1 @ X3 @ X4 ) )
                         => ( X2 @ X3 @ X4 ) )
                     => ~ ! [X3: a,X4: a,X5: a] :
                            ( ~ ( ( X2 @ X3 @ X4 )
                               => ~ ( X2 @ X4 @ X5 ) )
                           => ( X2 @ X3 @ X5 ) ) )
                 => ( X2 @ eigen__24 @ X1 ) ) )
       => ! [X2: a > a > $o] :
            ( ~ ( ! [X3: a,X4: a] :
                    ( ( ~ ( eigen__0 @ X3 @ X4 )
                     => ( eigen__1 @ X3 @ X4 ) )
                   => ( X2 @ X3 @ X4 ) )
               => ~ ! [X3: a,X4: a,X5: a] :
                      ( ~ ( ( X2 @ X3 @ X4 )
                         => ~ ( X2 @ X4 @ X5 ) )
                     => ( X2 @ X3 @ X5 ) ) )
           => ( X2 @ eigen__23 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h35,assumption,
    ~ ( ~ ( sP9
         => ~ sP6 )
     => ! [X1: a > a > $o] :
          ( ~ ( ! [X2: a,X3: a] :
                  ( ( ~ ( eigen__0 @ X2 @ X3 )
                   => ( eigen__1 @ X2 @ X3 ) )
                 => ( X1 @ X2 @ X3 ) )
             => ~ ! [X2: a,X3: a,X4: a] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X3 @ X4 ) )
                   => ( X1 @ X2 @ X4 ) ) )
         => ( X1 @ eigen__23 @ eigen__25 ) ) ),
    introduced(assumption,[]) ).

thf(h36,assumption,
    ~ ( sP9
     => ~ sP6 ),
    introduced(assumption,[]) ).

thf(h37,assumption,
    ~ ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( ~ ( eigen__0 @ X2 @ X3 )
                 => ( eigen__1 @ X2 @ X3 ) )
               => ( X1 @ X2 @ X3 ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ( X1 @ eigen__23 @ eigen__25 ) ),
    introduced(assumption,[]) ).

thf(h38,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h39,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h40,assumption,
    ~ ( ~ sP21
     => sP17 ),
    introduced(assumption,[]) ).

thf(h41,assumption,
    ~ sP21,
    introduced(assumption,[]) ).

thf(h42,assumption,
    ~ sP17,
    introduced(assumption,[]) ).

thf(h43,assumption,
    sP39,
    introduced(assumption,[]) ).

thf(h44,assumption,
    sP22,
    introduced(assumption,[]) ).

thf(35,plain,
    ( ~ sP22
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP14
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP15
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP30
    | sP20
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP20
    | ~ sP26
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP9
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP18
    | sP21
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP6
    | sP46 ),
    inference(all_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP46
    | sP21
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP21
    | ~ sP39
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h43,h44,h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[35,36,37,38,39,40,41,42,43,44,h38,h39,h43,h44,h42]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,45,h43,h44]) ).

thf(47,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h40,46,h41,h42]) ).

thf(48,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__26)],[h37,47,h40]) ).

thf(49,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h38,h39])],[h36,48,h38,h39]) ).

thf(50,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,49,h36,h37]) ).

thf(51,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__25)],[h34,50,h35]) ).

thf(52,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__24)],[h33,51,h34]) ).

thf(53,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__23)],[h16,52,h33]) ).

thf(54,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h13,34,53,h15,h16]) ).

thf(55,plain,
    ( ~ sP35
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(56,plain,
    ( ~ sP41
    | sP28
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(57,plain,
    ( ~ sP28
    | ~ sP3
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[55,56,57,h11,h12,h10,h14]) ).

thf(59,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h7,54,58,h13,h14]) ).

thf(60,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,59,h11,h12]) ).

thf(61,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,60,h9,h10]) ).

thf(62,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__4)],[h6,61,h8]) ).

thf(63,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,62,h6,h7]) ).

thf(64,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,63,h5]) ).

thf(65,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,64,h4]) ).

thf(66,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,65,h3]) ).

thf(67,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,66,h2]) ).

thf(68,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0]) ).

