TSTP Solution File: SEV119^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV119^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:32:39 EDT 2023

% Result   : Theorem 1.08s 1.32s
% Output   : Proof 1.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :  162
% Syntax   : Number of formulae    :  192 (  50 unt;  18 typ;  10 def)
%            Number of atoms       :  493 (  20 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1357 ( 279   ~;  72   |;   0   &; 649   @)
%                                         (  63 <=>; 294  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  174 ( 174   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   84 (  82 usr;  76 con; 0-2 aty)
%            Number of variables   :  284 (  38   ^; 246   !;   0   ?; 284   :)

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

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

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

thf(ty_eigen__44,type,
    eigen__44: a > a > $o ).

thf(ty_eigen__70,type,
    eigen__70: a ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__42,type,
    eigen__42: a > a > $o ).

thf(ty_eigen__69,type,
    eigen__69: a ).

thf(ty_eigen__4,type,
    eigen__4: a ).

thf(ty_eigen__65,type,
    eigen__65: a ).

thf(ty_eigen__15,type,
    eigen__15: a ).

thf(ty_eigen__66,type,
    eigen__66: a ).

thf(ty_eigen__14,type,
    eigen__14: a ).

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

thf(ty_eigen__68,type,
    eigen__68: a ).

thf(ty_eigen__43,type,
    eigen__43: a > a > $o ).

thf(ty_eigen__67,type,
    eigen__67: a ).

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

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

thf(eigendef_eigen__68,definition,
    ( eigen__68
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__1 @ eigen__67 @ X1 )
           => ( eigen__44 @ eigen__67 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__68])]) ).

thf(eigendef_eigen__15,definition,
    ( eigen__15
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ~ ( eigen__1 @ eigen__14 @ X1 )
             => ( eigen__2 @ eigen__14 @ X1 ) )
           => ( eigen__5 @ eigen__14 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__15])]) ).

thf(eigendef_eigen__14,definition,
    ( eigen__14
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( ~ ( eigen__1 @ X1 @ X2 )
               => ( eigen__2 @ X1 @ X2 ) )
             => ( eigen__5 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__14])]) ).

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

thf(eigendef_eigen__42,definition,
    ( eigen__42
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ~ ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__1 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__14 @ eigen__15 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__42])]) ).

thf(eigendef_eigen__69,definition,
    ( eigen__69
    = ( eps__0
      @ ^ [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__44 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__69])]) ).

thf(eigendef_eigen__43,definition,
    ( eigen__43
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ~ ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__2 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__14 @ eigen__15 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__43])]) ).

thf(eigendef_eigen__66,definition,
    ( eigen__66
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( eigen__2 @ eigen__65 @ X1 )
           => ( eigen__44 @ eigen__65 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__66])]) ).

thf(eigendef_eigen__67,definition,
    ( eigen__67
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( eigen__1 @ X1 @ X2 )
             => ( eigen__44 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__67])]) ).

thf(eigendef_eigen__65,definition,
    ( eigen__65
    = ( eps__0
      @ ^ [X1: a] :
          ~ ! [X2: a] :
              ( ( eigen__2 @ X1 @ X2 )
             => ( eigen__44 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__65])]) ).

thf(eigendef_eigen__70,definition,
    ( eigen__70
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( ( ~ ! [X2: a > a > $o] :
                    ( ~ ( ! [X3: a,X4: a] :
                            ( ( eigen__1 @ X3 @ X4 )
                           => ( X2 @ X3 @ X4 ) )
                       => ~ ( eigen__0 @ X2 ) )
                   => ( X2 @ eigen__69 @ X1 ) )
             => ! [X2: a > a > $o] :
                  ( ~ ( ! [X3: a,X4: a] :
                          ( ( eigen__2 @ X3 @ X4 )
                         => ( X2 @ X3 @ X4 ) )
                     => ~ ( eigen__0 @ X2 ) )
                 => ( X2 @ eigen__69 @ X1 ) ) )
           => ( eigen__44 @ eigen__69 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__70])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ( ( ~ ( eigen__1 @ eigen__65 @ X1 )
         => ( eigen__2 @ eigen__65 @ X1 ) )
       => ( eigen__44 @ eigen__65 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ! [X1: a > a > $o] :
            ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__1 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__14 @ eigen__15 ) )
     => ! [X1: a > a > $o] :
          ( ~ ( ! [X2: a,X3: a] :
                  ( ( eigen__2 @ X2 @ X3 )
                 => ( X1 @ X2 @ X3 ) )
             => ~ ( eigen__0 @ X1 ) )
         => ( X1 @ eigen__14 @ eigen__15 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ! [X1: a,X2: a] :
          ( ( eigen__1 @ X1 @ X2 )
         => ( eigen__42 @ X1 @ X2 ) )
     => ~ ( eigen__0 @ eigen__42 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [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(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( eigen__1 @ X1 @ X2 )
         => ( eigen__2 @ X1 @ X2 ) )
       => ( eigen__44 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__44 @ eigen__69 @ eigen__70 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( ~ ( eigen__1 @ eigen__14 @ eigen__15 )
       => ( eigen__2 @ eigen__14 @ eigen__15 ) )
     => ( eigen__5 @ eigen__14 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ! [X1: a,X2: a] :
          ( ( eigen__2 @ X1 @ X2 )
         => ( eigen__43 @ X1 @ X2 ) )
     => ~ ( eigen__0 @ eigen__43 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ ( ! [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,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: a,X2: a] :
        ( ( eigen__2 @ X1 @ X2 )
       => ( eigen__44 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ~ ( ! [X1: a,X2: a] :
              ( ( eigen__1 @ X1 @ X2 )
             => ( eigen__44 @ X1 @ X2 ) )
         => ~ ( eigen__0 @ eigen__44 ) )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( eigen__1 @ eigen__67 @ eigen__68 )
     => ( eigen__44 @ eigen__67 @ eigen__68 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ~ sP4
     => ( eigen__42 @ eigen__14 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ! [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__44 @ X1 @ X2 ) )
     => ~ ( eigen__0 @ eigen__44 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: a] :
        ( ( ~ ( eigen__1 @ eigen__67 @ X1 )
         => ( eigen__2 @ eigen__67 @ X1 ) )
       => ( eigen__44 @ eigen__67 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: a] :
        ( ( ~ ! [X2: a > a > $o] :
                ( ~ ( ! [X3: a,X4: a] :
                        ( ( eigen__1 @ X3 @ X4 )
                       => ( X2 @ X3 @ X4 ) )
                   => ~ ( eigen__0 @ X2 ) )
               => ( X2 @ eigen__69 @ X1 ) )
         => ! [X2: a > a > $o] :
              ( ~ ( ! [X3: a,X4: a] :
                      ( ( eigen__2 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) )
                 => ~ ( eigen__0 @ X2 ) )
             => ( X2 @ eigen__69 @ X1 ) ) )
       => ( eigen__44 @ eigen__69 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: a] :
        ( ( ~ ! [X2: a > a > $o] :
                ( ~ ( ! [X3: a,X4: a] :
                        ( ( eigen__1 @ X3 @ X4 )
                       => ( X2 @ X3 @ X4 ) )
                   => ~ ( eigen__0 @ X2 ) )
               => ( X2 @ eigen__14 @ X1 ) )
         => ! [X2: a > a > $o] :
              ( ~ ( ! [X3: a,X4: a] :
                      ( ( eigen__2 @ X3 @ X4 )
                     => ( X2 @ X3 @ X4 ) )
                 => ~ ( eigen__0 @ X2 ) )
             => ( X2 @ eigen__14 @ X1 ) ) )
       => ( eigen__5 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