thf(0,theorem,
    ! [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 ) )
               => ~ ! [X6: a,X7: a,X8: a] :
                      ( ~ ( ( X5 @ X6 @ X7 )
                         => ~ ( X5 @ X7 @ X8 ) )
                     => ( X5 @ X6 @ X8 ) ) )
           => ( X5 @ X3 @ X4 ) )
     => ~ ( ~ ( ! [X5: a,X6: a] :
                  ( ( ~ ! [X7: a > a > $o] :
                          ( ~ ( ! [X8: a,X9: a] :
                                  ( ( X1 @ X8 @ X9 )
                                 => ( X7 @ X8 @ X9 ) )
                             => ~ ! [X8: a,X9: a,X10: a] :
                                    ( ~ ( ( X7 @ X8 @ X9 )
                                       => ~ ( X7 @ X9 @ X10 ) )
                                   => ( X7 @ X8 @ X10 ) ) )
                         => ( X7 @ X5 @ X6 ) )
                   => ! [X7: a > a > $o] :
                        ( ~ ( ! [X8: a,X9: a] :
                                ( ( X2 @ X8 @ X9 )
                               => ( X7 @ X8 @ X9 ) )
                           => ~ ! [X8: a,X9: a,X10: a] :
                                  ( ~ ( ( X7 @ X8 @ X9 )
                                     => ~ ( X7 @ X9 @ X10 ) )
                                 => ( X7 @ X8 @ X10 ) ) )
                       => ( X7 @ X5 @ X6 ) ) )
                 => ! [X7: a > a > $o] :
                      ( ~ ( ! [X8: a,X9: a] :
                              ( ( ~ ( X1 @ X8 @ X9 )
                               => ( X2 @ X8 @ X9 ) )
                             => ( X7 @ X8 @ X9 ) )
                         => ~ ! [X8: a,X9: a,X10: a] :
                                ( ~ ( ( X7 @ X8 @ X9 )
                                   => ~ ( X7 @ X9 @ X10 ) )
                               => ( X7 @ X8 @ X10 ) ) )
                     => ( X7 @ X5 @ X6 ) ) )
             => ~ ! [X5: a,X6: a,X7: a] :
                    ( ~ ( ! [X8: a > a > $o] :
                            ( ~ ( ! [X9: a,X10: a] :
                                    ( ( ~ ( X1 @ X9 @ X10 )
                                     => ( X2 @ X9 @ X10 ) )
                                   => ( X8 @ X9 @ X10 ) )
                               => ~ ! [X9: a,X10: a,X11: a] :
                                      ( ~ ( ( X8 @ X9 @ X10 )
                                         => ~ ( X8 @ X10 @ X11 ) )
                                     => ( X8 @ X9 @ X11 ) ) )
                           => ( X8 @ X5 @ X6 ) )
                       => ~ ! [X8: a > a > $o] :
                              ( ~ ( ! [X9: a,X10: a] :
                                      ( ( ~ ( X1 @ X9 @ X10 )
                                       => ( X2 @ X9 @ X10 ) )
                                     => ( X8 @ X9 @ X10 ) )
                                 => ~ ! [X9: a,X10: a,X11: a] :
                                        ( ~ ( ( X8 @ X9 @ X10 )
                                           => ~ ( X8 @ X10 @ X11 ) )
                                       => ( X8 @ X9 @ X11 ) ) )
                             => ( X8 @ X6 @ X7 ) ) )
                   => ! [X8: a > a > $o] :
                        ( ~ ( ! [X9: a,X10: a] :
                                ( ( ~ ( X1 @ X9 @ X10 )
                                 => ( X2 @ X9 @ X10 ) )
                               => ( X8 @ X9 @ X10 ) )
                           => ~ ! [X9: a,X10: a,X11: a] :
                                  ( ~ ( ( X8 @ X9 @ X10 )
                                     => ~ ( X8 @ X10 @ X11 ) )
                                 => ( X8 @ X9 @ X11 ) ) )
                       => ( X8 @ X5 @ X7 ) ) ) )
         => ! [X5: a > a > $o] :
              ( ~ ( ! [X6: a,X7: a] :
                      ( ( ~ ( X1 @ X6 @ X7 )
                       => ( X2 @ X6 @ X7 ) )
                     => ( X5 @ X6 @ X7 ) )
                 => ~ ! [X6: a,X7: a,X8: a] :
                        ( ~ ( ( X5 @ X6 @ X7 )
                           => ~ ( X5 @ X7 @ X8 ) )
                       => ( X5 @ X6 @ X8 ) ) )
             => ( X5 @ X3 @ X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[67,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV157^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 28 12:00:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  % Mode: mode213
% 0.19/0.49  % Inferences: 121
% 0.19/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------