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

thf(sP20,plain,
    ( sP20
  <=> ( eigen__2 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ~ ( eigen__1 @ eigen__14 @ eigen__15 )
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ~ ( eigen__1 @ eigen__67 @ eigen__68 )
     => ( eigen__2 @ eigen__67 @ eigen__68 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( eigen__5 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__43 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ~ sP15
     => ( eigen__44 @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP19
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( eigen__0 @ eigen__44 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__2 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__69 @ eigen__70 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: a] :
        ( ( eigen__2 @ eigen__65 @ X1 )
       => ( eigen__44 @ eigen__65 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( eigen__42 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( sP3
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ~ ! [X1: a > a > $o] :
            ( ~ ( ! [X2: a,X3: a] :
                    ( ( eigen__1 @ X2 @ X3 )
                   => ( X1 @ X2 @ X3 ) )
               => ~ ( eigen__0 @ X1 ) )
           => ( X1 @ eigen__69 @ eigen__70 ) )
     => sP28 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ( ~ ( eigen__1 @ eigen__65 @ eigen__66 )
       => ( eigen__2 @ eigen__65 @ eigen__66 ) )
     => ( eigen__44 @ eigen__65 @ eigen__66 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( eigen__1 @ eigen__67 @ eigen__68 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ( eigen__2 @ eigen__65 @ eigen__66 )
     => ( eigen__44 @ eigen__65 @ eigen__66 ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__1 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__14 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( eigen__1 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( sP20
     => sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ! [X1: a,X2: a] :
          ( ( eigen__1 @ X1 @ X2 )
         => ( eigen__44 @ X1 @ X2 ) )
     => ~ sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__14 @ X1 )
       => ( eigen__42 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ! [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,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( eigen__44 @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( eigen__44 @ eigen__65 @ eigen__66 ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( ~ ( eigen__1 @ eigen__65 @ eigen__66 )
     => ( eigen__2 @ eigen__65 @ eigen__66 ) ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( eigen__5 @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( eigen__2 @ eigen__65 @ eigen__66 ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ! [X1: a,X2: a] :
        ( ( eigen__1 @ X1 @ X2 )
       => ( eigen__44 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ! [X1: a,X2: a] :
        ( ( eigen__1 @ X1 @ X2 )
       => ( eigen__42 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ! [X1: a,X2: a] :
        ( ( eigen__2 @ X1 @ X2 )
       => ( eigen__43 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ! [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__44 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ! [X1: a] :
        ( ( ~ ( eigen__1 @ eigen__14 @ X1 )
         => ( eigen__2 @ eigen__14 @ X1 ) )
       => ( eigen__5 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__2 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__14 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( ~ ( sP11
         => ~ sP27 )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( sP37
     => sP30 ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ! [X1: a] :
        ( ( eigen__1 @ eigen__67 @ X1 )
       => ( eigen__44 @ eigen__67 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( eigen__44 @ eigen__67 @ eigen__68 ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( ~ sP9
     => sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ( sP11
     => ~ sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( sP22
     => sP56 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ! [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,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ! [X1: a > a > $o] :
        ( ~ ( ! [X2: a,X3: a] :
                ( ( eigen__1 @ X2 @ X3 )
               => ( X1 @ X2 @ X3 ) )
           => ~ ( eigen__0 @ X1 ) )
       => ( X1 @ eigen__69 @ eigen__70 ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ! [X1: a] :
        ( ( eigen__2 @ eigen__14 @ X1 )
       => ( eigen__43 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( sP32
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(cTHM252_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 ) ) )
      = ( ^ [X4: a,X5: a] :
          ! [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 ) ) )
        = ( ^ [X4: a,X5: a] :
            ! [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)],[cTHM252_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 ) ) )
        = ( ^ [X3: a,X4: a] :
            ! [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 ) ) )
        = ( ^ [X2: a,X3: a] :
            ! [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 ) ) )
   != ( ^ [X1: a,X2: a] :
        ! [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] :
            ! [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 ) ) )
        = ( ^ [X2: a] :
            ! [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(h7,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 ) ) )
   != ( ^ [X1: a] :
        ! [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(h8,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(h9,assumption,
    sP60 != sP5,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP60,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP60,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( ~ ( sP41
         => ~ sP1 )
     => sP45 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( sP41
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ sP45,
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP41,
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP38
    | ~ sP20
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP62
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP49
    | sP62 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP9
    | sP49 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP54
    | ~ sP37
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP40
    | sP54 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP48
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP4
    | sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP57
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP57
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP14
    | ~ sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP14
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP52
    | ~ sP57 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__43]) ).

thf(14,plain,
    ( sP36
    | ~ sP14 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__42]) ).

thf(15,plain,
    ( sP3
    | ~ sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP3
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP31
    | ~ sP3
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP18
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP41
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP21
    | sP37
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP8
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP8
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP51
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).

thf(24,plain,
    ( sP19
    | ~ sP51 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).

thf(25,plain,
    ( ~ sP26
    | ~ sP19
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP10
    | sP26
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP60
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,h10,h17,h18,h16]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,28,h17,h18]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,29,h15,h16]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h11,30,h14]) ).

thf(h19,assumption,
    ~ ( ~ ( sP6
         => ~ sP27 )
     => sP42 ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( sP6
     => ~ sP27 ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ sP42,
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h23,assumption,
    sP27,
    introduced(assumption,[]) ).

thf(32,plain,
    ( sP22
    | ~ sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP59
    | ~ sP22
    | sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP16
    | sP59 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP6
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( sP44
    | ~ sP46 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP33
    | ~ sP44
    | sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP2
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP6
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP53
    | sP58
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP12
    | sP39
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP28
    | sP53 ),
    inference(all_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP61
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP32
    | sP61
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( sP63
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(46,plain,
    ( sP63
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( sP17
    | ~ sP63 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__70]) ).

thf(48,plain,
    ( sP50
    | ~ sP17 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__69]) ).

thf(49,plain,
    ( ~ sP15
    | ~ sP50
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
    ( ~ sP25
    | sP15
    | sP42 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( sP13
    | ~ sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( sP13
    | sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    ( sP55
    | ~ sP13 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__68]) ).

thf(54,plain,
    ( sP47
    | ~ sP55 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__67]) ).

thf(55,plain,
    ( ~ sP39
    | ~ sP47
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( sP35
    | ~ sP43 ),
    inference(prop_rule,[status(thm)],]) ).

thf(57,plain,
    ( sP35
    | sP46 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    ( sP29
    | ~ sP35 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__66]) ).

thf(59,plain,
    ( sP11
    | ~ sP29 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__65]) ).

thf(60,plain,
    ( ~ sP58
    | ~ sP11
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( ~ sP5
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(62,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h22,h23,h20,h21,h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,h22,h23,h21,h13]) ).

thf(63,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h20,62,h22,h23]) ).

thf(64,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,63,h20,h21]) ).

thf(65,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__44)],[h12,64,h19]) ).

thf(66,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h9,31,65,h10,h11,h12,h13]) ).

thf(67,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h8,66,h9]) ).

thf(68,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h8])],[h7,67,h8]) ).

thf(69,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,68,h7]) ).

thf(70,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h6])],[h5,69,h6]) ).

thf(71,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,70,h5]) ).

thf(72,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,71,h4]) ).

thf(73,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,72,h3]) ).

thf(74,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[73,h1]) ).

thf(75,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[74,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 ) ) )
      = ( ^ [X4: a,X5: a] :
          ! [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])],[73,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV119^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n024.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  : 300
% 0.12/0.33  % DateTime : Thu Aug 24 02:41:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.08/1.32  % SZS status Theorem
% 1.08/1.32  % Mode: cade22grackle2xfee4
% 1.08/1.32  % Steps: 26388
% 1.08/1.32  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------